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8

You should break it into disjoint (non-overlapping) cases, and find the probability that you win with each case, and then add them up: Case 1. Heart on turn Occurs 8/45 times and your probability of winning is 0 Case 2. 8 (not heart) on turn Occurs 3/45 times and your probability of winning is 6/44 (three 3's and three 5's) Case 3. 5 on turn Occurs 3/...


4

Equity is simply how much of the pot is "yours" based on your odds to win it. If there's $100 in the pot, and you have a 50% chance of winning it, then you have $50 in equity. If you have a 30% chance to win it, you have $30 in equity. For a final call on the river, that's your only concern. Let's say the pot is $100, and your opponent bets $100 all-in, and ...


4

At first, I thought, OK, lets quickly answer this, returning the favor. But it turned out to be a rather tricky one! One online calculator gives 48.18%, the other 48.28%, off by 0.1%, already very strange. My first result was 49.09%, off by exactly the runner-runner 0.909%. You also confused me with your cases and some calculations. The tricky part is - of ...


2

Pokerstove is able to calculate the equity on flop (just don't enter the turn and river cards before calculating the equity) there are plenty of other tools around that do it, I personally use Pokerstrategy Equilab and this does exactly what you are looking for as well.


2

It is correct to say there are only 3 ways to get the AA, when you do that calculation you get 0.467 The rest of the difference in equity comes from the fact that AKs doesn't have the same equity over all cases of 76o. It depends on whether or not those cards share a suit with the AK. You will get the correct value for equity if you split it into all ...


2

I'm not sure how much it affects your equity calculation, but you are missing where the villain hits Aces full.


2

Based on simulations, no other hand besides AA will have higher equity vs. 9 players. The same goes for n number of players 2-8. The hand evaluator I used computes 27% "strength" for pocket aces vs. 9 players pre-flop. The next best hand, KK comes in at 23%. This is why it is in your best interest to isolate players and raise out some other players with AA ...


2

Your result adds up 1 (98.58% + 1.41%) and Site 1 and 4 do not, which means you do not calculate the tie case separately, while they do. This is definitely a difference in methods. Without computation on this particular hand and by looking at the numbers only: With site 4: 98.58-97.47 = 1.41 - 0.3 = 1.11%. So the probability of tie should be 2.22% which you ...


1

It's probably more interesting to think about this question for games like Omaha where players can't "play the board" (i.e. exactly 2 hole cards and 3 board cards are used to make the player's hand). In that case: Flushes and quads can never chop. Full House can only ever chop 2 ways. Trips, pairs, and high card winning hands could chop a maximum of 4 ...


1

Definitely possible, but exceptionally unlikely that all players would remain in a hand long enough to realize this possibility. The stronger and more correlated the board gets, the less likely it is that players' hole cards will play in the winning 5-card hand. Boards that contain an entire straight, flush, or full house are rare and will often result in a ...


1

Sure. If the flop comes AKQJT with no flush possibility, then everyone involved will tie


1

Given the following: we know AA is the best starting hand in regular 9-handed NLHE there is no action before the flop in double board bomb pots we are considering the strength of the hand before we know what the flops are We can conclude that AA is still the best starting hand if you are playing a double board bomb pot. It may not seem this way because a ...


1

Here are the equity values for each choice of 2 cards vs 8 other players with random holdings: AA 34.57% KK 29.21% QQ 24.86% AKs 22.65% JJ 21.68% AQs 21.18% KQs 20.50% AJs 19.89% KJs 19.39% AKo 19.20% TT 19.14% ATs 18.93% QJs 18.85% KTs 18.53% QTs 18.17% JTs 17.96% AQo 17.47% 99 17.20% A9s 16.90% KQo 16.90% K9s 16.26% A8s 16.22% AJo 16.10% T9s 16.08% ...


1

Keep in mind that a computer will only give you the final result of the calculation you do in your hand. It's not like the computer gives you a perfect knowledge of the possible outs because it still doesn't know what are the face-down cards of each other player (same as you). So it will only help you not make a human calculation mistake. In my opinion, it'...


1

The way I understand your question, it seems like b and a are the same thing. in your example of (a) you mention that the total combinations come out to 42. this number is not arbitrary, it has to come from somewhere. If you were up against a random hand, then there would be a lot more than 42 total combinations. I am assuming that this 42 total ...


1

I will try to answer briefly, and I will assume by JJ+ you mean JJ, QQ, KK, AA. I will also use the 2% 4% rule when counting outs as a shortcut. (google it if you aren't familiar, very useful at the table) for JJ: Hero is ahead and villain has 2 outs, villain has 6 combinations of JJ with 8% equity for QQ: Hero is drawing dead, villain has 1 combination of ...


1

Pokerstove is a good, opensource, free software that will give you these results (it can be found here: https://github.com/andrewprock/pokerstove). I am not sure if it will separate the hands out like you described, but maybe I can help you understand how the calculation is made by hand. The equity of a range against a range is calculated by comparing the ...


1

The metric is a ratio of what I think my equity is vs what the foe think my equity is. The higher the disparity the more volatile or different the perception of the outcome is to each ones perspective. It can be used, but it is definitely not even remotely worth it. My opinion is because: The ratio does not add anything above existing metrics. Why use 2 ...


1

There are 169 possible starting hands, so the top 25% is the top 42(.25) hands. As per this page, the top 25% of all starting hands are therefore: AA,KK,QQ,AKs,JJ,AQs,KQs,AJs,KJs,TT,AKo,ATs,QJs,KTs,QTs,JTs,99,AQo,A9s,KQo,88,K9s,T9s,A8s,Q9s,J9s,AJo,A5s,77,A7s,KJo,A4s,A3s,A6s,QJo,66,K8s,T8s,A2s,98s,J8s,ATo I haven't compared this to your stated top 25% range,...


1

You were getting 3:1 with top pair to call the river. If they were on KJ they probably would not have bet pot on the flop. If they were on AQ most likely they would have also bet the turn. Don't get why you call the flop getting 2:1 and then lay down the river getting 3:1. Easy call for me. Specifically what hand(s) did you put them on?


1

Absolutely you can exclude cards from your opponents range based on how they played the flop, however because people aren't rational 100% of the time, and poker being a game of probability with an element of human emotion, it's never necessarily something you can completely exclude. As your bot learns, and builds its range against specific players it will be ...


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