8 votes
Accepted

Can a decision be both + and - EV?

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 ...
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  • 478
6 votes

Probability Of Getting A Straight Flush Or Royal Flush When Holding QJs

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 ...
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6 votes

Missing the flop with AK

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 ...
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  • 361
6 votes

How precise is math in the heat of battle?

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, ...
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  • 361
6 votes

Best hand versus AA

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 ...
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  • 2,794
5 votes

How precise is math in the heat of battle?

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 ...
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5 votes

What's the Probability of hitting the board on the Turn or the River

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 ...
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5 votes
Accepted

Is there a calculator that shows what my "potential" odds are?

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....
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  • 2,794
4 votes
Accepted

What's wrong with my equity calculation?

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 ...
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4 votes
Accepted

What's the Probability of hitting the board on the Turn or the River

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 ...
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3 votes

PFR (preflop raise) statistics calculation with raise + 4bet in one single hand

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 ...
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  • 518
3 votes

Is there statistically any combination worse than 2 7 offsuit for preflop Texas Hold'em?

It depends on how many players are in the pot. Using the pre-flop calculator and assuming you only know your own hand, here is a table of the winning odds (calculated at https://www.888poker.com/poker/...
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3 votes

Is there statistically any combination worse than 2 7 offsuit for preflop Texas Hold'em?

I once spent an afternoon analyzing 7-2 with Poker Probe (An old program by Mike Caro). I was curious if there was any situation that justified making a call with 2-7. PP was a pretty simple program, ...
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  • 5,481
3 votes

Are there statistics that show the percentage of times you should fold at each stage of Texas Hold'em?

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 ...
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  • 6,483
3 votes

You have AA in the BB. The BU opens to 3.5x. What is your line?

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 ...
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  • 6,849
3 votes
Accepted

Number of combinations for 5 from 52 cards neglecting suit

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 /...
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  • 354
2 votes

Can a decision be both + and - EV?

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, ...
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2 votes

Can a decision be both + and - EV?

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 ...
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  • 3,878
2 votes
Accepted

Versus random hands

I expect most calculators online just run a subset of all possible boards as a representative sample - for example on ProPokerTools if you run a heads up hand against a random hand you get an ...
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  • 1,562
2 votes

What's wrong with my equity calculation?

I'm not sure how much it affects your equity calculation, but you are missing where the villain hits Aces full.
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  • 1,313
2 votes

Odds that someone makes or holds a pair on the flop, based on the # of players

If we assume that any player seeing the flop is equally likely to have any possible hand and that we do not take our own specific hand into account, we can provide an answer. Taking the simple case ...
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  • 1,562
2 votes

Best hand versus AA

According to this odds calculator site, the reason 56s is better, is because it loses less against AA. Here are the top 10 hands they list vs. AA: Best Hands Against Pocket Aces in Holdem Rank ...
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  • 1,313
2 votes

What mathematics should I learn to get better at Poker?

I think that learning about weighted probabilities is very useful to improving your game, especially when reviewing hands and developing an intuition for your true chances of creating a profitable ...
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  • 1,938
2 votes

Probability of flopping two flushes

there is a about a 25% chance that you get dealt suited cards. (12/51 ~ 23.5% to be exact) given that you already hold 2 suited cards, there is a 4.4% chance that your opponent also get dealt 2 cards ...
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  • 3,202
2 votes
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Poker tips backed by facts

These quick tips are all backed by the fundamental math and rules of poker. I would recommend that instead of memorizing facts/tips, it would be more beneficial to gain a thorough understanding of ...
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  • 3,202
2 votes

How to calculate my sample size to establish my real-WR?

The problem I see here is that if you are starting to become a professional player, your skills should be improving, thus I think you should track your performance based on shorter period of time, say ...
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  • 92
1 vote

Odds that someone makes or holds a pair on the flop, based on the # of players

Let's just call it 1/3 chance that a player makes a pair on the flop. Change it into an and so you can multiply. The chance of not having a pair is 2/3. So if three saw the flop 1 - (2/3 * 2/3 * 2/3) =...
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  • 6,849
1 vote

How do you express the statistics of turn/river possibilities to make a hand?

It is in this link Poker_probability c(4,1) * c(5,5) * c(47,2) / c(52,7) = 0.0000323206 = 30939 : 1 4 flushes * exactly 5 cards * 47 remaining cards for the other 2 c is combination It is ...
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  • 6,849
1 vote

Building specific situational calcualtion of pot equity and chance of winning. Setting up the formula.

There are far too many situations you'd need to work out to calculate by hand. 1a. Just for AQo vs P1 & P2 range, the permutations of hand matchups is already huge. P1 range: 40% x 1326 = ...
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