I've never played League nor have any clue how TFT works, but I still watched this entire video.. something about reckful on a notepad makes me excited
I feel weird, nostalgic a little sad and happy at the same time, watching this video... but the information is super good even for the current set if you tweak the number Thank you so much for everything byron RIP
The 66 gold scenario(for legendaries) just holds for one specific case(40 exp away). The gold threshold differs significantally for other "exp away" scenarios. The general function to figure the gold threshold out is: f(x) = 5x/3, where x is the amount of exp you´re away from level 8 and f(x) is the gold treshold from where its worth to level up first and then roll. So yeah if you are 46 exp away instead of 40, the gold threshold is 76 gold instead of 66. But ye, as you see, the function is linear and therefore its pretty easy to figure out the actual threshold based on the amount of exp you are away and can be calculated within seconds ingame. General conclusion for the level 7 legendary scenario: 1) If you are above 76 gold its always worth to level first and then roll, you dont even have to do calculations 2) The more exp you have, the lower the threshold gets 3) The gold threshold lowers by 16 gold for every 10 exp you gain 4) If you want to figure out the exact gold threshold for your scenario ingame just use the simple formula above Hope that helped, if anyone wants a detailed explanation on how to figure the acutal function out(its quiet simple) just hit me up. The graph looks like this if someones interested: puu.sh/DOTLG/b046e9cac2.png
@@BlackMamba-vl4ks Have I said that I have trouble doing this kind of math? I just said that the way Byron explains it makes it very interesting to watch.
@Reckful there is a much simpler way to calculate that the expected value for rolling an epic at level 8 is 1 than your brute force calculation, though I'm not trying to diminish your effort every slot has 0.2 expected value and there are five slots so the total expected value is 1 I'm not sure if you were aware of this or not so I just wanted do bring it up because math without brute force calculation is fun :)
Hey Byron thx for the nice and easy explanation. Actually that was exactly what I was looking for and your Streams helped me alot learning about AutoChess first and now TfT. Much Love
I mean, this calculation may be right if you're only thinking process is about when to roll. But you definitely need to consider the costs of opportunity of the 8th slot, and the subsequent losses. Like a gold/hp value would definitely make sense there, and this could easily be acquired by having a big dataset of game data.
The specific gold value is irrelevant because we are comparing spending equal sums of gold on either rerolls or levelup. So we lose the exact same amount of interest in both scenarios. This is NOT a three-choice question where we are choosing between rerolling, leveling, or econing/saving (that would be an interesting question that would yield a different calculation, but for the specific question Rekless was answering, his calculation is comprehensive). The specific hp value is irrelevant because health only matters when it reaches zero, it has zero impact on the strength of your comp beforehand. Go ahead and watch good tft players like Dog and you will see he won't do anything different from high hp compared to low hp right up until the point where he is within a single loss of dying.
Hold up there with your quick maths. For value of rolling, you need to take into account these additional factors: 1) Specific Epic/Legendaries. 2) Extra Board Slot 3) Free Rolls 4) Reduction of Previous Tiers 5) Combined Tier Probability 6) Number of Expected Upgrades Going through the list. 1) Specific Epic/Legendaries. Not all Epics/Legendaries are acceptable. You need to factor in the expected number of rolls to find those acceptable champions. (there's 5 legendaries, you have a 1/5 chance of seeing the legendary you need compared with a general legendary. This vastly improves the value of leveling up when evaluating rolling vs leveling) 2) Extra Board Slow. Generally the extra board slot adds a lot of value: It frees up a "hand-slot", it activates class/origin bonuses, it adds a character/meat shield. 3) Free Rolls. How many free rolls do you expect to see during any given round. This is minor, but can add up to 5+ free rolls over at the time of decision. 4) Reduction in Previous Tiers. Say you have a T1 or 2 unit that you are 1-2 copies away from upgrading. If you level up, you are reducing those odds quite substantially. Once you have your Tier 1 units at Level 3 you also want to reduce the chance of seeing those units. Which leads to the following point. 5) Combined Tier Probability. Your board has more than just one Tier of unit on the field. You should factor in your average expected across the tiers for when considering the value of leveling up. 6) Number of Expected Upgrades. Sometimes, Often, for everything other than legendary, you'll need your units to be at least level 2 to survive. This requires finding 3 of a specific unit. This multiplies the expected number of rolls by (The number of champions of that tier) by (The number of that unit remaining.) E.G. For Epic at level 7: (5) slots * (15/100) probability of epic * (1/9) specific epic * (13/13) number of that epic remaining = 5*15/100/9*1 = 0.0833 number of rolls: (0.0833*5) * (x + 20) = x; .4165x + 8.33 = x; 20 = x At 80 gold, to find a specific Epic, it is better to level up. *disclaimer, numbers may have changed since or before this post, the following is simply a demonstration of the calculation. numbers do not take into account any other factor such as: number of other legendaries owned by other players, desiring level 3+, free rolls, etc..
Just because something is more gold efficient with respect to getting some tier of champion at some level rather than another, doesn't mean it is better with respect to actually winning, as being higher level would allow you to put down more champions which in turn makes being higher level more appealing than what your calculations would otherwise imply (or rather be misinterpreted as being directly related to your winning odds)
@@humanoid52 6->7 is about the same as 7->8 for epic. IT would be profitable slightly earlier, maybe like 45-50 rolls it would be better. But still not worth if all you're thinking about is rushing epics usually. However you probably also want the extra unit etc so it might be worth over all.
Hell I must've missunderstood a lot of the information being dropped. From what I've gathered it is always best to roll over leveling to get a champ unless you are sitting at a 80-120g for a full level
@@VollFlippi If you are going for legendaries specifically, going from 7->8 could be worth it since it only takes 20 rolls until your chances get better overall. Basically, if you have >= 66 gold, then leveling from 7->8 is worth it for legendaries. Less than that, and it's not worth it to level. You also need to weigh the added benefit of putting in another unit.
Hate to break it, but that's not how you calculate probability. That's the "expected value" which is kinda of different. It gives you the general idea, but it's not the exact numbers.
Before the video started I tried to calculate it too.(from lvl7 to lvl8 ,tier5s) And I used this formula: 0,98^(20+x) = 0,95^x which later came to be ---> 0,98^20 = (0,95/0,98)^x , And if we calculate the x, then x=13 . Which is the same answer he got, but I have no idea why ? cause my calculation doesnt really include all combinations , just 1 or more.
Yeah but, the thing about this is @ level 7 you can get 7 units which is the optimal team comp for synergies. Also the difference from 6 units to 7 units is bigger than 7 to 8. So the number of roles lost via levelling is probably worth because you get an extra unit. Building tier 3 units is far more inconsistent than tier 2 units because you need 9 as oppose to 3 of one unit. It become harder to get more of the same unit as you buy them. Therefore you should only role for tier 3 early when the chances are higher, or not @ all and build a large team.
For the level 8 epic example he is using after 14:43: He wants to know the expected amount of epics you get on a roll. Each slot has a 20% chance to be an epic, hence the expected amount of epics you get in a slot is 0.2. Each roll gives you 5 slots, so the expected amount of epics per roll is 0.2 x 5 = 1. Think of it as groceries. If you expect each apple to cost 1 dollar and you are buying 5 apples then you expect those 5 apples to cost 5 dollars. Most of my confusion came from Reckful using % where he realy shouldn't (at 5:11 he wrote and said percent in stead of saying average amount).
All this calculation is based on the assumption that the champion drop rates is calculated per slot not on all 5 slots. Can someone clarify me on this? P.S. The explanation for why al lvl 8 the expected value is 100% for epics was AMAZING, it makes so much sense. Nice one.
I have 1 Question. When all people in the Game are Level 7 for example, they should have a chance of 2% for a legendary. But many 1,- 2- ,3- and 4- Tier are already out of the pool because they got picked.So the chance for a 5-Tier increases a lto doesnt it? If you imagine the Case all are lvl 9 and all 1-4 Tier unit got picked. The chance for a Tier 5 should be 100%
actually you could have skipped the whole math part, when looking at a binomial distribution (which the distribution of champions in the draw is) the expected value is always N*p ( N beeing the ammount of draws, p beeing the chance to draw it)
i get this is a rough account but reckfull is missing the natural roll on every turn when thinking about how many rounds will need to the value break even point. nice video anyway
That is a good point. Also if I'm not mistaken he only calculated how much gold is needed for just the rolls. For example, If I wanted to make an epic 2* that would also cost an additional 12 gold. This is also assuming that I only need the epic and no other unit.
@@vexx3277 well yeah, but the buying unit cost stay the same between levels; so he would spend 12 gold in either level. and there are a few things missing that would depend on the scenario like if i need a specific epic to get 2* how many epics will i need to roll on average to see this one specific 3 times and if the break even would be enough to make sense going in a roll spree, how much does it worth the extra space in the comp and the exponencial value thining into how much does the game goes vs the amount saved as intrest if not lvling up and such... but as i said its a rough account and im probably missing some other things that would influence as well
TLDR is the best way to explain it because, even though you role 5 times for 1 legendary @ level 9 or something like that, you might not get the one that your want.
Including the odds of a certain champ is impossible tho, because the champs are limited, so the percentage changes if more of the kind of champ u role for are already in play.
You have the correct ideas, but your explanations are a bit off. I may have a better explanation. Your focus is on expected values not probabilities. They mean different things although they are related. First of all, the distribution of card rarity seems to be binomial, so it has an expected value of p*n where p is the probability of a slot having that card's rarity and n is the number of slots available. Now your calculation at the end of the video, the portion that states "at x value to us" that is actually the number of cards you expect to see from that configuration after 100 rolls (100 since you scaled the numbers by 100). For example you calculated that the probability of rolling exactly 1 epic is .4096 or 40.96%, this means that if you rolled 100 times you should expect about 40.96 of those times to contain exactly one epic card, so in total 40.96 epic cards would come from this type of configuration. Now for the "at 2 value to us" you calculated that the probability of rolling exactly 2 epics is .2048 or 20.48%, this means that if you rolled 100 times you should expect about 20.48 of those time to contain exactly 2 epic cards, so in total 40.98 epic cards would come from this type of configuration. I hope this helps you explain why your system works.
I didn't finish the whole video, but does he take into account that leveling gives you an extra unit slot as well? The part i've watched up to is just to hit certain units, but I think taking into account the extra unit slot will also determine it's worth or not
This math is literally what you learn at 15 in a country with a real education system. Not even hating on my American friends but the fact that you guys find this impressive, or in some way complicated, is mind-blowing to me... The average person can learn this easily.
First off, to multiply the % chance by payout value to get to your 100% worth-to-us statistic you must believe that 2 gold = opportunity to buy one epic champion. I don't know if this leap can be made. Perhaps that opportunity is worth more or less depending on game state, your finances, and current team comp. And this doesn't even touch the % chance on legendaries mixing into it all. But let's assume 2 gold always exactly equals opportunity to buy one epic champion.... Your math works ONLY if you assume that any epic will definitely benefit your team AND that if you got multiple epics you could use them all on your field simultaneously (or saving them is equally beneficial) AND that having a second or third epic equally boosts your team as much as the first epic AND that you have the space/money to buy every epic you roll. The long and short of it, you can't simply say rolling two epics equals twice the benefit. Therefore you cannot reach that assumed 100% value. Then on the other side, rolling 3 of the same epic probably has more value than 3x because you can upgrade the three units into one stronger one and make space for other active units. All of this said, I simply feel deciding to level solely based on roll %s is more complicated than what you lay out here. I may sound overly picky and I know you are generalizing some, but I feel the cost/benefit varies so greatly that your breakdown leaves too much to assumption. Perhaps the value of leveling is still at similar money break points to what you say but the math you present assumes too much. Still I really appreciate the video. Thinking about leveling through this lens is essential if someone hopes to econ/level correctly. And I'm sure you're way better at TFT than I'll ever be so maybe I'm totally off base. Anyways, keep it up! ✌️
@@bray-7597 but we can work this 2% into his premise and make a value estimate. If you get an average 1 epic per roll at lvl 8 and 1/9 of these epics is the one you want then you get 18 gold is the cost to buy one specific epic on average (1 x 1/9 x z = 1 so z = 9 so 9 rolls at 2 gold per roll is 18 gold). At level 7 you have a comparative chance that is .75 worse. So you would need to roll .25 times more and pay .25 times more to roll one specific epic. So that's 24 gold (.75 x 1/9 x z = 1 so z = 12 so 12 rolls at 2 gold per roll is 24 gold). So you should expect to spend 18 gold to roll one specific epic at lvl 8 and 24 gold at lvl 7. That's a tiny difference of 6 gold. So leveling is DEFINITELY not worth it at his break point. If you're ONLY leveling for ONE specific epic monster and nothing else then you should only level when the cost is = or < 6 gold.
highschool dropout, yea i get why you got bored and said "fuck this shitty place" to be useful in life. I love watching your mind work like this, it's amazing.
I love it when you do stuff like this Byron; us Pepega math lads out here really do benefit from it. I don't agree with all of your conclusions but you put a lot into perspective for me with this video. Would love to see more content like this!
Wait the total chance to hit a legendary at 8 isn't 25% right? cuz u can't just multiply the 5% by 5 so far I know. I think u gotta add half each time. So 5+2.5+1.25+0.625+0.3125= 9.6875% to hit a legendary at 8 in total on ur roll.
I like how twitch chat was complaining that Reckful used the value instead of the chance that happened. it would be wrong to count 2,3,4, or 5 epics as 1 epic.
This fails to value the added benefit of having another slot for another unit (leveling). This creates a potentially high value to leveling that was completely ignored in the math.
Yeah, this only takes into account situations where you are looking for a specific unit and where having an extra slot wouldnt make a huge difference. But having that extra slot is impossible to evaluate mathematically.
I usually like this kind of analysis, but the crux is that the game decides that its an epic/legendary based purely off of the stated chances, rather than randomly selecting champions from a pool. That makes all the math you do completely redundant, since obviously if there's a 20% chance per slot to roll an epic, and theres 5 slots, your EV is 1 epic per roll.
TLDR: If you are looking to get a specific epic, stay at lv 7 and roll. If you are looking for a specific legendary, it's always best to rush to 8 and THEN roll. The caveat being, the closer you get to 8, the better rushing to 8 becomes, even IF you are looking for a specific epic.
You're supposed to add the chance to get legendary to your calculations at levels 7 and 8. It's not "Chance to hit epic vs etc" but rather "Chance to hit epic or better vs etc"
@@WistiPurpleday In what situation realistically would you ever upgrade something looking for an epic and not a legendary? Like I know he said exactly an epic but I don't see why anyone would ever make an upgrade decision looking at only the immediate upgrade and not potentially the dream scenario?
@@MisterMan4Twon In a comp that dont use legends. Or you might have been lucky and got it already. I agree most of the time you would look for it too. But that calculation is not as clean and more dependent on the specific game.
I think reckful was trying to speed run this one a bit too much. His calculation is trying to determine how many lvl 8 rerolls is worth 20 lvl 7 rerolls. Taking epics for example, his calculation should actually look like 0.75*20=1*x, where the x represents the number of lvl 8 rerolls required to match 20 lvl 7 rerolls. It turns out to be 15 rerolls. For legendries it should be 0.1*20=0.25*x which works out to be 8 rerolls. But this is way too oversimplified as other people can be holding certain epics/legendries which has a big impact on the probability of getting those units. BUT even after considering all this, the math itself is ALSO oversimplified and is not how you calculate number of rerolls required OMEGALUL
No, he was correct. You aren't factoring in that the 20 lvl 7 rerolls is the entry cost to begin lvl 8 rerolls, in which case you paid 40 gold for the higher rates. He was calculating the effect of lvl 8 rerolls with 40 gold sink in mind and comparing its value to straight up lvl 7 rerolls.
This math is wrong you can't just add up odds lmao 10% to hit legendary out of 5 doesn't mean you have 50% to hit it It is not like with 20% you have 100% is it? The correct odds will be 41% at 10% and at 5% it is 23%!
Yes but he didn't calculate the probability of hitting a legendary, he calculated the expected number of legendaries to hit per roll at lvl 9. So what he did was 5*10% = 50% = 1/2 which means you should expect "half" a legendary for each roll at lvl 9. A "half" legendary is ofc not possible but you should expect to get 1 legendary if you roll twice at lvl 9
I've never played League nor have any clue how TFT works, but I still watched this entire video.. something about reckful on a notepad makes me excited
What is TFT?
@@emilfilipov169 Ten Frotting Twinks
Same here, however I have no idea what's going on. Just a few seconds in he mentioned the 5th power, but I have no idea where the fuck that came from.
If you play a few games of tft yourself, this vid will start making more sense
luls it’s for the probability. In stats u use power for probability. Definitely still wouldn’t make sense to me either though if I hadn’t played tft
thank you Byron. Now I can be second place in every game as well.
PepeLaugh
LUL
topkek
OMEGALUL
"he can do this but not add 4 to 11 ?" OMEGALUL
somehow, even after the 1 millionth time, it still gets funnier. nice one dude. you are a true comedian.
Poor reckful. But wait that Shit does get funnier pog
it funny cuz Reckful gets a reaction to it
timestamp?
if you are gonna meme atleast do it right... its "11+4"
I feel weird, nostalgic a little sad and happy at the same time, watching this video... but the information is super good even for the current set if you tweak the number
Thank you so much for everything byron
RIP
The 66 gold scenario(for legendaries) just holds for one specific case(40 exp away). The gold threshold differs significantally for other "exp away" scenarios. The general function to figure the gold threshold out is:
f(x) = 5x/3,
where x is the amount of exp you´re away from level 8 and f(x) is the gold treshold from where its worth to level up first and then roll. So yeah if you are 46 exp away instead of 40, the gold threshold is 76 gold instead of 66. But ye, as you see, the function is linear and therefore its pretty easy to figure out the actual threshold based on the amount of exp you are away and can be calculated within seconds ingame.
General conclusion for the level 7 legendary scenario:
1) If you are above 76 gold its always worth to level first and then roll, you dont even have to do calculations
2) The more exp you have, the lower the threshold gets
3) The gold threshold lowers by 16 gold for every 10 exp you gain
4) If you want to figure out the exact gold threshold for your scenario ingame just use the simple formula above
Hope that helped, if anyone wants a detailed explanation on how to figure the acutal function out(its quiet simple) just hit me up.
The graph looks like this if someones interested: puu.sh/DOTLG/b046e9cac2.png
simple formula
I see...will this be on the test tomorrow?
I love when Reckful takes out the notepad, RIP Bryon
Thanks for uploading this to your youtube channel!
This kind of math really interests me and the way Byron explains it is just perfect.
bro you can just pay attention in 6th grade and get this information in school fr
@@BlackMamba-vl4ks Have I said that I have trouble doing this kind of math? I just said that the way Byron explains it makes it very interesting to watch.
Nice, he didn't give us homework today. I wonder if he'll test us next class
What is the triple value of hitting epics at lvl 7 given it is night time ? [5]
5Head quite the easy calculations
Simple really 5Head
I mean its probabilities 101
@@recurf7492 unironic 5Head
Now I can flex on my lol friends with this 5Head information
@Reckful there is a much simpler way to calculate that the expected value for rolling an epic at level 8 is 1 than your brute force calculation, though I'm not trying to diminish your effort
every slot has 0.2 expected value and there are five slots so the total expected value is 1
I'm not sure if you were aware of this or not so I just wanted do bring it up because math without brute force calculation is fun :)
This is literally what he did tho
The best videos on RUclips are of Reckful calculating stuff in his notepad.
Hey Byron thx for the nice and easy explanation. Actually that was exactly what I was looking for and your Streams helped me alot learning about AutoChess first and now TfT.
Much Love
I mean, this calculation may be right if you're only thinking process is about when to roll. But you definitely need to consider the costs of opportunity of the 8th slot, and the subsequent losses. Like a gold/hp value would definitely make sense there, and this could easily be acquired by having a big dataset of game data.
The specific gold value is irrelevant because we are comparing spending equal sums of gold on either rerolls or levelup. So we lose the exact same amount of interest in both scenarios. This is NOT a three-choice question where we are choosing between rerolling, leveling, or econing/saving (that would be an interesting question that would yield a different calculation, but for the specific question Rekless was answering, his calculation is comprehensive).
The specific hp value is irrelevant because health only matters when it reaches zero, it has zero impact on the strength of your comp beforehand. Go ahead and watch good tft players like Dog and you will see he won't do anything different from high hp compared to low hp right up until the point where he is within a single loss of dying.
Thank you for your hard work you will be missed
I don't play tft, but actually enjoyed watching that and thinking along.
Hold up there with your quick maths. For value of rolling, you need to take into account these additional factors:
1) Specific Epic/Legendaries.
2) Extra Board Slot
3) Free Rolls
4) Reduction of Previous Tiers
5) Combined Tier Probability
6) Number of Expected Upgrades
Going through the list.
1) Specific Epic/Legendaries. Not all Epics/Legendaries are acceptable. You need to factor in the expected number of rolls to find those acceptable champions. (there's 5 legendaries, you have a 1/5 chance of seeing the legendary you need compared with a general legendary. This vastly improves the value of leveling up when evaluating rolling vs leveling)
2) Extra Board Slow. Generally the extra board slot adds a lot of value: It frees up a "hand-slot", it activates class/origin bonuses, it adds a character/meat shield.
3) Free Rolls. How many free rolls do you expect to see during any given round. This is minor, but can add up to 5+ free rolls over at the time of decision.
4) Reduction in Previous Tiers. Say you have a T1 or 2 unit that you are 1-2 copies away from upgrading. If you level up, you are reducing those odds quite substantially. Once you have your Tier 1 units at Level 3 you also want to reduce the chance of seeing those units. Which leads to the following point.
5) Combined Tier Probability. Your board has more than just one Tier of unit on the field. You should factor in your average expected across the tiers for when considering the value of leveling up.
6) Number of Expected Upgrades. Sometimes, Often, for everything other than legendary, you'll need your units to be at least level 2 to survive. This requires finding 3 of a specific unit. This multiplies the expected number of rolls by (The number of champions of that tier) by (The number of that unit remaining.)
E.G.
For Epic at level 7: (5) slots * (15/100) probability of epic * (1/9) specific epic * (13/13) number of that epic remaining = 5*15/100/9*1 = 0.0833
number of rolls: (0.0833*5) * (x + 20) = x; .4165x + 8.33 = x; 20 = x At 80 gold, to find a specific Epic, it is better to level up.
*disclaimer, numbers may have changed since or before this post, the following is simply a demonstration of the calculation. numbers do not take into account any other factor such as: number of other legendaries owned by other players, desiring level 3+, free rolls, etc..
He covered the purpose of his math, this does not have to do with what he missed
Just because something is more gold efficient with respect to getting some tier of champion at some level rather than another, doesn't mean it is better with respect to actually winning, as being higher level would allow you to put down more champions which in turn makes being higher level more appealing than what your calculations would otherwise imply (or rather be misinterpreted as being directly related to your winning odds)
Conclusion: If you are going for specific epics, stay on lvl 7.
If you want a specific legendary go for lvl 8.
what about level 6? rush 7 for epic?
@@humanoid52 6->7 is about the same as 7->8 for epic. IT would be profitable slightly earlier, maybe like 45-50 rolls it would be better. But still not worth if all you're thinking about is rushing epics usually. However you probably also want the extra unit etc so it might be worth over all.
Hell I must've missunderstood a lot of the information being dropped. From what I've gathered it is always best to roll over leveling to get a champ unless you are sitting at a 80-120g for a full level
@@VollFlippi If you are going for legendaries specifically, going from 7->8 could be worth it since it only takes 20 rolls until your chances get better overall. Basically, if you have >= 66 gold, then leveling from 7->8 is worth it for legendaries. Less than that, and it's not worth it to level. You also need to weigh the added benefit of putting in another unit.
Hate to break it, but that's not how you calculate probability. That's the "expected value" which is kinda of different. It gives you the general idea, but it's not the exact numbers.
Hate to break it to you, but everyone fucking knows that. Low IQ Emanuele over there.
Emanuele Corbellini no shit bruh. Hes caculating the chances where he uses %
I had come to the same conclusion from experience playing the game, but hadn't don't the actual calculation. Interesting to see
Amazing video, learned a lot.
More of these please!
Thank you Reckful, i love it when you geek out on a notepad
Reckful would be a really cool teacher, love to listen to him!
Before the video started I tried to calculate it too.(from lvl7 to lvl8 ,tier5s) And I used this formula: 0,98^(20+x) = 0,95^x which later came to be ---> 0,98^20 = (0,95/0,98)^x , And if we calculate the x, then x=13 . Which is the same answer he got, but I have no idea why ? cause my calculation doesnt really include all combinations , just 1 or more.
Yeah but, the thing about this is @ level 7 you can get 7 units which is the optimal team comp for synergies. Also the difference from 6 units to 7 units is bigger than 7 to 8. So the number of roles lost via levelling is probably worth because you get an extra unit. Building tier 3 units is far more inconsistent than tier 2 units because you need 9 as oppose to 3 of one unit. It become harder to get more of the same unit as you buy them. Therefore you should only role for tier 3 early when the chances are higher, or not @ all and build a large team.
This shit is now at 13 k viewers .This gonna blow up and hit like 300 k real quick MARK MY WORDS
Man I love watching you teach. I Could watch you break down so many different things.You should do some Options videos :)
For the level 8 epic example he is using after 14:43:
He wants to know the expected amount of epics you get on a roll. Each slot has a 20% chance to be an epic, hence the expected amount of epics you get in a slot is 0.2. Each roll gives you 5 slots, so the expected amount of epics per roll is 0.2 x 5 = 1.
Think of it as groceries. If you expect each apple to cost 1 dollar and you are buying 5 apples then you expect those 5 apples to cost 5 dollars.
Most of my confusion came from Reckful using % where he realy shouldn't (at 5:11 he wrote and said percent in stead of saying average amount).
he forgot to put the sin over cos to equal tan. but logarithms aside, the 43 degree acute angle is slightly off.
lmao
All this calculation is based on the assumption that the champion drop rates is calculated per slot not on all 5 slots. Can someone clarify me on this?
P.S. The explanation for why al lvl 8 the expected value is 100% for epics was AMAZING, it makes so much sense. Nice one.
I have 1 Question. When all people in the Game are Level 7 for example, they should have a chance of 2% for a legendary. But many 1,- 2- ,3- and 4- Tier are already out of the pool because they got picked.So the chance for a 5-Tier increases a lto doesnt it? If you imagine the Case all are lvl 9 and all 1-4 Tier unit got picked. The chance for a Tier 5 should be 100%
actually you could have skipped the whole math part, when looking at a binomial distribution (which the distribution of champions in the draw is) the expected value is always N*p ( N beeing the ammount of draws, p beeing the chance to draw it)
Agreed, he couldve used binom dist. it wouldve taken 2 seconds
ah shit, here we go again...
Very interesting video, this is why I like Reckful
The numbers Reckful uses for his formula are not percentages but expected values per roll. I think this might have brought up some confusion.
A question. When would rolling be good if your going for a Voli-carry comp to get T3 Voli?
i get this is a rough account but reckfull is missing the natural roll on every turn when thinking about how many rounds will need to the value break even point. nice video anyway
That is a good point. Also if I'm not mistaken he only calculated how much gold is needed for just the rolls. For example, If I wanted to make an epic 2* that would also cost an additional 12 gold. This is also assuming that I only need the epic and no other unit.
@@vexx3277 well yeah, but the buying unit cost stay the same between levels; so he would spend 12 gold in either level.
and there are a few things missing that would depend on the scenario like if i need a specific epic to get 2* how many epics will i need to roll on average to see this one specific 3 times and if the break even would be enough to make sense going in a roll spree, how much does it worth the extra space in the comp and the exponencial value thining into how much does the game goes vs the amount saved as intrest if not lvling up and such... but as i said its a rough account and im probably missing some other things that would influence as well
TLDR is the best way to explain it because, even though you role 5 times for 1 legendary @ level 9 or something like that, you might not get the one that your want.
Including the odds of a certain champ is impossible tho, because the champs are limited, so the percentage changes if more of the kind of champ u role for are already in play.
he got so traumatized by the 14+1 fuck up that he became a math genius to compensate
chance for epic at 7: 20%/slot
expected epics/slot: 0.2
5 slots -> 1 epic per rol ( if there are more than 5 epics left in the pool)
Rest easy
Great video! I would love to see you do more math stuff.
my favorite comment in the middle of this was someone saying "just fuck me already" lol
You have the correct ideas, but your explanations are a bit off. I may have a better explanation. Your focus is on expected values not probabilities. They mean different things although they are related. First of all, the distribution of card rarity seems to be binomial, so it has an expected value of p*n where p is the probability of a slot having that card's rarity and n is the number of slots available. Now your calculation at the end of the video, the portion that states "at x value to us" that is actually the number of cards you expect to see from that configuration after 100 rolls (100 since you scaled the numbers by 100). For example you calculated that the probability of rolling exactly 1 epic is .4096 or 40.96%, this means that if you rolled 100 times you should expect about 40.96 of those times to contain exactly one epic card, so in total 40.96 epic cards would come from this type of configuration. Now for the "at 2 value to us" you calculated that the probability of rolling exactly 2 epics is .2048 or 20.48%, this means that if you rolled 100 times you should expect about 20.48 of those time to contain exactly 2 epic cards, so in total 40.98 epic cards would come from this type of configuration. I hope this helps you explain why your system works.
This is the actual correct explanation. Reckful's conclusions are correct but the explanation is slightly off.
The chat is freaking hilarious hahaha
My favorite type of ASMR, reckful on notepad :D
I didn't finish the whole video, but does he take into account that leveling gives you an extra unit slot as well?
The part i've watched up to is just to hit certain units, but I think taking into account the extra unit slot will also determine it's worth or not
Thanks much I always wondered this but knew I sucked too much at math to do it.
This math is literally what you learn at 15 in a country with a real education system. Not even hating on my American friends but the fact that you guys find this impressive, or in some way complicated, is mind-blowing to me... The average person can learn this easily.
First off, to multiply the % chance by payout value to get to your 100% worth-to-us statistic you must believe that 2 gold = opportunity to buy one epic champion. I don't know if this leap can be made. Perhaps that opportunity is worth more or less depending on game state, your finances, and current team comp. And this doesn't even touch the % chance on legendaries mixing into it all. But let's assume 2 gold always exactly equals opportunity to buy one epic champion....
Your math works ONLY if you assume that any epic will definitely benefit your team AND that if you got multiple epics you could use them all on your field simultaneously (or saving them is equally beneficial) AND that having a second or third epic equally boosts your team as much as the first epic AND that you have the space/money to buy every epic you roll.
The long and short of it, you can't simply say rolling two epics equals twice the benefit. Therefore you cannot reach that assumed 100% value.
Then on the other side, rolling 3 of the same epic probably has more value than 3x because you can upgrade the three units into one stronger one and make space for other active units.
All of this said, I simply feel deciding to level solely based on roll %s is more complicated than what you lay out here. I may sound overly picky and I know you are generalizing some, but I feel the cost/benefit varies so greatly that your breakdown leaves too much to assumption. Perhaps the value of leveling is still at similar money break points to what you say but the math you present assumes too much.
Still I really appreciate the video. Thinking about leveling through this lens is essential if someone hopes to econ/level correctly. And I'm sure you're way better at TFT than I'll ever be so maybe I'm totally off base. Anyways, keep it up! ✌️
he's talking about looking for specific champs only
@@bray-7597 but we can work this 2% into his premise and make a value estimate. If you get an average 1 epic per roll at lvl 8 and 1/9 of these epics is the one you want then you get 18 gold is the cost to buy one specific epic on average (1 x 1/9 x z = 1 so z = 9 so 9 rolls at 2 gold per roll is 18 gold). At level 7 you have a comparative chance that is .75 worse. So you would need to roll .25 times more and pay .25 times more to roll one specific epic. So that's 24 gold (.75 x 1/9 x z = 1 so z = 12 so 12 rolls at 2 gold per roll is 24 gold). So you should expect to spend 18 gold to roll one specific epic at lvl 8 and 24 gold at lvl 7. That's a tiny difference of 6 gold. So leveling is DEFINITELY not worth it at his break point. If you're ONLY leveling for ONE specific epic monster and nothing else then you should only level when the cost is = or < 6 gold.
highschool dropout, yea i get why you got bored and said "fuck this shitty place" to be useful in life. I love watching your mind work like this, it's amazing.
does hitting a certain rarity (say slot 1 of the roll) affect the remaining in the roll or are they all independent?
all independent as far as I know
Where tf did he get .25x from? Wouldn’t it be x/.75? because your dividing by .75 on both sides?
Math video Pog
thinking about turnaments already wow :o
that's some 5Head shit.
Really nice, please more!
I love it when you do stuff like this Byron; us Pepega math lads out here really do benefit from it. I don't agree with all of your conclusions but you put a lot into perspective for me with this video. Would love to see more content like this!
Wait the total chance to hit a legendary at 8 isn't 25% right? cuz u can't just multiply the 5% by 5 so far I know. I think u gotta add half each time. So 5+2.5+1.25+0.625+0.3125= 9.6875% to hit a legendary at 8 in total on ur roll.
You should watch the video
I like how twitch chat was complaining that Reckful used the value instead of the chance that happened. it would be wrong to count 2,3,4, or 5 epics as 1 epic.
You are brilliant
hi reckful! fan here since reckful 1- respect for that!
thank you reckful :) ill buy meow shirt now
Thank you proffessor.
Rest in Peace Byron 😢
Should’ve just used cumulative binomial distribution. So obvious. (Joking btw, A level maths is hard)
Why does rolling 2 epics have double value than rolling only 1? Are epics so strong that it's worth to take any one you roll?
It's assumed you're looking for a specific epic. In that case rolling two epics gives you two chances for that unit.
Any updates for new meta?
Byron seems happy
Pog He just sandbagged 11+4
Who would have thought 5 (5/1) chances to get 20%(1/5) would conclude to a net average of 1(5/5) per roll, goes to show what overthinking can do
With your explanation having a 20% chance to role a legendary means a 100% chance to get a legendary. You should just do (1-0.2)^5.
this was hilarious live, he kept makin mistakes and startin over and over again OMEGALUL
Thats one way of learning.
This fails to value the added benefit of having another slot for another unit (leveling). This creates a potentially high value to leveling that was completely ignored in the math.
Okay and how are you gonna put a value of synergy lol
Yeah, this only takes into account situations where you are looking for a specific unit and where having an extra slot wouldnt make a huge difference. But having that extra slot is impossible to evaluate mathematically.
So 20% = 20%?
Or, in other words, this: en.wikipedia.org/wiki/Expected_value#Finite_case
It's 3 am, what am I doing here learning math?
So essentially if you are losing kinda hard you want to roll for 4* at 6 whereas if you are doing fine you can easily go to 7 first?
I usually like this kind of analysis, but the crux is that the game decides that its an epic/legendary based purely off of the stated chances, rather than randomly selecting champions from a pool. That makes all the math you do completely redundant, since obviously if there's a 20% chance per slot to roll an epic, and theres 5 slots, your EV is 1 epic per roll.
PepoThink ah yes
Came to better understand the game, left a hell of a lot more confused. My dumbass couldn't handle all the math Im sorry.
TLDR: If you are looking to get a specific epic, stay at lv 7 and roll. If you are looking for a specific legendary, it's always best to rush to 8 and THEN roll. The caveat being, the closer you get to 8, the better rushing to 8 becomes, even IF you are looking for a specific epic.
Tachibana holy sh*t thanks men!
monkaHmm I see ....
You're supposed to add the chance to get legendary to your calculations at levels 7 and 8.
It's not "Chance to hit epic vs etc" but rather "Chance to hit epic or better vs etc"
No he is not because he is looking for a specific epic not a legendary in that example
@@WistiPurpleday In what situation realistically would you ever upgrade something looking for an epic and not a legendary?
Like I know he said exactly an epic but I don't see why anyone would ever make an upgrade decision looking at only the immediate upgrade and not potentially the dream scenario?
@@MisterMan4Twon In a comp that dont use legends. Or you might have been lucky and got it already. I agree most of the time you would look for it too. But that calculation is not as clean and more dependent on the specific game.
quick mafs.
500th time he attempted the intro PepeLaugh
Pepega chatt
What's an inverse?
Reckful the helpful
20% is 20%? Mind == blown
Basic math
I think reckful was trying to speed run this one a bit too much. His calculation is trying to determine how many lvl 8 rerolls is worth 20 lvl 7 rerolls. Taking epics for example, his calculation should actually look like 0.75*20=1*x, where the x represents the number of lvl 8 rerolls required to match 20 lvl 7 rerolls. It turns out to be 15 rerolls. For legendries it should be 0.1*20=0.25*x which works out to be 8 rerolls. But this is way too oversimplified as other people can be holding certain epics/legendries which has a big impact on the probability of getting those units. BUT even after considering all this, the math itself is ALSO oversimplified and is not how you calculate number of rerolls required OMEGALUL
No, he was correct. You aren't factoring in that the 20 lvl 7 rerolls is the entry cost to begin lvl 8 rerolls, in which case you paid 40 gold for the higher rates. He was calculating the effect of lvl 8 rerolls with 40 gold sink in mind and comparing its value to straight up lvl 7 rerolls.
Muh jewih mafs
PRO Editor PogChamp
I think it's 1 or maybe 2?
Yes.
This math is wrong you can't just add up odds lmao 10% to hit legendary out of 5 doesn't mean you have 50% to hit it
It is not like with 20% you have 100% is it?
The correct odds will be 41% at 10% and at 5% it is 23%!
Yes but he didn't calculate the probability of hitting a legendary, he calculated the expected number of legendaries to hit per roll at lvl 9. So what he did was 5*10% = 50% = 1/2 which means you should expect "half" a legendary for each roll at lvl 9. A "half" legendary is ofc not possible but you should expect to get 1 legendary if you roll twice at lvl 9
Learned alot by watching. Love u Byron
PS: please unban feelgoodnation & thanks for the quick edit Hiryl
alot?
@@TheNuub63 you dont know what a lot means? 4Head
@@kekerosberg1654 are you ok ?
@@TheNuub63 is your hobby asking stupid questions?
Feels like a Numberphile episode. xd
His math is Fked up a 4:00
nope its right