Obviously it's the kings+queens hearts flush house, because the tribulet and bloodstone jokers give x2 and x1.5 per card trigger, goes crazy with retrigger jokers too
Should be noted that "BEST" in poker is not always about what hand wins the most often, but which hand can be leveraged to win the most when it does win. For instance, KKKK may actually be better than AAAA because it makes it more likely that someone has AA or AAA and calls massive raises or makes raises themselves.
When I clicked on the video I assumed it would be going in that direction. While the math/odds part is interesting, it's definitely not realistic in regards to trying to "win" or "extract the most value while winning" which is extremely important in Poker, especially tournaments. AAAKK has a lot of blockers that prevent your opponent from getting decent enough "lesser" hands to give them the confidence to stick around all the way to showdown. In fact if they get a good enough hand they may do most of the raising for you. In those cases a lesser full house may be beneficial.
sometiems it poker you want to buy the antes specially in texas hold m you have pocket aces you w don't want to go to a flop as your two aces ae good hand but, you may hit nothing that helps them then they are just high pair. And, truth its isn' h thecards you ahve but hoyou play ththat wins pots. If yoplay the right bluff you can win more than having the best hand.
Yeah Data from Star Trek learned that the hard way!! As a matter of fact, the only time the cards do decide who wins the pot is if two or more players "go the distance" on betting...the cards are thus only ever used to break a tie!!
The tricky part is that in 5 card draw, your opponent doesn’t just draw 5 cards randomly and that's it. They might replace some of their cards based on some rules of thumb, which will make the probability a bit nightmarish.
Not to mention they'd have to know you had a monster hand and go for unlikely draws. If they were just playing the odds in a heads-up game, they'd often want to hold onto lesser but already made hands.
@@TheGuyCalledX I've never once played triple draw, but still occasionally play 5-card draw games so that's not entirely true. Maybe in certain circles or in many regions, but I know quite a few casual plays that enjoy variants of standard 5-card with a single draw.
The concept that's really being covered here are what we refer to as "blockers" or "removal" cards in a hand. These help to narrow an opponent's range of hands he'd be willing to play based on what's on the board and possible hand combinations.
I’ll have to say that there’s another way to get a full house that your opponent can’t beat with another full house, I’m jut referring to the full house not the other hands If you do KKKAA, it’ll also be impossible to get a stronger full house
This unfortunately only applies to games without community cards. In Holdem/Omaha for example you could still loose to AAAKK, unless you have 2 aces in your hand and the community cards are 3 kings
Yeah! But kings over aces allows 27 straight flushes (and a royal flush if you leave a gap suit); which means it's equally as good as aces over kings for this situation! But still loses out to aces over nines/eights/sevens/sixes at 24 straight flushes (and also to aces over tens or aces over fives which allow 25, or 26 if you have a gap suit. (Well technically aces over tens with a gap is 25 straight flushes and a royal.)
11:30 this is wrong. In Texas Hold‘em automatically the best 5 Card hand for the player out of the 7 cards (5 community cards + your 2 hand cards) counts. For example if there is a royal flush on the table, every player has the same hand. In this case it‘s a split pot because the 2 Hand cards of the players dosent matter
Which is also why calculating a “best full house” in Texas Hold Em is way less “mathy” than the 5 card draw example in the video. It’s all dependent and what the community cards are and where the 3 aces are. (And the answer is basically always Aces full of Kings) 1) If there’s 3 Aces on the table you want KKs 100% of the time. Any straight flush “blockers” are marginal compared to losing to higher full houses. 2)If you’ve got pocket Aces on a paired board with an ace (let’s say AXX rainbow is the flop) then it still barely matters what the board pair is. In actuality you’d still want the board pair to be kings because it means there’s only 7 board runouts that beat you by the river: with 4 of a kind kings, runner-runner 4 of a kind and three royal flush runouts and a K high straight flush runout (with villain having 10,9 suited in hand, QJ runout). (Also we want the flop to stay rainbow because despite it introducing an extra suit for royal flushes, having any suited AKs on the flop means a QJs runout allows any 10x of that suit to win a 4 card RF). 3) if there are 2 aces on the board it actually gets tricky again (I think it’s still AK but I’m less sure). You obviously want Ax where your paired hole card is just highest pair on the board for at least chopping the last identical combo of Ax. But for similar reasons to pocket Aces, AKo is ideal. You want your hand to be offsuit where your ace matches the board K’s suit blocking a RF and your king matching either A to block another RF. The board runout can then only lose to a runner-runner 4 of a kind, 1 straight flush combo suited to the second board ace and one straight flush suited to the board king.
@@picklenik9658it doesn’t necessarily matter where the aces are. If the board is 33222 then anyone with a 3 in their hand has the best full house possible, although they could still lose to someone with a 2 in their hand.
Just a note, some of the community card poker games require you to play one or more of your hole cards. Omaha for instance you have 4 hole cards and have to play 2 of them. In that case, if there is a royal flush on the table, NO ONE has it. The best hand possible in that case would be to have the 9 and 8 of matching suit for a queen high straight flush.
@@wingracer1614 a 9 plus any card of the same suit would be the stone cold nuts because you’d block anyone else from having the straight flush and no one could have a boat/quads.
@@picklenik9658 Some nice thoughts but one could argue that it is also allowed to have only one card of the full house in your pocket (0 obviously doesn't matter). This makes things much more complicated but AK is certainly not the worst Full house combination
Interesting! For what it's worth, this can be logically proven quite fast without including distributions: 1. AAA** or KKKAA is forced to prevent a beatable Full House. 2. Quads is not affected as we block two values fixed. 3. This leaves RF and SF which are conceptually the same, meaning that the pair should block as many straight flushes as possible. 4. It should be a pair that blocks as many SF that don't include A as they are already part of the hand, eliminating KKKAA in the process. 5. This leaves any trips A with any pair from 6 through 9.
@@regulus2033I’d say the video bloviated in its discussion of this same solution. I went through this exact same thought process, but the way it was explained in the video sort of obfuscated this main point.
However, in Texas Hold 'Em, it's important that two of the Aces are your hole cards. Otherwise, your opponent having the remaining Ace means that the hand comes down to the pair. If you have A-9 while your opponent has A-K, and the board reads A-A-K-9-X, you lose.
The best full house in Texas Hold 'Em is for the table to be AAK and two number cards from the middle of the pack, so something like AAK87 while you hold AK. This means that no other players can have a hand that beats yours. Other players can tie your hand if they have one of the kings and the final ace, this will mean you'll split the pot. Against a single opponent this means you have something like a 99.8% chance of winning, and a 0.2% chance of a split.
Super high quality video that is pretty informative as well! Obviously, the best full house is a flush house made entirely out of glass cards with red seals.
For Texas Holdem it becomes a lot more complicated, as plain odds and probabilities are not enough. In 5 card draw, if your opponent hits a weaker FH, a flush or even a straight, your chances of getting paid are huge. But if the community cards in Texas Holdem reveal 3 cards of the same rank or 2 pairs, the chances of getting called by a flush or straight decrease dramatically. Also, if you get Aces and don't underrepresent them a little pre-flop, when the board comes A99, the opponent is highly likely to fold. And lastly, a weaker full house means your opponent can have a lot of AA and Axs (that can make flushes) to call you with. That being said, I'd prefer something like 9s full of 6s, with pocket 9s in my hand and the board looking something like T9664, with a potential flush (but not straight flush) there. Yes, I lose to pocket 6s and pocket Ts, but the amount of weaker hands that might pay me is just too juicy.
In this example i beleive both you and your opponent are going all in preflop and in the your able to pick your two card hand and 3 flop cards while the turn, river and opponents hand will be random cards.
11:14 - 6 is better because it leaver better cards that lose to you on the deck making your opponent likely to be more confidend due to probably better cards in possible losing hands.
You know, I do actually agree with you haha. It's like having a category in between high card and pair that's called "high ace". Royal flushes are just subsets of straight flushes. But according to official ruling, a royal flush counts as its own category so I'm just following that :)
@@YATAQi i feel there may be some variants of poker using wilds where a royal flush made without wilds beats 5 of a kind but 5 of a kind still beats any other straight flush, but i'm not entirely certain.
@@wfchannel4673 One more thing: Is the probability of 5 of a kind lower or higher than Royal Flush. I guess it depends on how many wild cards are included… If it’s only one wild card then 5 of a kind should be the most rare.
My intuition told me AAA99, happy it was partly correct. I was thinking more from a texas hold 'em perspective with shared community cards and reducing chances of getting coolered by a straight flush. So when I realized it wasn't involving community cards I started second guessing my intuition. Regarding the question you posed at the end, looking forward to that video to see if it still holds true, but I just think it might :)
Was FLOORED to see the number of subs this channel had compared to the quality of the video. Instant like+sub plus you know I had to drop a comment for algorithm's sake.
The problem is ambiguous. Do you get to choose all seven cards, and force your best hand to be a full house, or do you get to pick five cards which make your full house (some combination of community and at least one pocket), then the other two are just constrained to not give you a better hand? The latter makes the problem much harder to answer (as how do you randomly sample the opponents two cards when there's constraints on your best hand). EIDT: Gut feel on the answer is pocket A10, community A,A,10,6,5. Opponent can't connect a straight flush or quads. So you win every time. As long as your pocket is not a pair, you can block your opponent getting quads. Opponent can draw with you on any A10 hand. OTOH if a single loss is worth a few draws, then you should pocket AA, community A,10,10,6,5 and you will never tie, and lose only once to pocket 10s.
7:51 I've been knocked out playing hold em in a live event as the bubble guy after calling an all in on the flop while I had AA in hand and flopped AKK, other guy had KK😑
Years ago, playing online Hold 'em, I saw the most insane hand imaginable. Four of us playing, I had 10-Q clubs. The flop was J, K, A clubs. So I'm sitting with a royal flush, knew I had won, and was trying to figure out how to bet to get the most out of the other players, but to my surprise they all stayed in, and all bet heavy. Turn was an Ace. River a Jack. All of us stayed in. First player reveals a J-K, giving them a full house, jacks over kings. They'd hit two pairs on the flop, the full house on the river. Second player shows King-King, giving them full house, kings over jacks. They'd hit three of a kind on the turn, full house on the river. Third player turns over a pair of aces, giving them four of a kind, so three of a kind on the flop, four of a kind on the turn, and then I was last with the royal flush. Every single one of us with what would normally be a winning hand, and by utter fluke the order was each hand beat the one before it. It was like a scene out of a freaking movie, and one of the players types in chat that they could not believe that could possible happen. First time I ever hit a royal flush and never saw anything like it again.
In terms of probability to win, that choice is definitely the best, but if I could choose a hand to have, I would still prefer AAA22 because it maximises the probability that the oppoenent will have something that I beat, but isn't valueless. With the given choice of AAA66/77/88/99, it eliminates a *lot* of straight possibilities that many people would bet with.
Exactly, by blocking straight flushes, we are also blocking straights and flushes that might call, especially the broadway straight or an A-high flush... A hand like KKK22 would be much more preferred compared to AAA 66-99
The thing about Texas Hold'em, is that the best full houses are always going to include the highest cards. Not for the probability of getting beaten, but because those full houses are the ones where your two cards are strong enough to bully your opponents off weaker hands pre flop so they'll never get to see their mid range straight flush.
imo, a bit more should be said about "3 aces not going anywhere" KKKAA would also not have any stronger fullhouses (tho it covers same number of flushes as AAAKK, thus losing to AAA66 obv) and the rest of KKK__ needs an explicit computation that greatly diminished number of stronger AAA__ full houses is still too large compared to covering some flushes with K rather than A
That's a great point! KKKAA would kind of serve the same purpose as AAA__ as far as being an unbeatable full house. But AAA__ offers the flexibility of being able to adjust the pair to your liking. And yes KKK__ would also be a solid full house no matter what the pair ends up being, but like you said, there are too many AAA__ full houses that can beat it and so it does not end up being a good idea. But definitely a thought worth considering. Thank you :)
@@YATAQithis is wrong. In 5 card draw, the #1 card we want to unblock if we have boats or quads is the Ace. So many strong hands that can call have an Ace in them, so we don't want them in our own hand-- as we'd be blocking a ton of combos of 2nd best hands. Likewise with the idea of blocking straight flushes. Straight flushes are so uncommon that to build a strategy around them is completely not worth it. I'm far less concerned with blocking straight flushes that I lose to than unblocking straights, flushes, trips, two pair that I beat.
@@YATAQiBecause the question is far more interesting than "which full house loses to the least hands." If you had tried to answer the question "which full house makes the most money on average," it would be a far more interesting and useful question to answer for poker players
not really if you play pro where millions of dollars are on the line. that said... most of said pros probably already know these probabilities by heart so...
@Bjarkus3 you clearly don't watch competitive poker then. the hypest things that happen in these games are when people bet it all on the slimmest of odds and coming out on top through sheer charisma and social deduction.
An interesting follow up would be to look at what choice gives the greatest difference between your expected chance of winning vs the average chance of winning your opponent would calculate for you (averaging across their possible hands, but without them knowing your hand). E.g., by not choosing aces your chance of winning goes down, but it opens more scenarios where the opponent can get a fairly strong hand (like 3 aces) while still not being able to beat you. So maybe this would result in your opponent underestimating your chances more (on average).
A full house with three Kings and two Aces (preferably containing an ace of a different suit from your kings) cannot be beat by any full house. By having three kings rather than three aces you reduce the number of straight flushes.
@@baileydwyer453it also blocks more straights. When we have a boat, we should not be thinking about the hands we lose to, but rather second-best hands that we beat. If you get coolered you get coolered.
I think AAA99 is still the best full house in holdem? But it definitely needs to be pocket aces with 2 ace, and 2 9s on the board. No connectivity between the ace and 9s for straight flushes, don't lose to any full houses, and no 3 of a kind on the board to make quads more likely. Another interesting one is what is the best full house in 7 card stud. You get 2 more blockers, they get 2 more cards. Trying to figure out if you are in a better or worse spot. Surely worse.....right?
i’d like to argue that the full house is the 3rd best hand in the game and that a straight flush is the 1st because a royal flush is really just a straight flush
Understandable but the reason for the rarity is that you need those 5 cards in that order, and there is only 4 possible unlike the straight flush itself which has way more possible combinations.
In Texas Hold'em, you'd also have to consider what cards would likely be part of your opponent's range on each street, and how likely they'd be to check, call, raise or fold. And how each possibility would affect your chance of getting maximum value. Or any value at all.
Intuiting that it's be lower 10s or 9s (cause Ace - 5) at the beginning of video, because they're in the middle of most possible straight "flushes", and that all cards par one should be different colors to spread the love, then watching and having it nicely explained in a video, made me feel more competent that it probably should have.
For the holdem case having pocket aces with an ace and the two kings matching your aces on the board. This leaves your lose conditions with two more kings turning up with at least one in the opponents hand or Q,J,10,9 of the suit of either king being the remaing 4 cards. The finaly 11 lose cases would be the remaing cards being quads. This is the best case scenario as without same suited kings or not having kings there are additional straight flushes you can lose to.
AAA with a pair of 66, 77, 88, of 99 so that you can block more straight flushes that might allow your opponent to cooler you as its impossible for the opponent to have AAA since we already block three Aces
for texas hold em: If we have the entire pair in the shared cards and only one of the triple the opponent can make a four of a kind, but there is only one hand that can do so (the one with the other two cards of the same rank as the pair). if the triple is an ace though the opponent cannot tie the player so all other hands are losing assuming we pick our cards such that there is no possible straight flush; this is the best-case-scenario for this case. for example the shared cards can be A, K, K, 6, 2 and our hand can be A, A. Otherwise, at least two of the triple will be shared, so the opponent can also get a full house, and this time there are at least two tying hands. for example the shared cards can be A, A, K, 6, 2 and our hand can be A, K. Then the opponent would need another ace and either of the two remaining kings to win. We can also have something like A, A, K, K, 2 be shared and A, A be our hand so we get both a four of a kind and a full house and the four of a kind is unbeatable but that isn't really a full house.
In Texas Holdem, we can eliminate the chance of Royal/Straight Flushes by removing the possibility of flushes completely in the community cards. So our full house can be only be beaten by 4 of a kind if there is a pair in the community cards. If we hold AA and community has AKK**, then we will be beaten by KK (1 in 990). If we hold AK and the community is AAK**, then we will split pot if the opponent also draws an AK (2 in 990). The expected gain in both of them is same.
The answer to your new question 'What full house would you choose in hold em?' is that it depends on which cards are on the board. 3 aces on the board is a different scenario than A99 on board.
Not to mention chances of actually getting called depending on the community cards. A weaker but better disguised FH unblocks more weaker hands your opponent might be enticed to call with (high overpairs, suited aces that make a flush, maybe some straights). You might still have the best hand if the board shows AAA or AA99, but you'll never get money from any flush or straight in this scenario.
For Texas holdem you can start with a pair of aces and then build the five community card such that there is no possible flushes and includes a pair and an ace. In this situation the only hand that will have you beat is the Four of a kind made from the same pair than the one used for your full house.
The huge advantage of knowing all of these computations is that while you are doing them, everyone else at the table as fallen asleep and you can go through the deck and pull out the best hand after first looking at everyone else's hand to know exactly what you have to beat, then wake them all up and continue the game......but they will never play with you again!
I Texas Hold'em, I believe, having AK in hand with AAK all different suits on board, eliminates all combinations higher than yours Edit: forgot about the situation where 2 other cards on the table are the same rank, so the opponent has 11 possible hand-table combinations to win, don't really want to count the exact probability
It depends on the rules of the particular poker game you are playing... and it is a trivial question because no matter how strong your full house, you could be betting into a straight flush.
I feel like it's worth noting that if the pair in your full house is Aces, it still prevents the opponent from having three Aces in their hand, so a full house such as KKKAA would still be unbeatable by another full house
I have a feeling the best full house would be Ace and King in hand with the board having 2 Ace 1 King a 2 and a 8, minimum suit lineups (specifically no Ace or King lineup), and your Ace being the Ace of Spades for the very unlikely mirror.
The main idea here is to take out as many flushes (Royal Flushes included) as possible by spacing your two kinds far enough so they squat more flushes, that means, they have to be spaced out by at least five cards, so the cards on your hand don't share a single flush.
Great video, glad i stumpeld on this channal, 1 note tho. At 11:30 you say "keep in mind that texas holdm allows you to share up to 3 cards to be shared between players best hands" this is actually incorrect. It actually requires you to minimally share 3 cards with your oppenent. Since there are 5 community cards and 2 personal whole cards and you can use any combination of those cards to make the strongest 5 card hand
@@jeffreyweevers3919 The key word here is “best”. Because you’re right, both players do share the same 5 community cards which they have to use 3 cards from, both those 3 cards don’t necessarily have to be the same ones. Consider this example: Player 1’s hand is A,2 and player 2’s hand is 8,9 while the community cards are 3,4,5,6,7. Player 1’s BEST hand is the straight A,2,3,4,5 while player 2nd BEST hand is the straight 5,6,7,8,9. So their respective best hands only share 1 card in common here. I guess a more accurate statement would have been “1-3 cards” instead of “up to 3” because 1 is the minimum. Good observation :)
@YATAQi sorry, english is not my mother tongue so i probably didnt explain it very well. The point i was trying to make was that you could share 4 or even 5 cards of your best five card hand with your opponment via the community cards as you are not required to use any of the whole cards in your hand. If the board where to run out to a royal flush, it would be an auto split pot since both 2 cant makr 5 hand better with their whole cards
@@jeffreyweevers3919 Oh I see what you mean - you're totally right! Both players' best hands can technically share 5 cards in common (if the community cards make up the best hand). Not sure how I missed that, thank you haha!
@@YATAQiyes that’s correct. For anyone still confused, with rules of holdem, Players A Hand of A2 on a board of 34567- the best hand here is 34567. The players own cards don’t play, only the board. This is important since this means another player with 67 will have the same hand as player 1 with A2. This changes the probability slightly.
You said this is "Draw," but in draw games, typically you can get discard some cards and get new cards. That messes up your calculations - unless you're only referring to final hand configurations, but I think it does so in a way you haven't really accounted for. I think it'd be better to refer to this as "Stud," where you cannot discard cards to replace them.
Balatro Players be like: "Flush House with Polychrome Red Seal Glass Kings and Queens with Triboulet and Sock and Buskin with Blueprint and Brainstorm, and with 3 Red Seal Steel Kings with a Baron and a Mime."
Going with the title of this video as it is written, 3 aces and 2 kings is the best Full House period. There are 5 cards in your hand and 47 other cards and every hand that beats that hand is still up in the air. However, the video title doesn't say "Which hand beats a 3 ace Full House" does it
Depends on your definition of what the best hand is. Is it the hand that beats one direct opponent’s hand or is it that hand that takes other winning options off the table.
10c, 10h, 10s, 6d, 6x. This prevents the opponent from getting a straight flush in the most possible ways. Tho im not entirely sure if this is the most optimal, because it allows the opponent to have more full houses against you, which might be more likely than straight flushes... Optimizing full houses though, you would simply shift the numbers all the way up to three aces & two 9s-6s, each preventing the same amount of straight flushes
I interpreted the question differently, I was trying to figure out what cards most people would pass on. For instance, in 5 card draw, if all you have is a jack high, you might keep the jack and try for a pair of them. Or if you're one card off from a royal flush, you're not going to give those four up. So I figured it would be three 9's and something else.
Nice video. I think that you should've done the calculation on the full house of kings to show that it's worse than aces, and blocking more straight flushes doesn't make up for allowing full houses of aces to beat you.
Lowk two’s full of three’s might be the best full house in holdem bc you unblock all the combos of Aces’s and high cards that they will likely call your larger bets with. If you have Ace’s full of Kings, you’re almost never getting paid off because you hold all the cards that are likely to be the winner at showdown
These probabilities are wildly inaccurate for 5-card draw, as the opponent can replace cards strategically in the draw round. These probabilities would be for Cold Hands Poker, which is 5 cards with no draw or betting rounds (beyond the ante).
I feel like there should’ve been an analysis of tens over fives done as well, just to ensure the benefit of removing the most possible straight flushes isn’t greater than the loss of allowing some stronger full houses.
Texas Holdem seems more trivial, as the board can basically make it impossible for you to be beaten by anything. For example (AA) AKK82 only loses to one hand (KK), while (AK) AAK82 never loses, but draws to two combinations of (AK).
In Texas Hold’em it would be pocket aces with any pair, because you have pocket aces they lose access to 2 of them meaning they can only get a pair of aces
5 distinct cards means that a hand with 3 aces beats any other full house. Nobody else can have 3 aces, so you can choose 3 aces and whatever other 2 cards you want.(*) The only 2 hands that are by default higher than a full house are 4 of a kind and straight. And no matter what triple and double you choose, you always "block" a 4-of-a-kind in 2 of the 13 ranks. And the best way to block straight flushes (and straights) is to hold a card 5 or more from either end. I.e. 5 to 10 (inclusive). This leaves 2 candidates for the best full house: "10s full of 5s" or "Aces full of 9s". The latter doesn't use 10's because a straight flush with the lower end on a 10 would already be blocked by the aces. I think the chance of someone having another full house is more relevant than the chance of someone having a straight flush, so "Aces full of 9s" would be my guess for the best full house. (*) The same blocking also means that "aces full of kings" is just as good as "kings full of aces". ...except that having an extra king blocks the "king-through-9 straight flush" of that suit, which having the ace in that suit doesn't block. So paradoxically the slightly lower valued full house is technically beaten by exactly one less hand.
What's the point of distinction between Royal Flush and Straight flush? Royal flush is a straight flush by definition, and especially for purposes of this video it makes no sense to distinct it in the probabilities table.
Is allowing a better Full House so much more damaging probability-wise that three Aces is still better than, say, Tens full of Fives, which would cover a lot more Straight Flushes, and only allow a few better Full Houses?
I think a lot of people went into watching this video with the wrong mindset. Or maybe I did. It seems the question posed is strictly you have the magical power to create any full house you want in 5-card draw, so what's the best full house to pick to reduce the chances you'd lose to a better hand. It has nothing to do with betting or trying to get your opponent to play because he thinks he has a strong hand. You can even say both of you are all-in. Then the video shifts to asking you what's the best full house in Texas Hold 'Em and isn't implying the AAA(6-9) is the best if there's 2 Aces on the board. So you have to play with the same scenario. You can create any full house you want, which also means your 2 hold cards are your choice. So which full house will you create? Again, you're both all-in at the start, so betting doesn't matter.
At 11:30 he erroneously says that Texas hold'em allows for up to three cards to be shared by players' best hands. I got the sense that he has never played Texas hold'em because it seems like anyone who has ever played already knows that his statement is wrong.
This is an excellent analysis, but it's missing a crucial part of poker -- betting and calling. If I have three aces in my full house, and make a big bet, the likelihood of my opponent calling with, say, one pair, is small. If I have KKKAA instead, then there's a slightly higher chance my opponent calls my big bet with a pair, since he now has a pair of aces in his range. The same argument applies to hands with two pairs, with aces up more likely to call than any other two pairs. With ace high flushes and straights, you're now much more likely to get raised by those hands, and slightly less likely to get raised by smaller straights and smaller flushes. All things equal, I'll take my chances with KKKAA, because the added probability of getting bets called, plus the added probability of getting raised by an inferior hand, outweigh the added probability of more stronger hands beating mine. I'll win slightly less often, but I'll win bigger pots more often. I hope that makes sense.
For Texas holdem, here's my ideal hand for the strongest full house: Hole: A❤️, A♦️ Community: A♣️, 7❤️, 7♦️, 2♠️ , K❤️ In this case, the opponent can only beat us with pocket 7s. They can't make a straight or get a flush.
as far as i can tell from experience the full house you want is KKKAA. with three aces your opponent is unlikely to have a hand good enough to actually try matching you, unless it's actually better so they'll just nope out when they feel your confidence and all you'll do is steal the blinds. with three kings and two aces your full house still can't be beat by another full house, but your opponent might end up with two aces in their hand and this can lead them to think they got a good hand when yours is better.
My guess is the strongest full house is aces over 9s. However, any pair from 6-9 would be the same, as they'd limits the maximum amount of straight flushes.
Two comments: 1. It is more complicated and utterly unnecessary to treat 'royal' flushes and (non-royal) straight flushes as separate cases. 2. In Texas hold 'em different players' best hands can share up to the five cards (that is the whole hand), not just three cards as erroneously stated at the end of the video.
Are 3 aces necessarily the best choice? If you have two aces, wouldn't that also prevent your opponent from having 3 aces. I wonder how the 2 aces+3 kings/queens/jacks compare.
youtube got a great timing. just yesterday i was thinkin about whats the chance for a royal on a table of 10 players.i realies how complicatd it is and gave up
If your pair contains the spoiler for the fourth royal flush, though, you'd eliminate that along with its associated straight flushes. So wouldn't taking 10s including the suit that is missing from your triplet be better?
I'd like to see the math on 10s full of 5s. There are some higher full houses but you block 5/8 of all possible straight flushes since a straight requires a 10 or a 5.
My guess going in before watching is kings over jacks, because it limits the possibility of a royal flush or a king or queen high straight/straight flush
Not withstanding the probabilitys, having KKKAA fullhouse is more likely to draw an opponent in than AAAKK, since it allows for them to have a pair of aces, while still being the the highest possible FH, since you having two aces precludes them from being able to get the AAA?? Full house
Wouldn't all AAA-66/77/88/99 all have the same value, they all counter the same amount of straight flushes and they counter every full houses as well? So they would all be the best at winning the hand against other possible hands.
Too lazy to do the math but unlike in draw poker, you CAN have an unbeatable full house in hold 'em. You need to have: 1. The Top card paired on the board 2. Have hole cards that are the top card and second top card on the board 3. Have no straights possible One example would be: AJ on a board of A-A-J-7-4 Can't lose to quads because there's only once Ace left Can't lose to a straight flush because you can't make any on the board. There are actually many hands in hold em where a full house is the nuts, would be interested to see a video about how many there are.
Technically a royal flush does not really exist. It is just a straight flush. Otherwise there would be a royal straight as well. This makes a full house the third best hand.osinh only to 4 of a kind and a straight flush.
not a bad video. but not really relevant to any real poker theory. the goal in poker isnt to win the pot, but to maximise the ev you make. while AAA66 might be the strongest full house for p of winning the hand, it blocks the main ways you get paid. i believe that 77722 is the best full house, and specifically when the 2s have the same suits as the 7s. this unblocks the best trips, 2 pairs, flushes, and straights for your opponents to have. you dont really care if ur opponent has a better hand than you, because youll beat a full house as often as you lose with one (called a cooler). but with this specific full house, you maximise the amount you can actually win. in NLH its the same thing, you take the strongest full house that unblocks the most calls. on T4342, you want 33, as you unblock Tx and 4x that will pay you the max. however if ur in a 4bet pot 200bb deep on AAK72, you would want AK because if you have 77 or 22, its actually very likely ur opponent has AA/KK or AK themselves, and wont pay you off without those hands.
Uh duh its a flush house with a hand full of steel cards.
make sure you have a baron and that the steel cards are red seal kings as well
@the-persona mime for bonus mults
i knew i would find a balatro remark in the comments lmao
with mime brainstorm and blueprint too
no, 5 polychrome red seal kings and queens, and all other cards are steel kings with red seal, and a legendary joker of kings and queens and baron
Obviously it's the kings+queens hearts flush house, because the tribulet and bloodstone jokers give x2 and x1.5 per card trigger, goes crazy with retrigger jokers too
add photochad and sock and buskin
Should be noted that "BEST" in poker is not always about what hand wins the most often, but which hand can be leveraged to win the most when it does win. For instance, KKKK may actually be better than AAAA because it makes it more likely that someone has AA or AAA and calls massive raises or makes raises themselves.
Similarly, a lot of money can be had when you hit a small straight flush against someone else's ace-high flush.
When I clicked on the video I assumed it would be going in that direction. While the math/odds part is interesting, it's definitely not realistic in regards to trying to "win" or "extract the most value while winning" which is extremely important in Poker, especially tournaments. AAAKK has a lot of blockers that prevent your opponent from getting decent enough "lesser" hands to give them the confidence to stick around all the way to showdown. In fact if they get a good enough hand they may do most of the raising for you. In those cases a lesser full house may be beneficial.
Yeah i thought the video would be about maximizing strong flushes
sometiems it poker you want to buy the antes specially in texas hold m you have pocket aces you w don't want to go to a flop as your two aces ae good hand but, you may hit nothing that helps them then they are just high pair. And, truth its isn' h thecards you ahve but hoyou play ththat wins pots. If yoplay the right bluff you can win more than having the best hand.
Yeah Data from Star Trek learned that the hard way!! As a matter of fact, the only time the cards do decide who wins the pot is if two or more players "go the distance" on betting...the cards are thus only ever used to break a tie!!
The video is simpler if you don't distinguish between straight flushes and royal flushes. A royal flush is just the highest straight flush.
I agree. To me, treating "Royal Flush" as a separate hand from "Straight Flush" is like treating "Broadway" as a separate hand from "Straight".
Or quad Aces vs other quads
Nah a flush five with idol joker is gonna destroy any hands you come up with
The tricky part is that in 5 card draw, your opponent doesn’t just draw 5 cards randomly and that's it. They might replace some of their cards based on some rules of thumb, which will make the probability a bit nightmarish.
Not to mention they'd have to know you had a monster hand and go for unlikely draws. If they were just playing the odds in a heads-up game, they'd often want to hold onto lesser but already made hands.
Triple draw is really the only variant that people will still play these days
@@TheGuyCalledX I've never once played triple draw, but still occasionally play 5-card draw games so that's not entirely true. Maybe in certain circles or in many regions, but I know quite a few casual plays that enjoy variants of standard 5-card with a single draw.
@@aethere4l I really enjoy standard 5 crad draw and I think it's absolutely insane that there's no tournaments at the WSOP.
@@aethere4l well, high hand draw basically isn't played at all professionally. I'm talking about stuff like 2-7 triple draw.
The concept that's really being covered here are what we refer to as "blockers" or "removal" cards in a hand. These help to narrow an opponent's range of hands he'd be willing to play based on what's on the board and possible hand combinations.
Kind of but in this case there’s no board and in Texas holdem you never think of blockers to that strong of hands
I’ll have to say that there’s another way to get a full house that your opponent can’t beat with another full house, I’m jut referring to the full house not the other hands
If you do KKKAA, it’ll also be impossible to get a stronger full house
This unfortunately only applies to games without community cards. In Holdem/Omaha for example you could still loose to AAAKK, unless you have 2 aces in your hand and the community cards are 3 kings
For this video though, he did set the rule at 1:26 that players don't share hands, so you are right
I've been telling people this for forty years
Yeah! But kings over aces allows 27 straight flushes (and a royal flush if you leave a gap suit); which means it's equally as good as aces over kings for this situation! But still loses out to aces over nines/eights/sevens/sixes at 24 straight flushes (and also to aces over tens or aces over fives which allow 25, or 26 if you have a gap suit. (Well technically aces over tens with a gap is 25 straight flushes and a royal.)
True. This will also increase the likelihood that opponent will have an A and put more money in the pot.
11:30 this is wrong. In Texas Hold‘em automatically the best 5 Card hand for the player out of the 7 cards (5 community cards + your 2 hand cards) counts. For example if there is a royal flush on the table, every player has the same hand. In this case it‘s a split pot because the 2 Hand cards of the players dosent matter
Which is also why calculating a “best full house” in Texas Hold Em is way less “mathy” than the 5 card draw example in the video. It’s all dependent and what the community cards are and where the 3 aces are. (And the answer is basically always Aces full of Kings)
1) If there’s 3 Aces on the table you want KKs 100% of the time. Any straight flush “blockers” are marginal compared to losing to higher full houses.
2)If you’ve got pocket Aces on a paired board with an ace (let’s say AXX rainbow is the flop) then it still barely matters what the board pair is. In actuality you’d still want the board pair to be kings because it means there’s only 7 board runouts that beat you by the river: with 4 of a kind kings, runner-runner 4 of a kind and three royal flush runouts and a K high straight flush runout (with villain having 10,9 suited in hand, QJ runout). (Also we want the flop to stay rainbow because despite it introducing an extra suit for royal flushes, having any suited AKs on the flop means a QJs runout allows any 10x of that suit to win a 4 card RF).
3) if there are 2 aces on the board it actually gets tricky again (I think it’s still AK but I’m less sure). You obviously want Ax where your paired hole card is just highest pair on the board for at least chopping the last identical combo of Ax.
But for similar reasons to pocket Aces, AKo is ideal. You want your hand to be offsuit where your ace matches the board K’s suit blocking a RF and your king matching either A to block another RF. The board runout can then only lose to a runner-runner 4 of a kind, 1 straight flush combo suited to the second board ace and one straight flush suited to the board king.
@@picklenik9658it doesn’t necessarily matter where the aces are.
If the board is 33222 then anyone with a 3 in their hand has the best full house possible, although they could still lose to someone with a 2 in their hand.
Just a note, some of the community card poker games require you to play one or more of your hole cards. Omaha for instance you have 4 hole cards and have to play 2 of them. In that case, if there is a royal flush on the table, NO ONE has it. The best hand possible in that case would be to have the 9 and 8 of matching suit for a queen high straight flush.
@@wingracer1614 a 9 plus any card of the same suit would be the stone cold nuts because you’d block anyone else from having the straight flush and no one could have a boat/quads.
@@picklenik9658 Some nice thoughts but one could argue that it is also allowed to have only one card of the full house in your pocket (0 obviously doesn't matter). This makes things much more complicated but AK is certainly not the worst Full house combination
Interesting! For what it's worth, this can be logically proven quite fast without including distributions:
1. AAA** or KKKAA is forced to prevent a beatable Full House.
2. Quads is not affected as we block two values fixed.
3. This leaves RF and SF which are conceptually the same, meaning that the pair should block as many straight flushes as possible.
4. It should be a pair that blocks as many SF that don't include A as they are already part of the hand, eliminating KKKAA in the process.
5. This leaves any trips A with any pair from 6 through 9.
Great explanation!
That's basically is what was in the video, no new information...
@@regulus2033I’d say the video bloviated in its discussion of this same solution. I went through this exact same thought process, but the way it was explained in the video sort of obfuscated this main point.
However, in Texas Hold 'Em, it's important that two of the Aces are your hole cards. Otherwise, your opponent having the remaining Ace means that the hand comes down to the pair. If you have A-9 while your opponent has A-K, and the board reads A-A-K-9-X, you lose.
@@regulus2033 never said the info is new, just providing the purely logical solution rather than mathematical!
Dude, this is an insanely well put together video. You’re going places. Super talented and visually pleasing. Great video!
The best full house in Texas Hold 'Em is for the table to be AAK and two number cards from the middle of the pack, so something like AAK87 while you hold AK. This means that no other players can have a hand that beats yours. Other players can tie your hand if they have one of the kings and the final ace, this will mean you'll split the pot. Against a single opponent this means you have something like a 99.8% chance of winning, and a 0.2% chance of a split.
But so does your opponent
I saw this and I immediately thought it was a balatro video until I realized it was just a normal poker video 😂
Super high quality video that is pretty informative as well!
Obviously, the best full house is a flush house made entirely out of glass cards with red seals.
For Texas Holdem it becomes a lot more complicated, as plain odds and probabilities are not enough. In 5 card draw, if your opponent hits a weaker FH, a flush or even a straight, your chances of getting paid are huge. But if the community cards in Texas Holdem reveal 3 cards of the same rank or 2 pairs, the chances of getting called by a flush or straight decrease dramatically. Also, if you get Aces and don't underrepresent them a little pre-flop, when the board comes A99, the opponent is highly likely to fold. And lastly, a weaker full house means your opponent can have a lot of AA and Axs (that can make flushes) to call you with.
That being said, I'd prefer something like 9s full of 6s, with pocket 9s in my hand and the board looking something like T9664, with a potential flush (but not straight flush) there. Yes, I lose to pocket 6s and pocket Ts, but the amount of weaker hands that might pay me is just too juicy.
In this example i beleive both you and your opponent are going all in preflop and in the your able to pick your two card hand and 3 flop cards while the turn, river and opponents hand will be random cards.
11:14 - 6 is better because it leaver better cards that lose to you on the deck making your opponent likely to be more confidend due to probably better cards in possible losing hands.
I was thinking the same. Good video.
Third best hand. A royal flush is a specific straight flush and is not its own category of hand.
You know, I do actually agree with you haha. It's like having a category in between high card and pair that's called "high ace". Royal flushes are just subsets of straight flushes. But according to official ruling, a royal flush counts as its own category so I'm just following that :)
@@YATAQi i feel there may be some variants of poker using wilds where a royal flush made without wilds beats 5 of a kind but 5 of a kind still beats any other straight flush, but i'm not entirely certain.
@@wfchannel4673
That’s an intriguing thought 😲🤯
@@wfchannel4673
One more thing: Is the probability of 5 of a kind lower or higher than Royal Flush. I guess it depends on how many wild cards are included…
If it’s only one wild card then 5 of a kind should be the most rare.
@@YATAQi
What was mentioned above would be an amazing topic for a video 🤯
this channel is a hidden gem, instant sub!
My intuition told me AAA99, happy it was partly correct. I was thinking more from a texas hold 'em perspective with shared community cards and reducing chances of getting coolered by a straight flush. So when I realized it wasn't involving community cards I started second guessing my intuition. Regarding the question you posed at the end, looking forward to that video to see if it still holds true, but I just think it might :)
❤Its always nice seeing videos animated with manim
you would have more likes if there were more math nerds here instead of texas holdem heebs.
Was FLOORED to see the number of subs this channel had compared to the quality of the video.
Instant like+sub plus you know I had to drop a comment for algorithm's sake.
The problem is ambiguous. Do you get to choose all seven cards, and force your best hand to be a full house, or do you get to pick five cards which make your full house (some combination of community and at least one pocket), then the other two are just constrained to not give you a better hand?
The latter makes the problem much harder to answer (as how do you randomly sample the opponents two cards when there's constraints on your best hand).
EIDT: Gut feel on the answer is pocket A10, community A,A,10,6,5. Opponent can't connect a straight flush or quads. So you win every time. As long as your pocket is not a pair, you can block your opponent getting quads. Opponent can draw with you on any A10 hand.
OTOH if a single loss is worth a few draws, then you should pocket AA, community A,10,10,6,5 and you will never tie, and lose only once to pocket 10s.
Balatro has taught me, a flush five of a kind is the best hand
Just want to say these are some **fantastic** animations for showing/explaining the math
Superb work! Keep it going!!!!!
7:51 I've been knocked out playing hold em in a live event as the bubble guy after calling an all in on the flop while I had AA in hand and flopped AKK, other guy had KK😑
That happened to me too, except with queens instead of kings.
Tbh no one should see flop in this instance unless u was somehow lik 2 hundo deep. It should preflop allin.
Years ago, playing online Hold 'em, I saw the most insane hand imaginable. Four of us playing, I had 10-Q clubs. The flop was J, K, A clubs. So I'm sitting with a royal flush, knew I had won, and was trying to figure out how to bet to get the most out of the other players, but to my surprise they all stayed in, and all bet heavy. Turn was an Ace. River a Jack. All of us stayed in. First player reveals a J-K, giving them a full house, jacks over kings. They'd hit two pairs on the flop, the full house on the river. Second player shows King-King, giving them full house, kings over jacks. They'd hit three of a kind on the turn, full house on the river. Third player turns over a pair of aces, giving them four of a kind, so three of a kind on the flop, four of a kind on the turn, and then I was last with the royal flush. Every single one of us with what would normally be a winning hand, and by utter fluke the order was each hand beat the one before it. It was like a scene out of a freaking movie, and one of the players types in chat that they could not believe that could possible happen. First time I ever hit a royal flush and never saw anything like it again.
In terms of probability to win, that choice is definitely the best, but if I could choose a hand to have, I would still prefer AAA22 because it maximises the probability that the oppoenent will have something that I beat, but isn't valueless. With the given choice of AAA66/77/88/99, it eliminates a *lot* of straight possibilities that many people would bet with.
Exactly, by blocking straight flushes, we are also blocking straights and flushes that might call, especially the broadway straight or an A-high flush...
A hand like KKK22 would be much more preferred compared to AAA 66-99
The thing about Texas Hold'em, is that the best full houses are always going to include the highest cards.
Not for the probability of getting beaten, but because those full houses are the ones where your two cards are strong enough to bully your opponents off weaker hands pre flop so they'll never get to see their mid range straight flush.
Amazing quality video, leaving a comment for engagement, keep up the great work!
High quality content as always! Keep it up!
imo, a bit more should be said about "3 aces not going anywhere"
KKKAA would also not have any stronger fullhouses
(tho it covers same number of flushes as AAAKK, thus losing to AAA66 obv)
and the rest of KKK__ needs an explicit computation that greatly diminished number of stronger AAA__ full houses is still too large compared to covering some flushes with K rather than A
That's a great point! KKKAA would kind of serve the same purpose as AAA__ as far as being an unbeatable full house. But AAA__ offers the flexibility of being able to adjust the pair to your liking. And yes KKK__ would also be a solid full house no matter what the pair ends up being, but like you said, there are too many AAA__ full houses that can beat it and so it does not end up being a good idea. But definitely a thought worth considering. Thank you :)
@@YATAQithis is wrong. In 5 card draw, the #1 card we want to unblock if we have boats or quads is the Ace. So many strong hands that can call have an Ace in them, so we don't want them in our own hand-- as we'd be blocking a ton of combos of 2nd best hands.
Likewise with the idea of blocking straight flushes. Straight flushes are so uncommon that to build a strategy around them is completely not worth it. I'm far less concerned with blocking straight flushes that I lose to than unblocking straights, flushes, trips, two pair that I beat.
This is the most well researched and well produced poker video that I hsve ever seen that is also UTTERLY and funnily pointless 😂😂😅
I’m not sure how to feel about this comment.. but it made me laugh. So thank you I guess haha
@@YATAQiBecause the question is far more interesting than "which full house loses to the least hands." If you had tried to answer the question "which full house makes the most money on average," it would be a far more interesting and useful question to answer for poker players
not really if you play pro where millions of dollars are on the line. that said... most of said pros probably already know these probabilities by heart so...
@remixtheidiot5771 no pro worry about 0.1% probabilities.
@Bjarkus3 you clearly don't watch competitive poker then. the hypest things that happen in these games are when people bet it all on the slimmest of odds and coming out on top through sheer charisma and social deduction.
An interesting follow up would be to look at what choice gives the greatest difference between your expected chance of winning vs the average chance of winning your opponent would calculate for you (averaging across their possible hands, but without them knowing your hand).
E.g., by not choosing aces your chance of winning goes down, but it opens more scenarios where the opponent can get a fairly strong hand (like 3 aces) while still not being able to beat you. So maybe this would result in your opponent underestimating your chances more (on average).
A full house with three Kings and two Aces (preferably containing an ace of a different suit from your kings) cannot be beat by any full house. By having three kings rather than three aces you reduce the number of straight flushes.
Yes but the 6-9 blocks more straight flushes than your king does
@@baileydwyer453it also blocks more straights. When we have a boat, we should not be thinking about the hands we lose to, but rather second-best hands that we beat. If you get coolered you get coolered.
Is this your answer for 5 card draw or Texas hold em?
@@TheGuyCalledX Very well put.
@@picklenik9658it would have to be for 5 card draw because this 3K2A in texas hold would not be the best FH if the flop is exactly 2A and 1K.
I think AAA99 is still the best full house in holdem? But it definitely needs to be pocket aces with 2 ace, and 2 9s on the board. No connectivity between the ace and 9s for straight flushes, don't lose to any full houses, and no 3 of a kind on the board to make quads more likely.
Another interesting one is what is the best full house in 7 card stud. You get 2 more blockers, they get 2 more cards. Trying to figure out if you are in a better or worse spot. Surely worse.....right?
i’d like to argue that the full house is the 3rd best hand in the game and that a straight flush is the 1st because a royal flush is really just a straight flush
🤮
Understandable but the reason for the rarity is that you need those 5 cards in that order, and there is only 4 possible unlike the straight flush itself which has way more possible combinations.
In Texas Hold'em, you'd also have to consider what cards would likely be part of your opponent's range on each street, and how likely they'd be to check, call, raise or fold. And how each possibility would affect your chance of getting maximum value. Or any value at all.
And in a lot of games it might help to pay attention to how much they are drinking.
Intuiting that it's be lower 10s or 9s (cause Ace - 5) at the beginning of video, because they're in the middle of most possible straight "flushes", and that all cards par one should be different colors to spread the love, then watching and having it nicely explained in a video, made me feel more competent that it probably should have.
For the holdem case having pocket aces with an ace and the two kings matching your aces on the board. This leaves your lose conditions with two more kings turning up with at least one in the opponents hand or Q,J,10,9 of the suit of either king being the remaing 4 cards. The finaly 11 lose cases would be the remaing cards being quads.
This is the best case scenario as without same suited kings or not having kings there are additional straight flushes you can lose to.
AAA with a pair of 66, 77, 88, of 99 so that you can block more straight flushes that might allow your opponent to cooler you as its impossible for the opponent to have AAA since we already block three Aces
for texas hold em:
If we have the entire pair in the shared cards and only one of the triple the opponent can make a four of a kind, but there is only one hand that can do so (the one with the other two cards of the same rank as the pair). if the triple is an ace though the opponent cannot tie the player so all other hands are losing assuming we pick our cards such that there is no possible straight flush; this is the best-case-scenario for this case. for example the shared cards can be A, K, K, 6, 2 and our hand can be A, A.
Otherwise, at least two of the triple will be shared, so the opponent can also get a full house, and this time there are at least two tying hands. for example the shared cards can be A, A, K, 6, 2 and our hand can be A, K. Then the opponent would need another ace and either of the two remaining kings to win.
We can also have something like A, A, K, K, 2 be shared and A, A be our hand so we get both a four of a kind and a full house and the four of a kind is unbeatable but that isn't really a full house.
very well produced video
I really like your graphics presentation.
In Texas Holdem, we can eliminate the chance of Royal/Straight Flushes by removing the possibility of flushes completely in the community cards. So our full house can be only be beaten by 4 of a kind if there is a pair in the community cards. If we hold AA and community has AKK**, then we will be beaten by KK (1 in 990). If we hold AK and the community is AAK**, then we will split pot if the opponent also draws an AK (2 in 990). The expected gain in both of them is same.
The unknown community cards matter too. The odds are worse due to e.g. **=QQ (giving opponent another quad opportunity or even a straight flush draw)
So it depends on what the definition of "best" is, under the circumstances and game structure?
The answer to your new question 'What full house would you choose in hold em?' is that it depends on which cards are on the board. 3 aces on the board is a different scenario than A99 on board.
Not to mention chances of actually getting called depending on the community cards. A weaker but better disguised FH unblocks more weaker hands your opponent might be enticed to call with (high overpairs, suited aces that make a flush, maybe some straights). You might still have the best hand if the board shows AAA or AA99, but you'll never get money from any flush or straight in this scenario.
Blockers are hard.
Anyways The best boat in Texas Hold-em is tens full of deuces. RIP Doyle ❤
For Texas holdem you can start with a pair of aces and then build the five community card such that there is no possible flushes and includes a pair and an ace.
In this situation the only hand that will have you beat is the Four of a kind made from the same pair than the one used for your full house.
Wow you make really nice videos, keep making more 🙏🏻
The huge advantage of knowing all of these computations is that while you are doing them, everyone else at the table as fallen asleep and you can go through the deck and pull out the best hand after first looking at everyone else's hand to know exactly what you have to beat, then wake them all up and continue the game......but they will never play with you again!
I went into the video thinking you were wrong but you convinced me
I Texas Hold'em, I believe, having AK in hand with AAK all different suits on board, eliminates all combinations higher than yours
Edit: forgot about the situation where 2 other cards on the table are the same rank, so the opponent has 11 possible hand-table combinations to win, don't really want to count the exact probability
underrated! THIS IS GREAT❤
It depends on the rules of the particular poker game you are playing... and it is a trivial question because no matter how strong your full house, you could be betting into a straight flush.
I feel like it's worth noting that if the pair in your full house is Aces, it still prevents the opponent from having three Aces in their hand, so a full house such as KKKAA would still be unbeatable by another full house
I have a feeling the best full house would be Ace and King in hand with the board having 2 Ace 1 King a 2 and a 8, minimum suit lineups (specifically no Ace or King lineup), and your Ace being the Ace of Spades for the very unlikely mirror.
Great math graphics. Just subbed.
The main idea here is to take out as many flushes (Royal Flushes included) as possible by spacing your two kinds far enough so they squat more flushes, that means, they have to be spaced out by at least five cards, so the cards on your hand don't share a single flush.
Great video, glad i stumpeld on this channal, 1 note tho. At 11:30 you say "keep in mind that texas holdm allows you to share up to 3 cards to be shared between players best hands" this is actually incorrect. It actually requires you to minimally share 3 cards with your oppenent. Since there are 5 community cards and 2 personal whole cards and you can use any combination of those cards to make the strongest 5 card hand
@@jeffreyweevers3919 The key word here is “best”. Because you’re right, both players do share the same 5 community cards which they have to use 3 cards from, both those 3 cards don’t necessarily have to be the same ones.
Consider this example: Player 1’s hand is A,2 and player 2’s hand is 8,9 while the community cards are 3,4,5,6,7.
Player 1’s BEST hand is the straight A,2,3,4,5 while player 2nd BEST hand is the straight 5,6,7,8,9. So their respective best hands only share 1 card in common here. I guess a more accurate statement would have been “1-3 cards” instead of “up to 3” because 1 is the minimum. Good observation :)
@YATAQi sorry, english is not my mother tongue so i probably didnt explain it very well. The point i was trying to make was that you could share 4 or even 5 cards of your best five card hand with your opponment via the community cards as you are not required to use any of the whole cards in your hand. If the board where to run out to a royal flush, it would be an auto split pot since both 2 cant makr 5 hand better with their whole cards
@@jeffreyweevers3919 Oh I see what you mean - you're totally right! Both players' best hands can technically share 5 cards in common (if the community cards make up the best hand). Not sure how I missed that, thank you haha!
@@YATAQiyes that’s correct. For anyone still confused, with rules of holdem, Players A Hand of A2 on a board of 34567- the best hand here is 34567. The players own cards don’t play, only the board. This is important since this means another player with 67 will have the same hand as player 1 with A2.
This changes the probability slightly.
You said this is "Draw," but in draw games, typically you can get discard some cards and get new cards. That messes up your calculations - unless you're only referring to final hand configurations, but I think it does so in a way you haven't really accounted for. I think it'd be better to refer to this as "Stud," where you cannot discard cards to replace them.
A mathematician has discovered card removal and blockers, which poker players have been aware of for decades.
You mean a RUclipsr has decided to make an educational video about it. It's educational, not new.
Balatro Players be like: "Flush House with Polychrome Red Seal Glass Kings and Queens with Triboulet and Sock and Buskin with Blueprint and Brainstorm, and with 3 Red Seal Steel Kings with a Baron and a Mime."
Going with the title of this video as it is written, 3 aces and 2 kings is the best Full House period. There are 5 cards in your hand and 47 other cards and every hand that beats that hand is still up in the air. However, the video title doesn't say "Which hand beats a 3 ace Full House" does it
Depends on your definition of what the best hand is. Is it the hand that beats one direct opponent’s hand or is it that hand that takes other winning options off the table.
10c, 10h, 10s, 6d, 6x. This prevents the opponent from getting a straight flush in the most possible ways. Tho im not entirely sure if this is the most optimal, because it allows the opponent to have more full houses against you, which might be more likely than straight flushes...
Optimizing full houses though, you would simply shift the numbers all the way up to three aces & two 9s-6s, each preventing the same amount of straight flushes
I interpreted the question differently, I was trying to figure out what cards most people would pass on. For instance, in 5 card draw, if all you have is a jack high, you might keep the jack and try for a pair of them. Or if you're one card off from a royal flush, you're not going to give those four up. So I figured it would be three 9's and something else.
Nice video. I think that you should've done the calculation on the full house of kings to show that it's worse than aces, and blocking more straight flushes doesn't make up for allowing full houses of aces to beat you.
W video, u need at least like 100k subs
Excellent explanation!
Gotta love how the first comment you see in a video talking about Poker, is just Balatro
Lowk two’s full of three’s might be the best full house in holdem bc you unblock all the combos of Aces’s and high cards that they will likely call your larger bets with. If you have Ace’s full of Kings, you’re almost never getting paid off because you hold all the cards that are likely to be the winner at showdown
These probabilities are wildly inaccurate for 5-card draw, as the opponent can replace cards strategically in the draw round. These probabilities would be for Cold Hands Poker, which is 5 cards with no draw or betting rounds (beyond the ante).
I feel like there should’ve been an analysis of tens over fives done as well, just to ensure the benefit of removing the most possible straight flushes isn’t greater than the loss of allowing some stronger full houses.
Texas Holdem seems more trivial, as the board can basically make it impossible for you to be beaten by anything. For example (AA) AKK82 only loses to one hand (KK), while (AK) AAK82 never loses, but draws to two combinations of (AK).
Thought this was a balatro guide for a sec
In Texas Hold’em it would be pocket aces with any pair, because you have pocket aces they lose access to 2 of them meaning they can only get a pair of aces
5 distinct cards means that a hand with 3 aces beats any other full house. Nobody else can have 3 aces, so you can choose 3 aces and whatever other 2 cards you want.(*)
The only 2 hands that are by default higher than a full house are 4 of a kind and straight. And no matter what triple and double you choose, you always "block" a 4-of-a-kind in 2 of the 13 ranks. And the best way to block straight flushes (and straights) is to hold a card 5 or more from either end. I.e. 5 to 10 (inclusive).
This leaves 2 candidates for the best full house: "10s full of 5s" or "Aces full of 9s". The latter doesn't use 10's because a straight flush with the lower end on a 10 would already be blocked by the aces.
I think the chance of someone having another full house is more relevant than the chance of someone having a straight flush, so "Aces full of 9s" would be my guess for the best full house.
(*) The same blocking also means that "aces full of kings" is just as good as "kings full of aces". ...except that having an extra king blocks the "king-through-9 straight flush" of that suit, which having the ace in that suit doesn't block. So paradoxically the slightly lower valued full house is technically beaten by exactly one less hand.
What's the point of distinction between Royal Flush and Straight flush? Royal flush is a straight flush by definition, and especially for purposes of this video it makes no sense to distinct it in the probabilities table.
Is allowing a better Full House so much more damaging probability-wise that three Aces is still better than, say, Tens full of Fives, which would cover a lot more Straight Flushes, and only allow a few better Full Houses?
I think a lot of people went into watching this video with the wrong mindset. Or maybe I did. It seems the question posed is strictly you have the magical power to create any full house you want in 5-card draw, so what's the best full house to pick to reduce the chances you'd lose to a better hand. It has nothing to do with betting or trying to get your opponent to play because he thinks he has a strong hand. You can even say both of you are all-in.
Then the video shifts to asking you what's the best full house in Texas Hold 'Em and isn't implying the AAA(6-9) is the best if there's 2 Aces on the board. So you have to play with the same scenario. You can create any full house you want, which also means your 2 hold cards are your choice. So which full house will you create? Again, you're both all-in at the start, so betting doesn't matter.
At 11:30 he erroneously says that Texas hold'em allows for up to three cards to be shared by players' best hands.
I got the sense that he has never played Texas hold'em because it seems like anyone who has ever played already knows that his statement is wrong.
This is an excellent analysis, but it's missing a crucial part of poker -- betting and calling. If I have three aces in my full house, and make a big bet, the likelihood of my opponent calling with, say, one pair, is small. If I have KKKAA instead, then there's a slightly higher chance my opponent calls my big bet with a pair, since he now has a pair of aces in his range. The same argument applies to hands with two pairs, with aces up more likely to call than any other two pairs. With ace high flushes and straights, you're now much more likely to get raised by those hands, and slightly less likely to get raised by smaller straights and smaller flushes. All things equal, I'll take my chances with KKKAA, because the added probability of getting bets called, plus the added probability of getting raised by an inferior hand, outweigh the added probability of more stronger hands beating mine. I'll win slightly less often, but I'll win bigger pots more often.
I hope that makes sense.
For Texas holdem, here's my ideal hand for the strongest full house:
Hole: A❤️, A♦️
Community: A♣️, 7❤️, 7♦️, 2♠️ , K❤️
In this case, the opponent can only beat us with pocket 7s. They can't make a straight or get a flush.
yes do more poker related puzzles please
Great idea for a video! You could do similar analyses in backgammon
as far as i can tell from experience the full house you want is KKKAA.
with three aces your opponent is unlikely to have a hand good enough to actually try matching you, unless it's actually better so they'll just nope out when they feel your confidence and all you'll do is steal the blinds.
with three kings and two aces your full house still can't be beat by another full house, but your opponent might end up with two aces in their hand and this can lead them to think they got a good hand when yours is better.
My guess is the strongest full house is aces over 9s. However, any pair from 6-9 would be the same, as they'd limits the maximum amount of straight flushes.
Two comments:
1. It is more complicated and utterly unnecessary to treat 'royal' flushes and (non-royal) straight flushes as separate cases.
2. In Texas hold 'em different players' best hands can share up to the five cards (that is the whole hand), not just three cards as erroneously stated at the end of the video.
Royal flush and straight flush is the same hand. Just one of them is a bigger hand. Not necessarily to separate them into different ranks.
Are 3 aces necessarily the best choice? If you have two aces, wouldn't that also prevent your opponent from having 3 aces. I wonder how the 2 aces+3 kings/queens/jacks compare.
youtube got a great timing. just yesterday i was thinkin about whats the chance for a royal on a table of 10 players.i realies how complicatd it is and gave up
If your pair contains the spoiler for the fourth royal flush, though, you'd eliminate that along with its associated straight flushes. So wouldn't taking 10s including the suit that is missing from your triplet be better?
I'd like to see the math on 10s full of 5s. There are some higher full houses but you block 5/8 of all possible straight flushes since a straight requires a 10 or a 5.
My guess going in before watching is kings over jacks, because it limits the possibility of a royal flush or a king or queen high straight/straight flush
Not withstanding the probabilitys, having KKKAA fullhouse is more likely to draw an opponent in than AAAKK, since it allows for them to have a pair of aces, while still being the the highest possible FH, since you having two aces precludes them from being able to get the AAA?? Full house
Wouldn't all AAA-66/77/88/99 all have the same value, they all counter the same amount of straight flushes and they counter every full houses as well? So they would all be the best at winning the hand against other possible hands.
Yes
Too lazy to do the math but unlike in draw poker, you CAN have an unbeatable full house in hold 'em. You need to have:
1. The Top card paired on the board
2. Have hole cards that are the top card and second top card on the board
3. Have no straights possible
One example would be:
AJ on a board of A-A-J-7-4
Can't lose to quads because there's only once Ace left
Can't lose to a straight flush because you can't make any on the board.
There are actually many hands in hold em where a full house is the nuts, would be interested to see a video about how many there are.
At 5:39 shouldn’t high card be 100%?
High card is guaranteed if you don’t hit anything better. So it should be 100% minus all the other probabilities (of better hands)
@ ahhhh gotcha since you have to play the best hand
Technically a royal flush does not really exist. It is just a straight flush. Otherwise there would be a royal straight as well. This makes a full house the third best hand.osinh only to 4 of a kind and a straight flush.
not a bad video. but not really relevant to any real poker theory.
the goal in poker isnt to win the pot, but to maximise the ev you make.
while AAA66 might be the strongest full house for p of winning the hand, it blocks the main ways you get paid.
i believe that 77722 is the best full house, and specifically when the 2s have the same suits as the 7s.
this unblocks the best trips, 2 pairs, flushes, and straights for your opponents to have. you dont really care if ur opponent has a better hand than you, because youll beat a full house as often as you lose with one (called a cooler). but with this specific full house, you maximise the amount you can actually win.
in NLH its the same thing, you take the strongest full house that unblocks the most calls.
on T4342, you want 33, as you unblock Tx and 4x that will pay you the max. however if ur in a 4bet pot 200bb deep on AAK72, you would want AK because if you have 77 or 22, its actually very likely ur opponent has AA/KK or AK themselves, and wont pay you off without those hands.