8

My interpretation is that mathematically, the expectation in EV is taken across the probability distribution of poker cards that are yet to be dealt in a particular hand as well as the randomness in opponents' play, and it is assumed that every other piece of information (including situation, position, etc) you can have is already taken into account when you ...


6

The common conditions/rules of being independent from luck in the tournament: 1) You are playing tournament with deep stacks and reasonable blind level lengths. It means turbo tournaments with 5 minutes per level contain enough luck-dependent situations. Not playing "turbos" will allow to avoid rapid short stack preflop all-in situation. 2) You don't ...


6

There are five board cards in hold'em. Since you start with two known cards, there are 50 unknown. That means there are 50x49x48x47x46 ways the board can come. Since the order of the cards on the board doesn't matter, divide that by the number of ways 5 cards can be arranged (120), that's 2118760 total distinct boards. There are 47x46/2 of those boards that ...


6

This is a binomial distribution: either you miss the flop or you don't. If your probability to NOT miss is .32, then your probability to miss is 1 - .32 = .68. Your number of trials is 22. The expected number of missing is 22 * .68 = 14.96. The variance of the binomial distribution is np(1-p). In your case, 22*.68*(1-.68) = 4.7872. The standard deviation ...


6

If such a player is approximating a game-theoretic-optimal (GTO) strategy, then they are essentially putting their opponent in a situation where it doesn't matter what they do. In other words, whatever information you believe you could glean from their play will not help you alter their expectation (i.e., reduce their expectation while increasing yours). ...


5

Judging from what you wrote in the question, I think you are misunderstanding a few concepts here. First, math is math. Math doesn't care if you play poker, running, feeding your dog or doing something else. Math's laws are universal. This means that the math will have the same precision both in the heat of the battle and after the session is over and you ...


5

When facing an "at least one of" problem, you can't just add probabilities. You have to calculate the probability of missing everything, then subtract from one. Assuming 47 unknown cards, 6 of which are outs, the exact probability of missing both the turn and river is 41/47 * 41/46, or 1681/2162, so the probability of hitting either or both the turn and ...


5

I exhaustively simulated (every possibility is run) AA vs any pocket pair and AA vs any suited connector. Firstly let's cover the pocket pairs: Obviously it is best for the under-pair to have different suits, in order to win with flushes. The best pocket pair to have is pocket eights. This is because all straight possibilities will result in a win. This is ...


5

If you have an android phone you can download "Poker calculator", logo is a clover as you can see topleft. It is a great app. It supports hold 'em but also 4 and 5 card omaha high and omaha high/low. You can add multiple players and can input the cards by voice. I recommend it to anyone.


4

One of the easiest things you can look at is which hands are making money and which hands are losing money. Sort by number of blinds won/lost per hand type if you can, and then start at the bottom. These are the hands that are losing the most money and are very likely your worst leaks. You will probably be surprised at which hands you find here! Either ...


4

TL;DR Given a flush on the board, five players will split 19.7% of the time, or about once every 5 hands. Given a fresh deal, the deal will come up with a flush showing and a five-way split 0.0389% of the time, or once every 2,569 hands. Some general probabilities Overall odds that none of the five players have a given suit (say, hearts): comb(39,10) / ...


4

Sometimes during play you want a quicker method that isn't 100% but gives you very close percentages. The rule of 2 and 4. If you have 2 cards left to reveal (ie the turn & river) then you multiply your outs by 4. If you have 1 cards left to reveal (ie just the river) then you multiply your outs by 2. So in your example, 6 outs with 2 chances left = ...


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 ...


3

This is likely to be very situation dependent. There is however, a section in the PokerTracker tool that analyses the range of common actions that players have taken, (eg. Cbet flop, fold to flop Cbet, 3bet stats, aggression stats, etc.), and gives a broad estimate of how often profitable players are taking those actions, whilst comparing your stats ...


3

Your partition (underdog/favorite, hand won/lost) won't reveals many things as you will have to work on average. This will give you the performance of your hand range (supposed constant) versus and average hand range met in tournaments. A long term moving average will give you the evolution of your handrange performance. The deviation will give you the ...


3

They have an obvious advantage and so will earn more in the long run, that's pretty clear! Also playing together and playing both separately would lead to the same amount money, so they are not risking more money just together (same argument for the profits.) Now I don't really know to much about collusion and specifically what edge it can give you but I ...


3

First off, the statement in your question is not the norm: They have an obvious advantage of knowing about more cards that are in the play than they should, and they can strategically bet against one another to increase the pot (encouraging other players to play in hopes of winning). Almost always when players collude, they are typically protecting each ...


3

Your VP would still be 33% as you could have raised/called when you were in SB and BB - the tracker will only exclude walks where action was folded round to your BB. As for the PFR, this generally means 2-bets so will also be 33% given you raised once out of three hands where you had the option to. Your 3-bet and 4-bet stats are recorded separately and ...


3

The standard line would be to re-raise to what ever your defend re-raise is. Depending on how often the BU raises you should be defending with a re-raise a decent range. If you defend with 88+ and sometimes just suited connector then AA will not stick out. Just call with some of your re-raise range sometimes but I would always re-raise AA here. Give ...


3

quads: 13 * 12 = 156 full houses: 13 * 12 = 156 trips: 13 * 12 * 11 / 2 = 858 two pairs: 13 * 12 * 11 / 2 = 858 single pair: 13 * 12 * 11 * 10 / 6 = 2860 5 different cards: 13 * 12 * 11 * 10 * 9 / 120 = 1287 -- total: 6175 exemplary explanation for single pair: 13 possibilities for the rank of the pair, 12 possibilities for the first single card (...


2

Sadly, I dont know about any scientific proof, so I can give you just my thoughts. Lets say we have 2 players, each one with a skill to win 1bb/100 hands. If they dont collude, each of them wins 1bb/100 hands = 2bb When they start to collude, both of them get advantage as you mentioned, so lets say this increases their EV to win 2bb/hands. So they both ...


2

I'm not exactly what sure what you're talking about when you mention "stats". Playing profitable poker comes down to implementing two concepts: Identifying your opponents strategy. Implementing the best response. The first point is primarily improved through experience. As you play more poker, you will more easily be able to identify what your opponent ...


2

This information is not supposed to be public because no player would want to have their playstyle completely analyzed. Something you can do is approach players directly(maybe via forums like http://www.pokerstrategy.com/forum/) and ask is someone is willing to share his/her stats with you. I doubt that any pros would ever do that but if you explain why you ...


2

I think the real question here is with a 5 card flush on the board what is the chance that out of 5 players none have one of the remaining 8 flush cards? The answer is 12.3%. The odds of player one’s first card is not a flush suit is 39 of the remaining 47. We can see 5 cards, so 52-5 = 47 available cards. Of those 47 there are eight flush cards remaining ...


2

I have started doing a bit more analysis in my games. I load up HEM2 before a session and review a few tournaments from the day before. I mainly look at the hands where I have lost the most money and see how it could have been avoided. Look for the following: Should I have been in the hand in the first place? Did I play a marginal hand too aggressively? ...


2

In this case "short term" implies that you may have specific situational context that might be relevant to this narrow class of decisions. Say you're in a NLHE game and you have aces pre-flop and you know that you're sitting immediately to the right of a a big-stacked aggressive opponent who will very often punish your limp with a big raise. Since he's been ...


2

There's a 23.30% chance the other players have one of {66+, A7+}. Yes, there is an easy way to calculate the chance of a dominating hand behind you. You can use a program like ProPokerTools Odds Oracle to model the scenario and determine the probabilities. There is a free trial available. Below is a screenshot of the calculation as well as the log file. ...


2

No, the EV is the EV. But probability is a function of knowledge. Your estimate of the likelihood of the various events that go into your calculation of EV will change over time with new information, so that what may seem like the "same situation" to you at different times might actually be a very different situation when you take into account your added ...


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