# Questions tagged [probability]

deals with computing probabilities for many commonly occurring events in the game of poker

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### Pocket pair starting hands vs. probability of opponent having a pocket pair

According to Wikipedia, the probability of being dealt any pocket pair as the starting hand is ~6% (78/1326=0.0588), but yet the probability of facing another player holding a larger pair when holding ...
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### Starting hands probability

The following is a passage from Wikipedia on starting hands probability: The 1,326 starting hands can be reduced for purposes of determining the probability of starting hands for Hold 'em—since ...
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Suppose there is some situation where Player A moves all-in and ALL Players call such that all players are all-in (they have equal amounts of chips, so no side-pots). Is there a possible distribution ...
394 views

### Systematic all-in

This is a theoretical question, following what I have seen in some low blinds cash games. You generally cannot buy-in more than 100BB. Say at some point, you reached 10,000 BB. All you adversaries ...
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### Best hand versus AA

Statistically what is the best hand versus AA (other than AA) I had read 56, 67, 78 Suited not the suit of any ace 56 being the best I cannot figure how 56 is better Ran on poker stove ...
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977 views

### Equity calculation

Flop = T♥ 7♥ 6♥ Player 1 = 4♠ 3♥ Player 2 = 5♥ 2♠ Whats the equity of Player 1 on this flop ? Equity calculators give it 43.54% (18.5% for tie and ...
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### Probability of x pocket pairs at a table of n people (NLHE)?

With n people at a table, what is the probability that x of them are dealt pocket pairs? There are several easy ways to approximate this but I was wondering there was an elegant solution. Any takers?
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### What are the actual odds of being dealt pocket Aces?

I have been looking at the way people calculate the odds of poker hands for a few hours and i think there is a HUGE flaw. In poker a player is never dealt two CONSECUTIVE cards. This in my view ...
552 views

### Hold'em: Why does K♠️7♠️ beat A♠️2♠️ more frequently than K♠️8♠️ does?

According to this site: K♠️7♠️ beats A♠️2♠️ 39.10% of the time (and ties 0.62%). K♠️8♠️ beats A♠️2♠️ 38.71% of the time (and ties 0.61%). Why is this? I expected the two probabilities to be the ...
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### How do I calculate poker hand probabilities?

This is a tutorial for calculating poker probabilities from scratch. It is what I learned in my degree and even beforehand when I created and 5-card draw hand strength calculator. The intention of ...
215 views

### Why isn't every value player rich?

I'm a beginner, sorry if this question is absurd. If a player simply bets with probabilities in mind, and always made the correct move for every action, would s/he become rich in the long run? If ...
23k views

### What are the odds of having 2 Quads in the same hand?

Just watched a video that went as follows: Player 1 (Button): Q♥Q♠ Player 2: 9♥9⋄ Player 3: 2♣2♠ Flop: Q⋄9♠Q♣ Turn: 5♠ River: 9&...
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### Formula for making a single pair on the flop

I'm trying to get the probability of pairing only one hole card on the flop. According to this calculator, http://www.texasholdem-poker.com/calculator?card1=8&card2=13&chance_format=...
2k views

Does anyone have charts for starting hands heads by position up or even order of hands? I know any Ace and any pair is valuable but I cannot find more specific guidelines. I found order of hands ...
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### Chances of 5 way chop (flush board)

What is the exact probability that 5 players at a table will be dealt no clubs (or hearts or whatever) ? Happened to me when all 5 community were all clubs (2,3,5,K,9), thereby a 5 way chop.
2k views

### Can anyone suggest a limit holdem training app for Android?

First time poster in this part of the world, so apologies if I've posted this in the wrong area. In short; I used to play a lot of Poker in University over a decade ago, and then continued to play ...
• 161
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### Probability of flopping straight flush

Assume you're given 2 cards of the same suit, and the next three cards (flop) are also the same suit as your hole cards. What is the probability of that happening? So I figured out that 2 cards have ...
• 201
347 views

### hand distribution in 6 max vs full ring

I have heard that the distribution in a 6 max game is similar to that of a 9 or 10 handed game where the extra players have folded. I am wondering how true that is. Seems like there may be a higher ...
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### What's wrong with my equity calculation?

When answering this question, I went ahead and tried to do a manual equity calculation for the scenario described (7♥4♠ vs A♠8♣ on a board of 6♥2♥8♥), ...
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166 views

### Calculating Odds for 3 of a kind

I am confused by this odds calculation here: https://www.pokernews.com/poker-tools/poker-odds-calculator.htm Basically the scenario that I have is below: I understand everything except for the 3 of a ...
• 143
231 views

### Why are the odds 16 to 6 that any given player does not hold a pocket pair?

In the book Ken Warren teaches Texas Holdem, its explained that there are 1,326 possible combinations of hole cards. Then its explained that if you disregard suits, there are 169 possible two-hole ...
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### Texas Hold'em heads up pre-flop AK vs 89s

According to online calculators: A♥K♦ (57.91%) vs 7♣8♣ (41.71%) A♥K♦ (59.42%) vs 8♣9♣ (40.19%) A♥K♦ (58.59%) vs 9♣T♣ (41.00%) Why is 8♣9♣ worse odds than the other 2? I assume it has something to ...
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### What is the probability of seeing a royal flush and a four of a kind in the same round with ten players?

We were wondering and concluded it is possible to have two players, one having a royal flush, the other having four of a kind, if there is a pair and three high cards on the table. But the situation ...
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### What are the odds of flopping a straight flush with 62s?

I've been wondering what the odds are of flopping a straight flush with 62s.
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### Probability Of Getting A Straight Flush Or Royal Flush When Holding QJs

Given that you are dealt the J♥ and Q♥, what is the probability that you will eventually make a straight flush or royal flush? Having these cards in your hand means that: 1). the only ...
• 201
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### Chance of winning heads-up by always shoving pre-flop

I've been generally wondering about what sort of winrate good players can expect vs. worse players, and thought of an interesting limit to this winrate. In NLHE, if the worse player just blindly ...
2k views

### Versus random hands

I have written a program to rate 2 hole cards (your hand) against a single random hand. It works - I compared its results to a published list. Your two hole cards are combined with a common 5 card ...
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### What are the chances of losing with a King high Straight Flush?

Also: is the probability so small that this has never happened?
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### Probability your opponent has a pocket pair when you are paired versus not

If I am holding a pocket pair does that effect the probability my opponent has a pocket pair.
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### Probability of forming a flush question (dependent vs independent event)

I'm slightly confused at the probability calculations for hands. Here's the problem: Suppose you have two hearts. The flop comes and has two hearts. What is the probability of forming a flush on the ...
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### Draw poker should you keep AK

5 card draw and you have AK and junk. Assume unsuited. A♠K♣T⋄8♣5♠ Should you keep AK or just the A?
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### Quads sevens 5 times in one night

I got quad sevens five times in 3 hours . The first three times were within the same round of ten hands. Without a technical explanation what are the odds of three times in ten hands and five times ...
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### Probability of flopping a straight

I was thinking about calculating the probability of flopping straights, with certain hands. First, I thought about situations: obviously the difference between two cards can't be higher than 4. If the ...
530 views

### What are the 5 card hand probabilities

Of all the 5 card poker hands what are the probabilities? And how are probabilities derived?
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### Probability of flush on board and no player has a flush card

What is the chance the board has a flush. And two players have no flush card.
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### Short deck probability

Short deck is remove 2-5 so 36 cards left. A6789 is a straight. What is the hand order and probability. For example a flush is harder to make but a straight is easier. Ideally post the ...
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570 views

### What are the odds of drawing a seven card straight flush

I had the unbelievable experience of drawing a seven-card straight flush while playing with five other players with one deck. The hand started with the ace of spades and ended with the seven of ...
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### What are the odds of the river containing a full house?

I was watching a game in a bar the other day and the river ended up containing a full house. What are the odds of this?
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### How to count the number of starting hands in Texas Hold 'em

I'm revisiting the excellent book by Tony Guerrera, Killer Poker by the Numbers. In the first chapter he goes over how to count the number of possible starting hands but leaves, as an exercise for the ...
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### Realistic Community Cards

I play online poker on a few sites and recently, I have marked that I'm actually getting a series of bad beats from some awful (ly "lucky") players. My question is what are the odds of following ...
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### Straight draw in heads up?

With a stack of 3000, 50/100 blinds, I was holding: 2 4 (not suited) I'm big blind in a heads up game. Opponent matches the big blind, so I end up playing a hand I'd never play otherwise. Flop:...
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### Poker pre-flop probability training tool

Is there a freeware, better FLOSS, online or preferably offline trainer for preflop probabilities. I imagine different play modes with entering percentages under measurement of time resulting in ...
298 views

### What are the odds of at least one player getting a hand from a range?

I've been trying to work this out for a while but I'm really struggling. I know the odds for a single player getting a hand from a range is simply: Combinations of hands in range / Total possible ...
1 vote
580 views

### Outs when needing more than one card

I recently learnt about outs, and the magic 4-2 rule. However all the examples that I see use the example of needing one card to complete your set. Why we don't consider the fact that I can have two ...
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1 vote
329 views

### Chances of an opponent not having a flush on 3-flush board

If there are 5 cards on the board and 3 of them are hearts and I don't have any hearts in my hand, what is the probability of someone else NOT having 2 hearts in their hand?
1 vote
1k views

### Does AA have the highest Equity in "double-board-bomb-pot" with 9 players?

I fielded a Poker StackExchange question the other day about whether AA is the best starting hand in Texas Hold-Em No Limit vs. 8 other players. Indeed, it is so. Now I have a variant of this ...
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### How to calculate probability of flopping a set (with pocket pairs)?

Building a poker program and would like to make sure I have my calculation correct. If a player is holding pocket pair, how does one calculate the probability of flopping a set (one card out of the ...
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1 vote
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### Poker hand suited connector

6 handed 1/2 cash All around 100 bb but bb at 30 Pre Hero in CO with T♠ 8♠ UTG open for 4 bb with one caller, I call, btn fold, sb fold, bb calls. I am lovin it. Flop Pot is 17 ...
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1 vote
750 views

### Distinct 7 card poker hands

From this link The number of distinct 5-card poker hands that are possible from 7 cards is 4,824. Does anyone have the break down of the 4,824? A list of the 4824? Better yet a program to ...
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1 vote