My favorite quote from my time playing pokemon is "if it isn't 100% accurate its 50% accurate" this comes from focus blast seeming to miss more times then it hits.
I think its also worth mentioning that, in 5e, anything above a +1 or +2 modifier is a *significant* improvement from what you would get normally. So "only" getting effectively +3 or +4 is still pretty huge. Additionally, there is never any downside to advantage, so you should always be trying to seek it - which (in theory) leads to more interaction with the environment and creative solutions to problems.
While the proliferation of advantage on so many features means players often have enough ways of getting it that they don't often look to the environment to get advantage, this is definitely a key detail and a fun thing to implement as a DM.
TLDR, since this went long, Stacking bonuses act as incentive to interact with multiple systems, vs the one and done of advantage. There are many ways to get advantage, but since they dont stack, you actually only need a handful of methods for most situations. Add in the fact that a single case of disadvantage negates any number of sources of advantage, and I find that they engage in less of the system, not more. For example, I will pull something that happened from a pathfinder game that uses stacking bonuses as opposed to adv/disadv. We had a cover for a tomb that we needed to get into. The lid was extraordinarily heavy, and the intended interaction was some kind of sacrifice to activate a magic that would lift the lid. Instead, as a group we were able to employ our tools, spells, a magic nail that would never pull out once set, an extremely good knowledge: engineering roll, and the strength of three strength based characters to lift it. We were interacting with so many different systems in order to pull off something incredibly hard. Contrast that to if you had the same situation in 5e. You could get advantage from a number of the things we did, but if the DC is higher than a 24, you arent going to get it. This leaves the DM with 1 of 3 options. The lid is impossible to lift, the lid is impossible to lift, but the dc gets lowered by all the things the party does, or the lid could be lifted all along, and a single thing to gain advantage gives them their best shot. The first I find unsatisfying as a player. The second is the same as pathfinder, just with extra steps. The third I also find unsatisfying. If I was to ever run 5e again, Id seriously consider making 1 case of advantage canceled out by one case of disadvantage at the very least. I am curious at how unbalanced having 2 cases of advantage would let you roll 3 dice keep highest. In the end, Id prefer to just work with static stacking bonuses like in pathfinder.
@@robertellis6853 Stacking bonuses bog things down though. Say what you willabout 5e, having one primary source of combat advantage prevents bogging down each round with ways to get bonuses up. Like, stacking accuracy bonuses are fun... for the one person but like... let's get to everyone's turn, let's keep the game moving. Analysis paralysis is bad enough as it is.
One thing you’re forgetting is that advantage nearly eliminates a critical miss, while disadvantage nearly eliminates critical hits. To get either, you need to roll both 1s or both 20s, respectively. When compared with the likelihood of rolling any other combination of rolls, the odds of rolling a critical miss or critical hit are 1 in 400.
Ah the joys of pathfinder 1e lol, critical hits required a second confirmation roll that also had to meet or exceed target AC. Made it very hard to crit high AC enemies, glad they scrapped it for 2e 👍
I was about to point this out. In my experience advantage on attack rolls is almost always desirable more for the critical hit chance than the actually success/failure rate. The other side is for circumstantial opportunities like a high level spell attack roll that you really don't want to miss.
odds are also very useful for Bayesian inference. If you use odds instead of probability, Bayes' rule becomes just multiplication of the prior odds of A to B with the Bayes factor: P(measurement|A)/P(measurement|B). 3blue1brown has a very nice video on it
In probabilities: 30% vs 70% vs 90% vs 95% vs 99% They don't look all that different In odds: 3:7 vs 7:3 vs 9:1 vs 19:1 vs 99:1 MASSIVE difference (which is how they feel intuitively in Pokémon) And the odds in decimals: 0.42 vs 2.33 vs 9 vs 19 vs 99
@@xXJ4FARGAMERXxPersonally I prefer fractions to odds. 1/10 just makes more sense to me than 1:9 and 1/2 makes more sense to me than 1:1. I do see your point comparing odds though.
Yes, the appropriate term for this sort of power-gamer among the groups I've been part of would be "munchkin" rather than "nerd". I've also seen "roll-player" as opposed to "role-player" but this only works in writing.
@@Alge_ I have kind of mixed feelings about munchkins. On one hand I don't mind a dip or two to get a skill, but some folks overdo it too much to the point that their character is a fighter / ranger / mage / barbarian / cleric / monk / thief / druid. I mean that's not a character anymore, unless you're playing someone with multiple personality disorder. 🤣
There is one case that I know of where the rules of 5e DO convert the advantage/disadvantage system to a direct modifier. That is with passive scores: "If the character has advantage on the check, add 5. For disadvantage, subtract 5" (Player's Handbook p. 175)
Makes sense in a way, since at 50/50 odds the advantage is equivalent to a +5 bonus and the passive score is your modifier + 10. Both take from the middle. Too bad that it's slightly off because a DC 10 means a roll of 10 would succeed so with a +0 modifier you'd have 55% chance of success. They probably rounded the numbers to multiples of 5 because that's just pleasing
@@roelant8069 yeah it's not even meant to be perfectly balanced. there is also a rule that lets you "take 20", in which you can assume to try something as long as it takes to get the utmost result you can ever muster, but also suffer all consequences of failure too. The thing is, you are not guaranteed to roll a 20 ever. while slim, it's possible you already got your last nat 20. tldr: even throwing a coin one billion times is slightly off from a perfect 50/50
The mention to Pokémon when you brought up the perspective of looking into thw chance to fail is spot on. A 95% accuracy move is only slightly worse than a 100% one but the same 5% drop from 90% to 85% feels like a ravine
With a 95% accuracy, unless you have to very slowly whittle the enemy down, you are unlikely to see a miss in a given battle, and in case you do, it doesn't impact the overall damage per turn much With an 85% accurate move, you are much more likely to see a miss in a battle if all enemies are one or two-hits, and then a single miss is also far more impactful
Makes sense if you think about the failure rate. 95% to hit means 1 out of every 20 will miss, so it's unlikely you'll see even one in a normal battle. Compare that to 90% or 80% where 1/10 and 1/5 will miss and it starts to become a "every battle, maybe multiple times" thing.
I'm of the opposite opinion. A 95% accuracy move is only slightly better than a 90% move, but a 100% accuracy move is infinitely better than a 95% accuracy move.
How to lie with statistics. A classic. All the numbers mean the same but our perception is what is changing. 10/10 explanation i loved to revisit this topic.
@@itszeroday Personally, for me the most fun part of the old Kenku were character ideas that came up with creative hacks to get around the character limitation. One character I had was a Kenku Illusionist Wizard whose backstory was that he cast the Minor Illusion cantrip hundreds of thousands of times over the course of months to produce a voice speaking every single word in every single language that he knew, and then mimicked the voice in order to regain the ability to talk through sheer brute force. He went by Webster, and while he could talk, he always spoke in a completely flat, robotic monotone. Another was a Kenku Great Old One Warlock who was using the power of his patron to bypass the curse by gaining telepathy, and was almost always completely silent because he started exclusively using his telepathy to communicate. He went by Whisper.
I have never understood why people think kenku only being able to mimic was somehow “unplayable.” How did you learn to talk? By listening to other people talk, right? You should be able to talk just as well as anyone else, and basically being a kenku meant you couldn’t read aloud written words that you didn’t already know, which I feel like is a minor inconvenience at best.
The graph at 8:02 is exactly why I Iike advantage (as a long term 3.5 player to boot) , simply because it accurately models the actual 'advantage''s meaning. Like, say you're shooting at someone who has been webbed. Even a lousy shot is going to have an easier time shooting at a target that doesn't move, but for an experienced shot, it makes it go from 'this will go well, trust me' to 'I can do it with both hands up my arse'. Which makes advantage a very apt go-to tool for resolving unknown situations.
I like Advantage because it plays nicely with our brains' flawed instinctive understanding of probability. Once it gets above 80%, and especially 90%, most people think it's basically guaranteed to happen, which Advantage reinforces. (Of course, first hand experience can replace this flawed intuition, but for I'm speaking in regards to the "average person.") Similarly, it turns coinflips into "pretty likely, but still not guaranteed" which usually feels better from the perspective of the player. I dislike it because once you have Advantage, there's no point in trying to get further increases/benefits because Advantage doesn't stack. Pros and cons to every system, and all that.
Another fun one comes from the RPG realm outside of D&D. Some games, like the "kids on bikes" system, use "exploding dice", where if you roll the maximum of an n-sided die, you get to roll again and sum the results, and this can repeat. This has a number of fun effects: on a D4, it's impossible to roll any multiple of 4. Exploding with a D4 _twice_ is more likely than exploding once with a D20. The probability of getting any given number is never 0, as the exploding has the potential to go on forever.
There also exists a slightly different type of exploding dice system which on top of allowing you to roll an extra time also removes 1 every time the die explodes. It is for example used in Dominions 5, a video game very much inspired by tabletop RP. With that system, 1d4 CAN result in exactly 4 if you first explode (nat 4) then roll 1 (4-1+1 is the final operation). With this system, 1d6 averages to exactly 4 (instead of 3.5 without explosions).
Lol I sent this to a friend saying "first time ever I've seen someone be comprehensive on each of these angles and he does it in under 10 minutes" then GASPED when youtube recommended me "more from..." and I realized you were the cursed units guy. This is another amazing vid.
I had to do a sneaky re-upload to fix an error, so apologies if your comment or like got overwritten or if you got double notifications. Feel free to re-comment or re-like!
advantage and disadvantage are a pretty key part of the snowball effect in DND 5e, its also a major factor of death spiraling in it too. a good rule of thumb is advantage *feels* like a plus five unless you were never able to succeed the check in the first place, and disadvantage is the same for failure rate. so if you have the choice of a +3 or adv, the choice should basically always be the advantage unless you cant pass without the added bonus.
5% probability of success is "that sniper across the map who's safe has only 1 target available at 5% hit chance. Why not? It's not like he was doing anything else!" 99% probability of success is "rushing this shotgun toting Ranger at close range to shred a target. Do I have a plan B if things go south?" There, I, an Xcom player, have just explained the difference between 5% and 99% probability of success. You've been proven wrong, you're welcome.
Murphey's Law will always be your god in those games. Same thing goes with Fire Emblem games: if I'm not at 100% on the screen, I am just as likely to miss as if I was at 35%.
I appreciate this video because I’ve never heard anyone else complain about the phrase “twice as likely” but I’ve always hated when people say that, this made me feel less insane
@@billy1bob2ones3 I always interpreted that as meaning "half as expensive," just instead emphasizing that the 1st item already had a low cost and now the 2nd item is even lower.
what I like about replacing modifiers with adv/disadv is that modifiers are hard to learn, but easy to house rule. so instead of learning every single modifier, leave it to the control of the DM when add positive/negative modifiers.
This is used in the Traveller system by Mongoose publishing. Two d6 added up then with numerical modifiers is the usual way of modifiers, but certain situations invoke boon and bane die which are an extra d6 which replaces the highest or lowest rolled due dependingly. What’s fun is that besides circumstantial boon and bane die, the players can also make “leadership” rolls in combat situations which let them get a few boon die to hand out to other players during the encounter when they’re most needed
@@danilooliveira6580but it becomes so flat and boring in combat, and its why spellcasters rarely buff or debuff in 5e. You either have it or you don't, so why try to get multiple advantages in a fight?
@@NihilTruth that doesn't make much sense considering most buffs are not adv/disadv. and I would argue adv/disadv is good as a buff because now you don't need to list what buffs stack and what buffs don't, because you know you can't get to roll 3 D20s. so if you don't want a buff to stack you just make it give the player adv/disadv, and if you want it to stack you make the buff give extra dice to roll or a modifier.
@@danilooliveira6580 I like the game part of the Table Top Role Playing Game. Advantage/Disadvantage alone, with no modifiers, is too simplistic a system that makes combat boring, but it's not the only reason behind that. It's not hard at all to stack modifiers, I can assure you of that. Especially in more current games, especially with the advent of VTTs.
Great video, especially the breakdown of how using the complement or the odds can lead to a better intuition of these kinds of probabilities. Love how you present quite complex concepts in a very approachable way without dumbing it down. Some thoughts: A good way to look at the counterexample is to go from something like 0.9999 chance to hit to 1. Even though you're only landing around 0.01% more hits, your odds increase by a factor of infinity. This discrepancy seems WEIRD when you think about it in those terms, but a simple way of thinking about it is "how much does this increase my average damage?" vs "how much money could I theoretically bet on this outcome?" The concept behind moving from flat modifiers in previous versions that result in the weirdness you see at 8:22 is called "bounded accuracy" specifically to avoid this problem. Higher level characters in earlier editions completely trivialised low level encounters, and the devs wanted to be able to keep lower level monsters relevant while making the characters still feel like they were improving in power. A lot of the massively broken 3E builds abused exactly this mechanic (eg the 'Diplomancer'). The reason many DnD players like to look at flat %increase in hit rate is because it follows on to a metric that's generally more practical (and easier to understand) when optimising a character - ADPR (average damage per round). If your hit damage is 10 on average, a hit rate of 50% would give you 5ADPR (assuming you can always place your character in a position to make an attack) In this calculation the %increase to hit directly equates to %increase in ADPR (doubling your chance to hit from 50% to 100% gives a straight 2x multiplier to your ADPR). This helps making general decisions like "should I take this feat for +2 damage or a IAP for +1 to hit and +1 damage?" a little easier. Things start to get quite convoluted when you start to factor in things like damage ranges (is 2-80 damage better than 41-41 damage?), nat 1 (auto miss) and nat 20 (auto crit), critical misses (variant rule), and other abilities that proc off advantage (sneak attack being the obvious one). Also sometimes the cost of failing an attack or skill check can be extremely high (ie if I don't lockpick this door open our party is gonna get crushed by the trap, or if I don't hit this monster with this attack he will kill a party member or two) - which makes misses feel far more impactful. All this is why building a strong intuition is far more valuable than making a formula and blindly following numbers without understanding its limitations. The most notable feature of the advantage system to me is that it turns your roll from a flat probability distribution into a kind of lopsided bell curve. Binomial distribution works well to analyse this imo.
Great video! Im glad you analyzed both the “effective flat bonus” and “factor multiplier”. I did similar calculations on my own a while back when I was comparing the War Caster vs Resilient (Con) feats, and I wish I saw this video before I went through all that math myself
Obviously this is mostly about skill checks, but something I also like to consider is critical hits/misses. Advantage simultaneously making a Critical Failure a 1/400 chance, while Critical Successes become a 9.75% chance. Or viewed alternatively, it turns a "5% to 5%" to a ".25% to 9.75%" split. Critical hits are 39x more likely than Critical Misses. As you mentioned it's about a ~+4 to rolls. But also important to keep in mind is the DPS bonus of Critical Hits. 9.25/5, and you have bonus damage (average DPS) due to critical hits being 1.95x as much. This is the part where I mention I don't know anything about statistics, but it seems like that could make a difference. Perhaps getting a critical hit in once a combat vs. every other combat. Which then we get into the nitty gritty details of taking a Rogue or Paladin w/ smite and mentioning how managing to get a critical hit off once per combat could be massive damage and yada yada. Because combats aren't graded on a scale and are instead Pass/Fail, you realize that once a combat critical hits can be huge.
In general critical hits don't increase DPR significantly, even with increased crit chance from Advantage. It does have an increase, but in calculations it may change the DPR from 35 DPR to 36 or 37 DPR. It's not significant, unless we're looking at something like Rogue who can almost double their damage on a round based off crit hits alone
No joke, shifting from explaining how modifiers work to instead explaining how advantage works was what convinced my group of friends to start playing DnD
5:46 I swear pokémon attack probabilities are rigged, a 95% feels like a 98% but then a 90% feels like a 30% and when you think you've figured it out there comes the 50%'s that feel like a 10% and the 55%'s that feel like 95%. Please, WTH IS FIRE BLAST (85%) LIKE 10 TIMES MORE ACCURATE THAN CRABHAMMER (90%)!?
This is a lot of really useful information for someone like me who is making some sweeping homebrew systems. I oftentimes use advantage in balencing as if it were a +4.5 modifier to a roll not giving the actual math much thought. Very interesting
5:13 EXACTLY! Check the ratio between the probabilities! We were doing these exact calculations just last week to show the, uh, *advantages* of advantage. Your chances on the highest difficulty checks like critting nearly double!
Chance of failure is also huge, that's basically how we calculate what incremental increases to defense do to effective HP when we're playing RPGs. When you have no defense and get a 10% damage reduction buff, that obviously reduces the damage you take by 10%. But when you already have an 80% damage reduction buff and you get an additive 10% reduction, that cuts the damage you're taking in half (from 20% getting through to 10% getting through).
Great video but I think you are wrong about one thing; hours long combat with enemies you can hit easily but just soak up hitpoints are NOT more fun than hard to hit enemies that you have to take down with luck or clever tactics
Hey friend, I gotta push back on this. I've run thousands and thousands of hours of different TTRPGs through the years and, anecdotally, I find that enemies who are very difficult to hit can easily feel frustrating and unfun for players, in general. This doesn't mean that you should never use enemies with high defenses, just be very sparing with them. The recommendation to make enemies generally easier to hit and compensate with higher HP is almost guaranteed to improve your game experience, especially compared to the opposite. Clever tactics and luck will play a role either way, but swinging and missing repeatedly turn after turn sucks. Combat may be longer or shorter depending on a number of things, but very difficult-to-hit baddies will always only extend combat in the worst way. Remember: the problem isn't long/difficult combat-it's boring, frustrating combat that people dislike! Addendum: you can build encounters around high defense, but add a twist that makes it fun (and make sure your players can find out about it beforehand if they are smart about it and ask around) such as an enemy with very high AC which decreases every time it's hit (clearly signal this by describing the armor breaking off), or who has a lower AC against a type of damage (eg: 18AC; 12AC vs melee piercing).
I think everyone is right here. The best thing to do is create a variety of enemies and keep the players guessing and engaged. I built an encounter with dozens of relatively easy to hit goblins who died in one hit (or rarely 2 hits), but then threw in a difficult to hit, and tanky automaton.
@@manicpixiedreambuoy I can concur with this. Recently ran a game using a system that allowed blocking, dodging, and parrying all incoming attacks, on top of the attacker having to make a roll to see if the attack was even going to hit in the first place, and that was the most universally disliked thing about the system among my players because it meant that, while they got hit less and HP pools for enemies were small, they didnt feel like they were making any progress in combat.
@@greed0599I guess people have been playing computer games so much every enemy is seen as a health bar you have to whittle down and that is "progress".
4:35 Been playing for many years, and my group tends to hate damage sponges. Hitting something is cool.... until you've done it 10 times and so has the rest of the party. Just another nuance to consider, not all DMs prefer to run low AC high HP creatures.
Yes! not all DM's prefer that, most DMs are however Forced to play that way. DM should not want to TPK their players, but players having bad characters force DMs to play crappy DnD creating a very low risk encounters, such as dumm damage sponges. Most games of DnD are run on tutorial difficulty with 1-2 combats per adventuring day, where decisions dont matter, resource management doesnt matter. This is mostly critique to the whole community for being trash players and noone should single out DM's as them being the problem by using easy monsters as damage sponges instead of deadly, tricky ones, forcing mental saves and such. Imagine how popular is the 3rd level spell Waste... How many idiots were twinning it as Sorcerer and inviting TPK? Many. Make good character, focus on initiative, saves and good spells/features. So your DM can take you for a spin in real DnD game! Not your typical fuck a bartender game.
I've seen a lot of attempts to explain the value of advantage, but this is probably the best blend of clear, thorough, and yet concise in covering the topic. Well done, and I will definitely be saving this to refer people to in the future!
My favourite instance of an intuitive notion not well-defined is temperature.. say it's rather chilly outside one night but then the next night - ho boy it's twice as cold now! But what does that mean? what are the units? to what are you possibly multiplying by 2 to get the new result? My best guess is a sort of exponential graph of 'perceived cold/hot' that works outwards from whatever that individual considers 'comfortable'.. 🤔Like a parabola where the lowest point intersects the X axis at whatever temperature is considered perfect comfort, since the perceived distance from comfort is being doubled then the temperature units don't actually matter. And while that zero point and the curve function would be different for every individual, I suspect they're close enough for us to correctly intuit what someone means when they say it's twice as cold as the night before Thanks for coming to my Ted Talk
I think the "Ideal comfortable point" is just homeostasis, where your body doesn't need to do any extra heating or cooling work to keep your core temperature stable. This point changes throughout days and seasons as your metabolism changes, which is why spring feels so much warmer than fall, and why morning is always colder than evening. Thus, twice as cold or hot is approximately twice as far from homeostasis. Which scale of twice might be tricky (like in the video!); I would think it's either twice as expensive to maintain homeostasis, or some order of magnitude greater, like decibels.
we need temperature decibels. let's say 0dBT is 20C, and the unit is 10C, twice as cold means a change of ~-3db, so 10C would be 10dB, and 0C would be 13 dB though it doesn't actually work that well on the other end I think a curve that takes into account the livability might work, but it would be weird too, because 50C is ~6 times hotter than 45, and 45 is ~6 times hotter than 38C on the other hand -6.5C is ~ twice as cold as 4.5C, which is twice as cold as 12C but the issue is that the 20-30 C range is not well defined, and it can't do low nor high temperatures
THANK YOU. This is the first time I've heard someone discuss the nuanced mismatch between a mathematical expression of probability and common English expressions.
What a great instructionary video on probability, particularly how you point out how faceted our colloquial terminology is when we describe this. The part about the Taylor expansion makes so much sense, without having thought about it prior
I love how he explains the basic mechanics of DnD at the start. It doesn't really help experienced players like me, however it's nice for people who have never played a TTRPG
The correct analysis is doing additive analysis, multiplying by your average damage, then multiplying by how often you get advantage. This collapses all this weirdness and definition stuff. As a simplification if you almost always have advantage you can just reduce it to the multiplicative analysis you showed and consider it a % damage increase . And as a simplification if you almost never have advantage you can reduce it to just a flat damage increase per advantage.
In the case of combat this is totally valid, one can just calculate expected damage, but in the case of skill checks it doesn’t. In that case the different ways of interpreting probabilities become interesting, and i for one like the idea of odds
@@mickschilder3633 Actually no you just utilize the effect. For example constantly having advantage may give you 15% more successful perception checks. Or say each advantage gives 5% of a stun.
I did not expect Mr. Cursed Units to make a video about tabletop game Advantage, and I expected even less for them to use a Kenku Rogue as their avatar for the video, but it's a very welcome surprise! (PS, no we will never stop being absolute NERDS)
I love how this channel goes absolutely in tune with my hobbies and likings over time; literally, I started with TTRPGs early this year and it is AMAZING, and also, I'm on my final year at a tech highschool, so I can create a FUNCTION to meassure exactly (or so I think) how much do I correlate with this channel and its contents, but with good representations. You can say it meassures in "likeness [Li]", where a factor of compatibility (Com), multiplying a moment in time, adds to an exponential function of excitement (Ex) powered by a period of time which the content is related. So we get something like: L(t) = Com*t + Ex(T) = Com*t + E^(T) I'm still not an engineer, but my math says that I'm pretty excited about it.
4:05 This is true for GMs that understand 5th edition and assigning appropriate DCs on the fly. If you, for example, have a GM who is accustomed to Pathfinder 1e types of DCs, you will almost always be facing Hard or Harder DCs relative to your character's level, often facing DCs of 15 to 20 when you should be facing DCs of 12 to 15. I'm not salty >_>
That's one of the more annoying practices in traditional GMing: the "DC treadmill", i.e. artificially inflating DCs as the characters level up and get better at doing what they do so that their probably of success remains more or less the same. 5e put a stop this practice with its bounded accuracy rule, but the proficiency bonus it gives you is so small that leveling up doesn't change your probability of success very much anyway.
Much as I love 3.5 in the early game, I hate it past level 4 or 5 for that exact reason. The DCs just get arbitrarily high, and it practically forces skill point min-maxing. I keep finding myself drawn to the OSR space now. I think simplicity truly is the way to do it, and the numbers don't get too crazy
This is a delightful video. I really love all the cute little details in the artwork. I think you did a great job articulating your points, too. Outstanding work, subscribing to you was the easiest decision of my life.
Another fun mechanic like this is crit chance in League of Legends. Rather than having a fully random probability of let's say 50%, the probability starts out lower than that and then increases with every crit miss in such a way that the total probability still is 50%. I don't know the actual numbers, I just know the mechanic. The reasoning behind this is that true randomness could and over enough games would result in long series of misses which would make players feel like the game is cheating them out of crit damage. Doing it this way forces the streak to break eventually which feels more fair, even though it mathematically isn't. It's like if DnD gave you a +1 after your last roll was a failure and a -1 after your last roll was a success.
I know DotA 2 does the same. It's called "psuedo-random" chances, because while there is still probability involved it reduces the chance of extremely bad or extremely good luck swinging a fight/game suddenly while still keeping luck as a factor.
This is not the usual video RUclips recommends to me… but i get it. I spent pretty much all my time spread between D&D/World of Warcraft vids and Science/Philosophy deep dives. While i am not nearly smart enough to understand how this is all managed, i still enjoyed it. Thank you
It is a house rule. The players and DM agree to say that a nat 1 is a failure. In my games a nat 20 allows you to add your modifiers twice and still could cause a failure. Auto success and auto fails are only in context of attack rolls. But for skill checks don't benefit from this. But it still always comes down to the DM.
@@herobrineking2514 I love the open-ness to get creative as a DM. Player rolls a 1 to lockpick DC15 with a +14? They break the lock and the gate swings open
Love this explanation, relatively simple topic but there's so much interesting insightful deep things to dive into. Wonderfully explained as well, not over explained but easy to grasp
Unless it changed in the new 2024 rules this is only true for saves and attacks. Skill and Ability Checks don't care about nat 1/nat 20, only the result of the roll+modifier
@@ZttackFrmBhind It does because teachers teach it with the amount of motivation and desire as someone who found out their wife cheated on them with their boss and because of that their wife got a promotion while they didn't
I did advance maths in yr10. I was fantastic at it. Month 5 or 6 came about and we learnt about probability. I gave up and left school. I still don't understand the maths behind probability. Thanks man! :)
It's simple but doesn't mean it is the best tool for the job. I was quite happy with the +2 standard bonus that was key to 3/3.5/Pathfinder with how simple it worked and was still intuitive and sensible. Yes there (especially at later levels) are many things' players could instantly pass with how many bonuses there could be, but that is why a good DM needed to increase the stakes. No, it's no longer climbing that ladder, it is climbing that ladder with kobolds stabbing at your feet while arrows strike at you from a distance. It no longer swimming across a pond, but swimming across the sea with 10-foot waves and a Megalodon trying to reach you before you get to shore. If you were creative enough you could put together very exciting challenges at higher levels really easy. Just pile on enough to the situation to make that +15 bonus either be necessary or compounded by penalties so it is more of a +5. Adv/Dis always felt like it removed a little of that. I would rather give it out only when the situation demands an extreme bonus or penalty and not for every single situation like 5e does.
Thank you for going over this. I'm writing a TTRPG and understand what mechanics like this actually do is something that takes up a lot of thought for me.
1:35 no you won’t, depending on the dm. a nat 1 is an automatic fail in combat, regardless of modifiers, and some dms will extend that to out of combat
@@zebanon5 funky thing with this is its also a rule that you probably do see in a large portion of the groups that say they don't use it - but the reasoning is vastly different. Its a common house rule, that's more common than people would let on - since its also almost inherent with a simple dm facing rule of "don't ask for a roll if there's no chance of success or no chance of failure", a rule simply used to get the story rolling at times.
Feels like it'd also be a bit bullshit especially out of combat? Like say a professional musician with a +11 to performance isn't going to fuck up anything major to an untrained ear. You cannot sit them down in front of an easy piece on their signature instrument and it not turn out decent (unless the instrument fails, but the chance of that is also nowhere near 5% and even then odds are they know it well enough to improvise around it).
When I read the title I was like, ugh this is gonna be lame, 10 minutes to tell us the avg roll is 14, but I love it, it's actually really helpful, and I never even thought about it in this way.
Glad you mentioned it, as I see the factorized results as much more important. If I have a hard check, which are quite common at some tables, then I can almost double my chances of succeeding.
I try and think about this often, I never come up with a satisfactory number myself but I liked that you did all the math and the short answer is "it just isn't easy" which helps. I usually consider it to be closer to a +5 so I'm glad my head canon is close enough
just.. thank you. as a an algebraic, abstract, and physical math person, with meh statistics background, this unironically put the physics of statistics into such a cool perspective. i am happy now. :D
Very good video. Your graph on flat modifiers explains also why Pathfinder 2 added the idea that under shooting by 10 or over shooting by 10 changes the result. So no matter where you are on the graph the flat modifier changes dramatically the odds of SOMETHING.
Great video, I would have liked to have seen the later talk about odd be rephrased for disadvantage too. I know they're just inversed, but getting language statements correct feels like a significant point of this video.
From the perspective of someone trying to make a TTRPG system that is simple, yet interesting and balanced, this is incredibly useful... and unfortunately necessary because you just know people will pick it apart like absolute nerds. Thanks for making this!
I am currently creating a game that (like DnD) uses an advantage/disadvantage system while fighting monsters. This is mainly because I genuinely only want there to be 4 dice *(2d8 & 2d10), but have 12 different monsters relying on this system. Thus, I am grateful for your analysis on the topic involving the concept.
The big thing about advantage is also that the chance to critical increases by 80,5% (assuming that a natural 20 is a critical). It's a big swing in one's favor.
Thank you for this very insightful video, the game path of exile has a similar mechanic called lucky, that means a chance or damage value is rolled twice and the higher number is used, I didn't really think that it was very powerful but now I understand how it works in DND and can see why that's good in that game too
How you explained closer to zero probability and the phrase 'twice as likely' being reasonably undefined explains '2x boost bonus/whatever' slot machine buttons very well.
Thank you! The summation math IS correct mathematically, but didn’t make sense to me in terms of the actual application. But this also highlights why I hate probability/statistics in my math classes! Beautiful work!
This is a great video, really helped me solidify my thoughts on Advantage/Disadvantage. I had a problem player in one of my campaigns previously who loved to power game, while insisting that wasn't what he was doing, and one of my biggest complaints was that he was able to deal absurd damage with the Great Weapon Master feat while all but negating its downside with Reckless Attacks. GWM lets you trade 5 points of accuracy for 10 points of damage on melee weapon attacks, and make one additional attack if you either crit or kill. Reckless Attacks let you make every melee attack with Advantage, in exchange for attacks on you being made with Advantage (not a problem for a raging Barbarian). The problem player tried to insist that Advantage did not make up for the -5 to their attack rolls, but given how the monsters we were fighting didn't have exceptionally high ACs (and even if they did, he could just choose not to apply GWM against them), the math disagrees with him. I would have loved to be able to point to this video back then and tell him to stuff it.
Your explanation of flat bonuses intrigued me. I have always played under the premise that if you roll a 1 you always fail and vice versa for 20... the assumption being that reality is a fickle bi**h and allows for unexpected greatness or inconceivable folly; the untrained can always get lucky and the most experienced/gifted can always become overconfident. ... I've played that way for so long with so many different groups, this is actually the FIRST time I'm hearing there are such a thing as "un-failable rolls". Crazy! Take an upvote for that, good sir.
as a great man named Punchy once said: have you seen the RPG community? it's all ABOUT the "number go up" around here! this was a very insightful video and I both thank and applaud you for making it good sir!!
My favorite quote from my time playing pokemon is "if it isn't 100% accurate its 50% accurate" this comes from focus blast seeming to miss more times then it hits.
70% accuracy? Maybe when the opponent uses it...
so like the Leper of darkest dungeon
@@bivcbmtgstgtssscqcrddgtrsm2257 pov:ur aaron "cybertron" zheng
And then there's the gen 1 addendum: If it _is_ 100% accurate, it's 99.6% accurate.
@SnakebitSTI dosent that also apply to gen 2 to an extent i forgot the exact odds
I think its also worth mentioning that, in 5e, anything above a +1 or +2 modifier is a *significant* improvement from what you would get normally. So "only" getting effectively +3 or +4 is still pretty huge. Additionally, there is never any downside to advantage, so you should always be trying to seek it - which (in theory) leads to more interaction with the environment and creative solutions to problems.
While the proliferation of advantage on so many features means players often have enough ways of getting it that they don't often look to the environment to get advantage, this is definitely a key detail and a fun thing to implement as a DM.
TLDR, since this went long, Stacking bonuses act as incentive to interact with multiple systems, vs the one and done of advantage.
There are many ways to get advantage, but since they dont stack, you actually only need a handful of methods for most situations. Add in the fact that a single case of disadvantage negates any number of sources of advantage, and I find that they engage in less of the system, not more. For example, I will pull something that happened from a pathfinder game that uses stacking bonuses as opposed to adv/disadv. We had a cover for a tomb that we needed to get into. The lid was extraordinarily heavy, and the intended interaction was some kind of sacrifice to activate a magic that would lift the lid. Instead, as a group we were able to employ our tools, spells, a magic nail that would never pull out once set, an extremely good knowledge: engineering roll, and the strength of three strength based characters to lift it. We were interacting with so many different systems in order to pull off something incredibly hard.
Contrast that to if you had the same situation in 5e. You could get advantage from a number of the things we did, but if the DC is higher than a 24, you arent going to get it. This leaves the DM with 1 of 3 options. The lid is impossible to lift, the lid is impossible to lift, but the dc gets lowered by all the things the party does, or the lid could be lifted all along, and a single thing to gain advantage gives them their best shot. The first I find unsatisfying as a player. The second is the same as pathfinder, just with extra steps. The third I also find unsatisfying.
If I was to ever run 5e again, Id seriously consider making 1 case of advantage canceled out by one case of disadvantage at the very least. I am curious at how unbalanced having 2 cases of advantage would let you roll 3 dice keep highest. In the end, Id prefer to just work with static stacking bonuses like in pathfinder.
There can be downsides to advantage. I've definitely had a couple rolls where the advantage a player got worked against them.
@@kiranaun9593No you didn't.
@@robertellis6853 Stacking bonuses bog things down though.
Say what you willabout 5e, having one primary source of combat advantage prevents bogging down each round with ways to get bonuses up.
Like, stacking accuracy bonuses are fun... for the one person but like... let's get to everyone's turn, let's keep the game moving.
Analysis paralysis is bad enough as it is.
One thing you’re forgetting is that advantage nearly eliminates a critical miss, while disadvantage nearly eliminates critical hits. To get either, you need to roll both 1s or both 20s, respectively. When compared with the likelihood of rolling any other combination of rolls, the odds of rolling a critical miss or critical hit are 1 in 400.
And they also make the opposite type of critical roll much more likely.
Ah the joys of pathfinder 1e lol, critical hits required a second confirmation roll that also had to meet or exceed target AC. Made it very hard to crit high AC enemies, glad they scrapped it for 2e 👍
I was about to point this out. In my experience advantage on attack rolls is almost always desirable more for the critical hit chance than the actually success/failure rate. The other side is for circumstantial opportunities like a high level spell attack roll that you really don't want to miss.
@@SeanQuinn4 That was a thing they directly took from D&D 3.5.
advantage also roughly doubles crit chance, so its very important for hit rolls
I've taken master's level statistics classes and this is the first time "odds" vs "probability" made sense to me
odds are also very useful for Bayesian inference. If you use odds instead of probability, Bayes' rule becomes just multiplication of the prior odds of A to B with the Bayes factor: P(measurement|A)/P(measurement|B).
3blue1brown has a very nice video on it
yeah, i was like "odds, eh useful i guess?" before
In probabilities: 30% vs 70% vs 90% vs 95% vs 99%
They don't look all that different
In odds: 3:7 vs 7:3 vs 9:1 vs 19:1 vs 99:1
MASSIVE difference (which is how they feel intuitively in Pokémon)
And the odds in decimals:
0.42 vs 2.33 vs 9 vs 19 vs 99
@@xXJ4FARGAMERXxPersonally I prefer fractions to odds. 1/10 just makes more sense to me than 1:9 and 1/2 makes more sense to me than 1:1. I do see your point comparing odds though.
"or you can just not over-engineer your character like an absolute nerd"
Sir, you are talking about TTRPG players. We are all nerds here.
Yes, the appropriate term for this sort of power-gamer among the groups I've been part of would be "munchkin" rather than "nerd". I've also seen "roll-player" as opposed to "role-player" but this only works in writing.
I think nerd is a relative term, because there's always a bigger nerd.
So absolute nerds don't exist
@@Alge_ ive also seen this over-engineering called "Min maxxing"
@@Alge_ I have kind of mixed feelings about munchkins. On one hand I don't mind a dip or two to get a skill, but some folks overdo it too much to the point that their character is a fighter / ranger / mage / barbarian / cleric / monk / thief / druid. I mean that's not a character anymore, unless you're playing someone with multiple personality disorder. 🤣
Either a nerd or a geek, or both
There is one case that I know of where the rules of 5e DO convert the advantage/disadvantage system to a direct modifier. That is with passive scores: "If the character has advantage on the check, add 5. For disadvantage, subtract 5" (Player's Handbook p. 175)
Indeed.
¾ cover also does this, as well as Sharpshooter and GWM feats.
@@aurvayNone of those have anything to do with advantage, they can each give their modifiers and *also* have advantage/disadvantage.
Makes sense in a way, since at 50/50 odds the advantage is equivalent to a +5 bonus and the passive score is your modifier + 10. Both take from the middle.
Too bad that it's slightly off because a DC 10 means a roll of 10 would succeed so with a +0 modifier you'd have 55% chance of success.
They probably rounded the numbers to multiples of 5 because that's just pleasing
@@roelant8069 yeah it's not even meant to be perfectly balanced. there is also a rule that lets you "take 20", in which you can assume to try something as long as it takes to get the utmost result you can ever muster, but also suffer all consequences of failure too.
The thing is, you are not guaranteed to roll a 20 ever. while slim, it's possible you already got your last nat 20.
tldr: even throwing a coin one billion times is slightly off from a perfect 50/50
The mention to Pokémon when you brought up the perspective of looking into thw chance to fail is spot on. A 95% accuracy move is only slightly worse than a 100% one but the same 5% drop from 90% to 85% feels like a ravine
With a 95% accuracy, unless you have to very slowly whittle the enemy down, you are unlikely to see a miss in a given battle, and in case you do, it doesn't impact the overall damage per turn much
With an 85% accurate move, you are much more likely to see a miss in a battle if all enemies are one or two-hits, and then a single miss is also far more impactful
@@zuthalsoraniz6764I’ve missed sacred fire too many times to count in short, Hyper Offense battles and it has lost me the game many times
Makes sense if you think about the failure rate. 95% to hit means 1 out of every 20 will miss, so it's unlikely you'll see even one in a normal battle. Compare that to 90% or 80% where 1/10 and 1/5 will miss and it starts to become a "every battle, maybe multiple times" thing.
I'm of the opposite opinion. A 95% accuracy move is only slightly better than a 90% move, but a 100% accuracy move is infinitely better than a 95% accuracy move.
@@gammaf8896 it's still a 1/20 chance for the -5% accuracy to matter, per move
How to lie with statistics.
A classic.
All the numbers mean the same but our perception is what is changing.
10/10 explanation i loved to revisit this topic.
I love how the Kenku must have put time and effort into getting people to say all the things like 'Taylor expansion' to make this rant.
Unless it's from MMoTM, where Kenkus are no longer cool and interesting, and can speak normally.
@@sipofsunscorchedsarsaparil6052 Cool race, but playing with a legacy Kenku was not fun
Just pay a traveling bard a couple gold to read the dictionary, and you're good. Also, homophones are useful. "Tailor" and "Taylor" ect.
@@itszeroday Personally, for me the most fun part of the old Kenku were character ideas that came up with creative hacks to get around the character limitation.
One character I had was a Kenku Illusionist Wizard whose backstory was that he cast the Minor Illusion cantrip hundreds of thousands of times over the course of months to produce a voice speaking every single word in every single language that he knew, and then mimicked the voice in order to regain the ability to talk through sheer brute force. He went by Webster, and while he could talk, he always spoke in a completely flat, robotic monotone.
Another was a Kenku Great Old One Warlock who was using the power of his patron to bypass the curse by gaining telepathy, and was almost always completely silent because he started exclusively using his telepathy to communicate. He went by Whisper.
I have never understood why people think kenku only being able to mimic was somehow “unplayable.” How did you learn to talk? By listening to other people talk, right? You should be able to talk just as well as anyone else, and basically being a kenku meant you couldn’t read aloud written words that you didn’t already know, which I feel like is a minor inconvenience at best.
The graph at 8:02 is exactly why I Iike advantage (as a long term 3.5 player to boot) , simply because it accurately models the actual 'advantage''s meaning. Like, say you're shooting at someone who has been webbed. Even a lousy shot is going to have an easier time shooting at a target that doesn't move, but for an experienced shot, it makes it go from 'this will go well, trust me' to 'I can do it with both hands up my arse'. Which makes advantage a very apt go-to tool for resolving unknown situations.
I like Advantage because it plays nicely with our brains' flawed instinctive understanding of probability. Once it gets above 80%, and especially 90%, most people think it's basically guaranteed to happen, which Advantage reinforces. (Of course, first hand experience can replace this flawed intuition, but for I'm speaking in regards to the "average person.") Similarly, it turns coinflips into "pretty likely, but still not guaranteed" which usually feels better from the perspective of the player.
I dislike it because once you have Advantage, there's no point in trying to get further increases/benefits because Advantage doesn't stack. Pros and cons to every system, and all that.
Another fun one comes from the RPG realm outside of D&D. Some games, like the "kids on bikes" system, use "exploding dice", where if you roll the maximum of an n-sided die, you get to roll again and sum the results, and this can repeat.
This has a number of fun effects: on a D4, it's impossible to roll any multiple of 4. Exploding with a D4 _twice_ is more likely than exploding once with a D20. The probability of getting any given number is never 0, as the exploding has the potential to go on forever.
"The probability of getting any given number is never 0"
Except for a multiple of the max number on the die, as you mentioned earlier.
@@NightKev Ah, yes. I should have said "Defeating a given difficulty class is never zero".
*NSBU has entered the chat*
Role master....
There also exists a slightly different type of exploding dice system which on top of allowing you to roll an extra time also removes 1 every time the die explodes. It is for example used in Dominions 5, a video game very much inspired by tabletop RP. With that system, 1d4 CAN result in exactly 4 if you first explode (nat 4) then roll 1 (4-1+1 is the final operation). With this system, 1d6 averages to exactly 4 (instead of 3.5 without explosions).
07:52 this felt like that moment when you're looking at your math book for too long and look up to see what the teacher has drawn on the board.
Wow, this is so well made. You explained how the different probability conversations worked so intuitively that anyone could understand
Indeed.
And nicely animated as well.
Great explanation of a complex topic.
Lol I sent this to a friend saying "first time ever I've seen someone be comprehensive on each of these angles and he does it in under 10 minutes" then GASPED when youtube recommended me "more from..." and I realized you were the cursed units guy.
This is another amazing vid.
I had to do a sneaky re-upload to fix an error, so apologies if your comment or like got overwritten or if you got double notifications. Feel free to re-comment or re-like!
:)
Good thing you were able to catch it early! The algorithm is still picking this version up it seems
advantage and disadvantage are a pretty key part of the snowball effect in DND 5e, its also a major factor of death spiraling in it too. a good rule of thumb is advantage *feels* like a plus five unless you were never able to succeed the check in the first place, and disadvantage is the same for failure rate. so if you have the choice of a +3 or adv, the choice should basically always be the advantage unless you cant pass without the added bonus.
U rolled a nat 1 on the video so u had to re do it but now with advantage 😂😂😂
Video uploaded with advantage
There is a Stand-up Maths video on this topic, called The unexpected logic behind rolling multiple dice and picking the highest.
Try it with 2d6. Roll 20 times and record the highest result each time. You'll get many more 6s than 1s and most of your results will be above 4.
@@mr.pavone9719 I like advantantage on 2d6 based rolls like PBTA, with advantage meaning one extra die and keeping your 2 best dices of the total 3
An Xcom player wouldn't be able to explain the difference between 5% and 99% propability of success, they might aswell be the same probabliity.
The funniest part is that xcom cheats on its probability calculations... In the player's favour.
@@Kasandra_ Unless you're playing on the hardest difficulty. That's the "fair" one.
@@Kasandra_ ALLELUJA! Someone else gets it!
5% probability of success is "that sniper across the map who's safe has only 1 target available at 5% hit chance. Why not? It's not like he was doing anything else!"
99% probability of success is "rushing this shotgun toting Ranger at close range to shred a target. Do I have a plan B if things go south?"
There, I, an Xcom player, have just explained the difference between 5% and 99% probability of success. You've been proven wrong, you're welcome.
Murphey's Law will always be your god in those games. Same thing goes with Fire Emblem games: if I'm not at 100% on the screen, I am just as likely to miss as if I was at 35%.
I appreciate this video because I’ve never heard anyone else complain about the phrase “twice as likely” but I’ve always hated when people say that, this made me feel less insane
Wait, who believes advantage makes something twice as likely?
That is not how statistics work
Have you ever pondered “twice as cheap”
@@billy1bob2ones3 Just means its only as cheap as the base price after markup.
@@billy1bob2ones3 I always interpreted that as meaning "half as expensive," just instead emphasizing that the 1st item already had a low cost and now the 2nd item is even lower.
@@billy1bob2ones3 "This footage have been slow down 400%"
What, you play it in reverse or something?
My immediate reaction to this information is "let's just use both depending on the situation", but I just like having lots of knobs to tweak.
what I like about replacing modifiers with adv/disadv is that modifiers are hard to learn, but easy to house rule. so instead of learning every single modifier, leave it to the control of the DM when add positive/negative modifiers.
This is used in the Traveller system by Mongoose publishing. Two d6 added up then with numerical modifiers is the usual way of modifiers, but certain situations invoke boon and bane die which are an extra d6 which replaces the highest or lowest rolled due dependingly.
What’s fun is that besides circumstantial boon and bane die, the players can also make “leadership” rolls in combat situations which let them get a few boon die to hand out to other players during the encounter when they’re most needed
@@danilooliveira6580but it becomes so flat and boring in combat, and its why spellcasters rarely buff or debuff in 5e. You either have it or you don't, so why try to get multiple advantages in a fight?
@@NihilTruth that doesn't make much sense considering most buffs are not adv/disadv. and I would argue adv/disadv is good as a buff because now you don't need to list what buffs stack and what buffs don't, because you know you can't get to roll 3 D20s. so if you don't want a buff to stack you just make it give the player adv/disadv, and if you want it to stack you make the buff give extra dice to roll or a modifier.
@@danilooliveira6580 I like the game part of the Table Top Role Playing Game. Advantage/Disadvantage alone, with no modifiers, is too simplistic a system that makes combat boring, but it's not the only reason behind that.
It's not hard at all to stack modifiers, I can assure you of that. Especially in more current games, especially with the advent of VTTs.
The ratio of how informative this video is to how much I learned from it, is off the charts.
Great video, especially the breakdown of how using the complement or the odds can lead to a better intuition of these kinds of probabilities. Love how you present quite complex concepts in a very approachable way without dumbing it down.
Some thoughts:
A good way to look at the counterexample is to go from something like 0.9999 chance to hit to 1. Even though you're only landing around 0.01% more hits, your odds increase by a factor of infinity. This discrepancy seems WEIRD when you think about it in those terms, but a simple way of thinking about it is "how much does this increase my average damage?" vs "how much money could I theoretically bet on this outcome?"
The concept behind moving from flat modifiers in previous versions that result in the weirdness you see at 8:22 is called "bounded accuracy" specifically to avoid this problem. Higher level characters in earlier editions completely trivialised low level encounters, and the devs wanted to be able to keep lower level monsters relevant while making the characters still feel like they were improving in power. A lot of the massively broken 3E builds abused exactly this mechanic (eg the 'Diplomancer').
The reason many DnD players like to look at flat %increase in hit rate is because it follows on to a metric that's generally more practical (and easier to understand) when optimising a character - ADPR (average damage per round). If your hit damage is 10 on average, a hit rate of 50% would give you 5ADPR (assuming you can always place your character in a position to make an attack) In this calculation the %increase to hit directly equates to %increase in ADPR (doubling your chance to hit from 50% to 100% gives a straight 2x multiplier to your ADPR). This helps making general decisions like "should I take this feat for +2 damage or a IAP for +1 to hit and +1 damage?" a little easier.
Things start to get quite convoluted when you start to factor in things like damage ranges (is 2-80 damage better than 41-41 damage?), nat 1 (auto miss) and nat 20 (auto crit), critical misses (variant rule), and other abilities that proc off advantage (sneak attack being the obvious one). Also sometimes the cost of failing an attack or skill check can be extremely high (ie if I don't lockpick this door open our party is gonna get crushed by the trap, or if I don't hit this monster with this attack he will kill a party member or two) - which makes misses feel far more impactful. All this is why building a strong intuition is far more valuable than making a formula and blindly following numbers without understanding its limitations.
The most notable feature of the advantage system to me is that it turns your roll from a flat probability distribution into a kind of lopsided bell curve. Binomial distribution works well to analyse this imo.
Great video! Im glad you analyzed both the “effective flat bonus” and “factor multiplier”. I did similar calculations on my own a while back when I was comparing the War Caster vs Resilient (Con) feats, and I wish I saw this video before I went through all that math myself
Obviously this is mostly about skill checks, but something I also like to consider is critical hits/misses. Advantage simultaneously making a Critical Failure a 1/400 chance, while Critical Successes become a 9.75% chance. Or viewed alternatively, it turns a "5% to 5%" to a ".25% to 9.75%" split. Critical hits are 39x more likely than Critical Misses.
As you mentioned it's about a ~+4 to rolls. But also important to keep in mind is the DPS bonus of Critical Hits. 9.25/5, and you have bonus damage (average DPS) due to critical hits being 1.95x as much. This is the part where I mention I don't know anything about statistics, but it seems like that could make a difference. Perhaps getting a critical hit in once a combat vs. every other combat.
Which then we get into the nitty gritty details of taking a Rogue or Paladin w/ smite and mentioning how managing to get a critical hit off once per combat could be massive damage and yada yada. Because combats aren't graded on a scale and are instead Pass/Fail, you realize that once a combat critical hits can be huge.
In general critical hits don't increase DPR significantly, even with increased crit chance from Advantage. It does have an increase, but in calculations it may change the DPR from 35 DPR to 36 or 37 DPR. It's not significant, unless we're looking at something like Rogue who can almost double their damage on a round based off crit hits alone
No joke, shifting from explaining how modifiers work to instead explaining how advantage works was what convinced my group of friends to start playing DnD
5:46 I swear pokémon attack probabilities are rigged, a 95% feels like a 98% but then a 90% feels like a 30% and when you think you've figured it out there comes the 50%'s that feel like a 10% and the 55%'s that feel like 95%. Please, WTH IS FIRE BLAST (85%) LIKE 10 TIMES MORE ACCURATE THAN CRABHAMMER (90%)!?
the myth that Stone Edge either crits or misses didnt come from nowhere, and we all remember that time Air Slash missed twice in a row
This is a lot of really useful information for someone like me who is making some sweeping homebrew systems. I oftentimes use advantage in balencing as if it were a +4.5 modifier to a roll not giving the actual math much thought. Very interesting
5:13 EXACTLY! Check the ratio between the probabilities! We were doing these exact calculations just last week to show the, uh, *advantages* of advantage. Your chances on the highest difficulty checks like critting nearly double!
Chance of failure is also huge, that's basically how we calculate what incremental increases to defense do to effective HP when we're playing RPGs. When you have no defense and get a 10% damage reduction buff, that obviously reduces the damage you take by 10%. But when you already have an 80% damage reduction buff and you get an additive 10% reduction, that cuts the damage you're taking in half (from 20% getting through to 10% getting through).
As a DM who has wondered about the merits of the Advantage/Disadvantage system, this is immensely helpful. Thank you!
Great video but I think you are wrong about one thing; hours long combat with enemies you can hit easily but just soak up hitpoints are NOT more fun than hard to hit enemies that you have to take down with luck or clever tactics
I think it depends on the person and game what's more fun.
Hey friend, I gotta push back on this.
I've run thousands and thousands of hours of different TTRPGs through the years and, anecdotally, I find that enemies who are very difficult to hit can easily feel frustrating and unfun for players, in general. This doesn't mean that you should never use enemies with high defenses, just be very sparing with them.
The recommendation to make enemies generally easier to hit and compensate with higher HP is almost guaranteed to improve your game experience, especially compared to the opposite.
Clever tactics and luck will play a role either way, but swinging and missing repeatedly turn after turn sucks.
Combat may be longer or shorter depending on a number of things, but very difficult-to-hit baddies will always only extend combat in the worst way.
Remember: the problem isn't long/difficult combat-it's boring, frustrating combat that people dislike!
Addendum: you can build encounters around high defense, but add a twist that makes it fun (and make sure your players can find out about it beforehand if they are smart about it and ask around) such as an enemy with very high AC which decreases every time it's hit (clearly signal this by describing the armor breaking off), or who has a lower AC against a type of damage (eg: 18AC; 12AC vs melee piercing).
I think everyone is right here. The best thing to do is create a variety of enemies and keep the players guessing and engaged.
I built an encounter with dozens of relatively easy to hit goblins who died in one hit (or rarely 2 hits), but then threw in a difficult to hit, and tanky automaton.
@@manicpixiedreambuoy I can concur with this. Recently ran a game using a system that allowed blocking, dodging, and parrying all incoming attacks, on top of the attacker having to make a roll to see if the attack was even going to hit in the first place, and that was the most universally disliked thing about the system among my players because it meant that, while they got hit less and HP pools for enemies were small, they didnt feel like they were making any progress in combat.
@@greed0599I guess people have been playing computer games so much every enemy is seen as a health bar you have to whittle down and that is "progress".
9:00 for some reason, I felt super cool when you said first order Taylor expiation and I knew what it was and what it meant.
4:35 Been playing for many years, and my group tends to hate damage sponges. Hitting something is cool.... until you've done it 10 times and so has the rest of the party. Just another nuance to consider, not all DMs prefer to run low AC high HP creatures.
Yes! not all DM's prefer that, most DMs are however Forced to play that way.
DM should not want to TPK their players, but players having bad characters force DMs to play crappy DnD creating a very low risk encounters, such as dumm damage sponges.
Most games of DnD are run on tutorial difficulty with 1-2 combats per adventuring day, where decisions dont matter, resource management doesnt matter.
This is mostly critique to the whole community for being trash players and noone should single out DM's as them being the problem by using easy monsters as damage sponges instead of deadly, tricky ones, forcing mental saves and such.
Imagine how popular is the 3rd level spell Waste... How many idiots were twinning it as Sorcerer and inviting TPK? Many.
Make good character, focus on initiative, saves and good spells/features. So your DM can take you for a spin in real DnD game! Not your typical fuck a bartender game.
I've seen a lot of attempts to explain the value of advantage, but this is probably the best blend of clear, thorough, and yet concise in covering the topic. Well done, and I will definitely be saving this to refer people to in the future!
Perfect timing! I subscribed before for the other math videos, but this new one came out right when I started getting into D&D!
My favourite instance of an intuitive notion not well-defined is temperature.. say it's rather chilly outside one night but then the next night - ho boy it's twice as cold now!
But what does that mean? what are the units? to what are you possibly multiplying by 2 to get the new result?
My best guess is a sort of exponential graph of 'perceived cold/hot' that works outwards from whatever that individual considers 'comfortable'.. 🤔Like a parabola where the lowest point intersects the X axis at whatever temperature is considered perfect comfort, since the perceived distance from comfort is being doubled then the temperature units don't actually matter. And while that zero point and the curve function would be different for every individual, I suspect they're close enough for us to correctly intuit what someone means when they say it's twice as cold as the night before
Thanks for coming to my Ted Talk
Doesn't need to be a parabola. Can just be a |x| function. You just go twice as far from the minimum 🤔
The was a time Google would convert to Kelvin if you asked it something like 20°F/2
I think the "Ideal comfortable point" is just homeostasis, where your body doesn't need to do any extra heating or cooling work to keep your core temperature stable. This point changes throughout days and seasons as your metabolism changes, which is why spring feels so much warmer than fall, and why morning is always colder than evening.
Thus, twice as cold or hot is approximately twice as far from homeostasis. Which scale of twice might be tricky (like in the video!); I would think it's either twice as expensive to maintain homeostasis, or some order of magnitude greater, like decibels.
Easy, if it's twice as cold you divide temperature (in Kelvin) by two. For example:
"Yesterday was chilly (280K) but today is tiwce as cold! (140K)"
we need temperature decibels.
let's say 0dBT is 20C, and the unit is 10C, twice as cold means a change of ~-3db, so 10C would be 10dB, and 0C would be 13 dB
though it doesn't actually work that well on the other end
I think a curve that takes into account the livability might work, but it would be weird too, because 50C is ~6 times hotter than 45, and 45 is ~6 times hotter than 38C
on the other hand -6.5C is ~ twice as cold as 4.5C, which is twice as cold as 12C
but the issue is that the 20-30 C range is not well defined, and it can't do low nor high temperatures
0:06 Gobbo on another adventure i see :)
I appreciate how much time you put into making the functions. This is the part of D&D no one of my table likes, the probabilities and number crunching
Still can’t watch this one right now bc I have school but I'm still confident it is a banger!
THANK YOU. This is the first time I've heard someone discuss the nuanced mismatch between a mathematical expression of probability and common English expressions.
Never seen this channel before, but I'm a big fan of the little crow guy explaining maths to me :)
What a great instructionary video on probability, particularly how you point out how faceted our colloquial terminology is when we describe this. The part about the Taylor expansion makes so much sense, without having thought about it prior
0:32 "In fifth edition, the most recent edition" well.. 😢
Hah well the most recent edition is still 5 it's just "5'th edition Director's cut"
@leritykay8911 as I like to call it 5.5
I love how he explains the basic mechanics of DnD at the start. It doesn't really help experienced players like me, however it's nice for people who have never played a TTRPG
The correct analysis is doing additive analysis, multiplying by your average damage, then multiplying by how often you get advantage. This collapses all this weirdness and definition stuff.
As a simplification if you almost always have advantage you can just reduce it to the multiplicative analysis you showed and consider it a % damage increase .
And as a simplification if you almost never have advantage you can reduce it to just a flat damage increase per advantage.
In the case of combat this is totally valid, one can just calculate expected damage, but in the case of skill checks it doesn’t. In that case the different ways of interpreting probabilities become interesting, and i for one like the idea of odds
@@mickschilder3633 Actually no you just utilize the effect. For example constantly having advantage may give you 15% more successful perception checks. Or say each advantage gives 5% of a stun.
This is the best and most in-depth look into advantage I have seen, and it's quite well contained into a sub-10-min video. Well done!
I did not expect Mr. Cursed Units to make a video about tabletop game Advantage, and I expected even less for them to use a Kenku Rogue as their avatar for the video, but it's a very welcome surprise!
(PS, no we will never stop being absolute NERDS)
Cute bird *and* cool math? Neat!
I love how this channel goes absolutely in tune with my hobbies and likings over time; literally, I started with TTRPGs early this year and it is AMAZING, and also, I'm on my final year at a tech highschool, so I can create a FUNCTION to meassure exactly (or so I think) how much do I correlate with this channel and its contents, but with good representations.
You can say it meassures in "likeness [Li]", where a factor of compatibility (Com), multiplying a moment in time, adds to an exponential function of excitement (Ex) powered by a period of time which the content is related.
So we get something like: L(t) = Com*t + Ex(T) = Com*t + E^(T)
I'm still not an engineer, but my math says that I'm pretty excited about it.
4:05 This is true for GMs that understand 5th edition and assigning appropriate DCs on the fly. If you, for example, have a GM who is accustomed to Pathfinder 1e types of DCs, you will almost always be facing Hard or Harder DCs relative to your character's level, often facing DCs of 15 to 20 when you should be facing DCs of 12 to 15. I'm not salty >_>
That's one of the more annoying practices in traditional GMing: the "DC treadmill", i.e. artificially inflating DCs as the characters level up and get better at doing what they do so that their probably of success remains more or less the same. 5e put a stop this practice with its bounded accuracy rule, but the proficiency bonus it gives you is so small that leveling up doesn't change your probability of success very much anyway.
Much as I love 3.5 in the early game, I hate it past level 4 or 5 for that exact reason. The DCs just get arbitrarily high, and it practically forces skill point min-maxing.
I keep finding myself drawn to the OSR space now. I think simplicity truly is the way to do it, and the numbers don't get too crazy
This is a delightful video. I really love all the cute little details in the artwork. I think you did a great job articulating your points, too. Outstanding work, subscribing to you was the easiest decision of my life.
Another fun mechanic like this is crit chance in League of Legends. Rather than having a fully random probability of let's say 50%, the probability starts out lower than that and then increases with every crit miss in such a way that the total probability still is 50%. I don't know the actual numbers, I just know the mechanic. The reasoning behind this is that true randomness could and over enough games would result in long series of misses which would make players feel like the game is cheating them out of crit damage. Doing it this way forces the streak to break eventually which feels more fair, even though it mathematically isn't.
It's like if DnD gave you a +1 after your last roll was a failure and a -1 after your last roll was a success.
I believe WoW also implemented that for drops. For every failed drop, the success chance goes up by a little.
I know DotA 2 does the same. It's called "psuedo-random" chances, because while there is still probability involved it reduces the chance of extremely bad or extremely good luck swinging a fight/game suddenly while still keeping luck as a factor.
I am deeply fascinated by the analysis you do here, and am gonna be looking at more of your stuff. Thank you for your work.
Did something change?
Yep, there was a fairly sizeable mistake in the formula at around 2:10, so I did a re-upload to fix it
I did my own math on this when 5e first came out, but I never thought to check if the "value" of advantage changed at different DCs. Interesting vid!
9:41 But being an absolute nerd is all I know!!
This is not the usual video RUclips recommends to me… but i get it. I spent pretty much all my time spread between D&D/World of Warcraft vids and Science/Philosophy deep dives. While i am not nearly smart enough to understand how this is all managed, i still enjoyed it. Thank you
1:38 ain't nat 1 a failure no matter what? (BG3 at least)
It is a house rule. The players and DM agree to say that a nat 1 is a failure. In my games a nat 20 allows you to add your modifiers twice and still could cause a failure. Auto success and auto fails are only in context of attack rolls. But for skill checks don't benefit from this. But it still always comes down to the DM.
Not in 5E rules-as- written. 1s and 20s don't have any additional effect on checks or saves specifically.
@@herobrineking2514 I love the open-ness to get creative as a DM. Player rolls a 1 to lockpick DC15 with a +14? They break the lock and the gate swings open
@@Supallcommthat's pretty short sided and dumb Imo. Larian rewrote a lot of rules a lot better than the nerds at wizards.
Rules as written, no. But a lot of DMs won't even call for you to make a check if you literally cant fail it.
Love this explanation, relatively simple topic but there's so much interesting insightful deep things to dive into. Wonderfully explained as well, not over explained but easy to grasp
1:41 nat 1s or if u roll a one is a crit fail. So even if it was a plus 14 modifier you fail
Unless it changed in the new 2024 rules this is only true for saves and attacks. Skill and Ability Checks don't care about nat 1/nat 20, only the result of the roll+modifier
That's a house rule
No such thing as a critical fail for ability checks, read the book.
So confidently wrong
@@olivermccarthy456 how I was taught by my DM and that’s how I’ll DM
this video is so well done! lovely visuals, clear explanations, and a fun insight into probability and d&d. great job!!
D&D is just math disguised as fun
Unless you play say “screw the math” and use it as a social simulator.
That's assuming that Math needs a disguise to be seen as fun
@@ZttackFrmBhind It does because teachers teach it with the amount of motivation and desire as someone who found out their wife cheated on them with their boss and because of that their wife got a promotion while they didn't
Thank you for making this video, I always assumed advantage was basically a 4 in general. You helped me confirm that I made a good guess
Hold up babe, the cursed unit guy just dropped a video
I did advance maths in yr10. I was fantastic at it. Month 5 or 6 came about and we learnt about probability. I gave up and left school. I still don't understand the maths behind probability. Thanks man! :)
It's simple but doesn't mean it is the best tool for the job.
I was quite happy with the +2 standard bonus that was key to 3/3.5/Pathfinder with how simple it worked and was still intuitive and sensible.
Yes there (especially at later levels) are many things' players could instantly pass with how many bonuses there could be, but that is why a good DM needed to increase the stakes. No, it's no longer climbing that ladder, it is climbing that ladder with kobolds stabbing at your feet while arrows strike at you from a distance. It no longer swimming across a pond, but swimming across the sea with 10-foot waves and a Megalodon trying to reach you before you get to shore.
If you were creative enough you could put together very exciting challenges at higher levels really easy. Just pile on enough to the situation to make that +15 bonus either be necessary or compounded by penalties so it is more of a +5.
Adv/Dis always felt like it removed a little of that. I would rather give it out only when the situation demands an extreme bonus or penalty and not for every single situation like 5e does.
In Pathfinder 2e +5 is a GODLY bonus. It blows my mind that is just the main mechanic in 5e.
Thank you for going over this. I'm writing a TTRPG and understand what mechanics like this actually do is something that takes up a lot of thought for me.
1:35 no you won’t, depending on the dm. a nat 1 is an automatic fail in combat, regardless of modifiers, and some dms will extend that to out of combat
I've found most of the groups I roll with don't use the Nat 1 house rule. It really doesn't make a lot of sense for most groups.
@@zebanon5 funky thing with this is its also a rule that you probably do see in a large portion of the groups that say they don't use it - but the reasoning is vastly different.
Its a common house rule, that's more common than people would let on - since its also almost inherent with a simple dm facing rule of "don't ask for a roll if there's no chance of success or no chance of failure", a rule simply used to get the story rolling at times.
Feels like it'd also be a bit bullshit especially out of combat? Like say a professional musician with a +11 to performance isn't going to fuck up anything major to an untrained ear. You cannot sit them down in front of an easy piece on their signature instrument and it not turn out decent (unless the instrument fails, but the chance of that is also nowhere near 5% and even then odds are they know it well enough to improvise around it).
When I read the title I was like, ugh this is gonna be lame, 10 minutes to tell us the avg roll is 14, but I love it, it's actually really helpful, and I never even thought about it in this way.
According to the presenter the answer is roughly a plus four to a die roll. You're welcome.
Glad you mentioned it, as I see the factorized results as much more important. If I have a hard check, which are quite common at some tables, then I can almost double my chances of succeeding.
DnD is just making math and social anxiety cool
I like your video so much, it actually makes me think to give statistics another chance
I try and think about this often, I never come up with a satisfactory number myself but I liked that you did all the math and the short answer is "it just isn't easy" which helps. I usually consider it to be closer to a +5 so I'm glad my head canon is close enough
This is a really great treatment of probability and odds. Great video!
just.. thank you. as a an algebraic, abstract, and physical math person, with meh statistics background, this unironically put the physics of statistics into such a cool perspective. i am happy now. :D
I love how this wasn’t opinion or rants, it was looking at it from different math angles. And I am super down for that.
ah excellent i can factor this new information into my dpr engine to make even more balanced homebrew. thank you sir!
5:50 Gigachad for showing best starter ever made.
Extremely good video. You sir can be proud of yourself
This was a fun video, I quite enjoy seeing some of the math behind the dice!
Hearing "these numbers all have the same first order Taylor expansion" and actually have an idea what you're talking about made my day
Very good video.
Your graph on flat modifiers explains also why Pathfinder 2 added the idea that under shooting by 10 or over shooting by 10 changes the result. So no matter where you are on the graph the flat modifier changes dramatically the odds of SOMETHING.
My luck is bad that i will take the comforting embrace of modifiers every day over the probability of failing two times on the same roll.
Great video, I would have liked to have seen the later talk about odd be rephrased for disadvantage too. I know they're just inversed, but getting language statements correct feels like a significant point of this video.
From the perspective of someone trying to make a TTRPG system that is simple, yet interesting and balanced, this is incredibly useful... and unfortunately necessary because you just know people will pick it apart like absolute nerds. Thanks for making this!
Well covered. Well explained. And without math errors!
I wish I had this video when I was learning probability, so easy to follow.
I am currently creating a game that (like DnD) uses an advantage/disadvantage system while fighting monsters. This is mainly because I genuinely only want there to be 4 dice *(2d8 & 2d10), but have 12 different monsters relying on this system. Thus, I am grateful for your analysis on the topic involving the concept.
The big thing about advantage is also that the chance to critical increases by 80,5% (assuming that a natural 20 is a critical). It's a big swing in one's favor.
As someone with a probability exam coming up and a DnD obession going on, this video is perfect for me.
The JoCat reference at 0:06 ❤️
(Also, awesome video)
Yesterday I was wondering exactly this. Today is a good day.
Thank you for this very insightful video, the game path of exile has a similar mechanic called lucky, that means a chance or damage value is rolled twice and the higher number is used, I didn't really think that it was very powerful but now I understand how it works in DND and can see why that's good in that game too
How you explained closer to zero probability and the phrase 'twice as likely' being reasonably undefined explains '2x boost bonus/whatever' slot machine buttons very well.
Thank you!
The summation math IS correct mathematically, but didn’t make sense to me in terms of the actual application.
But this also highlights why I hate probability/statistics in my math classes!
Beautiful work!
This is a cool approach, thank you for making this video!
This is a great video, really helped me solidify my thoughts on Advantage/Disadvantage. I had a problem player in one of my campaigns previously who loved to power game, while insisting that wasn't what he was doing, and one of my biggest complaints was that he was able to deal absurd damage with the Great Weapon Master feat while all but negating its downside with Reckless Attacks. GWM lets you trade 5 points of accuracy for 10 points of damage on melee weapon attacks, and make one additional attack if you either crit or kill. Reckless Attacks let you make every melee attack with Advantage, in exchange for attacks on you being made with Advantage (not a problem for a raging Barbarian). The problem player tried to insist that Advantage did not make up for the -5 to their attack rolls, but given how the monsters we were fighting didn't have exceptionally high ACs (and even if they did, he could just choose not to apply GWM against them), the math disagrees with him. I would have loved to be able to point to this video back then and tell him to stuff it.
I'm liking and commenting for the excellent thumbnail. I might come back and watch later.
Your explanation of flat bonuses intrigued me. I have always played under the premise that if you roll a 1 you always fail and vice versa for 20... the assumption being that reality is a fickle bi**h and allows for unexpected greatness or inconceivable folly; the untrained can always get lucky and the most experienced/gifted can always become overconfident.
... I've played that way for so long with so many different groups, this is actually the FIRST time I'm hearing there are such a thing as "un-failable rolls". Crazy! Take an upvote for that, good sir.
I loved coming back from photographing the super moon to see your video ❤
as a great man named Punchy once said: have you seen the RPG community? it's all ABOUT the "number go up" around here!
this was a very insightful video and I both thank and applaud you for making it good sir!!