12 votes

What are the actual odds of being dealt pocket Aces?

The odds of getting aces do not at all depend on the number of cards remaining in the deck. They depend solely on the number of cards in the deck (52), how many aces are in the deck (4), and how many ...
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  • 3,878
11 votes
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Hold'em: Why does K♠️7♠️ beat A♠️2♠️ more frequently than K♠️8♠️ does?

K7 steals one winner from A2 K7 wins 3456 and K8 does not K8 does not steal 4567 as A2 does not have a piece of it
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  • 6,849
8 votes
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Equity calculation

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 ...
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  • 1,033
8 votes

Drawing Dead Preflop?

This is an interesting question. The key consideration to me is "Player A cannot win the pot via a split pot", meaning that there should be no scenario whereby the board contains the nuts. This is ...
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  • 1,036
7 votes

How do I calculate poker hand probabilities?

Welcome to the world of probabilities! 1. Questions, Answers, Frequencies Probabilities calculation is about a question requiring an answer. It is about a question involving: An initial state. This ...
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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

Poker Strategy for all ins

It depends on what kinds of hands your opponent would go all-in with. If it's a tournament and he's short stacked in late position, he might have many types of hands. If it's a cash game or early in ...
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  • 3,878
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
6 votes

hand distribution in 6 max vs full ring

Probability is a measure of information. It's not about where the cards are--it's about what you know about them. Let's say you have a flush draw on the turn--9 outs. What odds should you use for ...
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5 votes
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Probability of flopping straight flush

The worst case for a possible straight flush is holding something like A2s, AKs, A5s, etc., where there's only one possible way to flop the straight flush. In that case, the probability is one in 50C3,...
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5 votes
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What are the chances of losing with a King high Straight Flush?

The only way to lose with a King high straight flush is to a royal flush of the same suit. That means that the KQJT must all be community cards. The last community card is either the 9 or you have it ...
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  • 1,033
5 votes

Are both a straight and a full-house possible on the same flop?

On the flop in hold-em, it is not possible for one player to have a straight flush (or even just a straight or just a flush) and another to have a full house. A full house requires at least two cards ...
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  • 3,878
5 votes
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What are the odds of flopping a straight flush with 62s?

You need to calculate the odds of getting the exact flop that you need. Since the order doesn't matter, the first card dealt would have three possibilities, and then if you got one of those you would ...
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  • 718
5 votes

Why don't you remove the element of luck in poker?

In general, if you remove luck from the game, it becomes much more difficult to win money. This is because the average poker player thinks they are better then average. Mathematically this cannot ...
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  • 689
5 votes

Drawing Dead Preflop?

As I mentioned in a comment above, this was not my answer, found it here. Although I did find you could also substitute the 7s with 8s, and then the Queens with Jacks, 10s or 9s. Suits matter in the ...
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  • 4,441
4 votes

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

A poker math geek gave me the following formula to use as an estimation. (Edit: The credit for this shortcut goes to Phil Gordon and is known as the Gordon Pair Principle.) Let's say you have 55: ...
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  • 41
4 votes
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What are the odds of a at least a certain amount of aces being dealt depending on the number of players?

These are the chances (assuming you have no ace): These are valid only preflop assuming that there are 50 cards left in the deck (you are holding 2) and you are one of the players (2 players = 1 ...
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  • 561
4 votes
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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

Why isn't every value player rich?

Rich? It's extremely hard to be "rich" just by playing poker, but it's simple enough to make a living off it. The reason being that you have to be vastly superior to the field to make steady money off ...
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  • 684
3 votes

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

Here is the maths for you. Or well my maths anyway. With 7 cards to choose from in hold'em, your hole cards and the board, the odds of making quads is about 1 in 595. (13 * (48 choose 3)) / (52 ...
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  • 4,441
3 votes

5 cards draw odds

This answer assumes you have no additional knowledge of the opponent's cards. You have five cards in your hand. Of those, three are spades and two are not spades, so you need two more spades to ...
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  • 3,878
3 votes

Distinct 7 card poker hands

The hands that can't happen with seven cards are exactly the five card hands that improve no matter which two cards are added to them. This basically means hands with low kickers. A high card hand (...
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  • 1,033
3 votes
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Which poker hand is this?

Each players' hand is comprised of their best 5 card hand... Ruane has Two Pair: Queens and Tens with a King kicker Hallaert has Two Pair: Queens and Tens with a 6 Kicker Ruane wins with the higher ...
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3 votes

Probability of ace on flop?

Assuming heads-up. Since you hold AQ and villain has AJ, there are 52-4=48 cards left on the deck, with 2 Aces remaining. So, Prob[at least an Ace on the Flop] = 1-Prob[no Ace on Flop]=1-(46/48)(45/...
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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
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Poker hand suited connector

I think that calling here would be the worst play and I agree with your reasoning. Additionally, one of your outs (9 of diamonds) either helps another player out even more or else kills your ...
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  • 1,938
3 votes

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

This is quite difficult to answer without making some assumptions. You could just calculate the chances of your opponent having a hand with a maximum of one heart based on the known and unknown cards, ...
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  • 1,562
3 votes
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Outs when needing more than one card

To elaborate on Paparazzi's answer, you can calculate the odds of a card being dealt next by dividing the number of cards you wish to know the chance of coming by all remaining unknown cards (...
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  • 1,562
3 votes

Quads sevens 5 times in one night

I will have to get technical, sorry. There are 35 possible ways to make quad sevens. They are all equally likely. You can get this number by writing out all possibilities like this: XXXXOOO XXXOXOO ...
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  • 2,794
3 votes
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How to calculate probability of flopping a set (with pocket pairs)?

total combinations = 19,600 assuming you have red 2s flops with 2s but no 2c [2s, 48, 47] = 48c2 = 1128 flops with 2c but no 2s [2c, 48, 47] = 48c2 = 1128 flops with 22x [2c, 2s, 48] = 48 2256/...
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