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Everything You Should Know About Poker Probability

Poker is a popular casino game played among two or more players. You can play poker online too.

While poker is considered a game of chance, it requires players to have substantial skills in understanding game theory and the mathematics of probability.

The game theory forms the core of poker winning strategies. It helps in mathematically determining the actions of players to get the best possible outcomes for themselves. Notably, the outcomes of the players are interdependent.

Basic probability lies at the heart of the game theory. Probability is a branch of mathematics that computes the likelihood of an event occurring given other conditions. Hence, gaining expertise in the same is essential to improve your poker winning chances.

Poker probability

Structure of the deck

Poker is played with a pack of 52 cards. A deck has 2 red suites – hearts(H) and diamonds(D), and 2 black suites – clubs(C) and spades(S). There are 13 ranks in each suite – Ace(A), numbers 2-10, Jack(J), Queen(Q), and King(K).

Basic probability calculation

The odds of your 1st card belonging to the H/D/C/S suite = 13/52 = 25%

The odds of your 1st card being A/numbers/J/Q/K = 4/52 = 7.69%

The deck’s composition changes with every deal. So, for example, if the odds of receiving a K is 4/52, then the odds of receiving the subsequent Ks are 3/51, 2/50, and 1/49 respectively.

Pocket pairs probability

Pocket pairs refer to getting 2 cards of the same ranking. The probability of getting pocket pairs is calculated as follows:-

4/52 X 3/51 X 13 = 156/2652 = 1/17 = 5.88%

Hand vs. hand probability

The probability of winning a game of poker depends on your opponents’ hand strength. Hence, you must calculate relative probabilities both pre-flop and post-flop. The below image gives an idea about winning probabilities for different hand combinations.

While poker is considered a game of chance, it requires players to have substantial skills in understanding game theory and the mathematics of probability.

The game theory forms the core of poker winning strategies. It helps in mathematically determining the actions of players to get the best possible outcomes for themselves. Notably, the outcomes of the players are interdependent.

Basic probability lies at the heart of the game theory. Probability is a branch of mathematics that computes the likelihood of an event occurring given other conditions. Hence, gaining expertise in the same is essential to improve your poker winning chances.

Poker probability

Structure of the deck

Poker is played with a pack of 52 cards. A deck has 2 red suites – hearts(H) and diamonds(D), and 2 black suites – clubs(C) and spades(S). There are 13 ranks in each suite – Ace(A), numbers 2-10, Jack(J), Queen(Q), and King(K).

Basic probability calculation

The odds of your 1st card belonging to the H/D/C/S suite = 13/52 = 25%

The odds of your 1st card being A/numbers/J/Q/K = 4/52 = 7.69%

The deck’s composition changes with every deal. So, for example, if the odds of receiving a K is 4/52, then the odds of receiving the subsequent Ks are 3/51, 2/50, and 1/49 respectively.

Pocket pairs probability

Pocket pairs refer to getting 2 cards of the same ranking. The probability of getting pocket pairs is calculated as follows:-

4/52 X 3/51 X 13 = 156/2652 = 1/17 = 5.88%

Hand vs. hand probability

The probability of winning a game of poker depends on your opponents’ hand strength. Hence, you must calculate relative probabilities both pre-flop and post-flop. The below image gives an idea about winning probabilities for different hand combinations.

In poker jargon, an ‘out’ is any card that will improve your hand strength post-flop. For example, you have 2 cards of spades. 2 more cards of spades appear on the flop. Now, you have 4 cards of the same suite. You need one more spades card to complete your flush. You have 9 outs to do it, as the deck has 9 more spades cards.

The 4-2 rule is commonly used to derive the odds of making a hand. As per this rule, compute the number of outs to complete your hand. Multiply this number by 4. The answer derived is your probability of getting this card on the river or the turn. If you miss your draw on the turn, then multiply your outs by 2. This figure will give you the probability of getting the requisite card on the river to complete your hand.

In the above example, the odds of getting a spade card on the turn is 36% (9 X 4) and on the river is 18% (9 X 2).

Other helpful poker probabilities

Pot odds: It is the ratio of the total pot size to the size of the bet you are facing. If the pot odds are greater than the odds of improving your hands then call a bet, else fold.

Bad beats: A bad beat occurs when you feel you have a stronger hand than your opponents but end up losing. In other words, bad beats are consequences of poor probability computations. In short, hands with a low probability of winning are bad beats.

The bottom line

Mastering the mathematical skill set required to win poker comes with practice and patience. You may play free online poker games before betting real money. Many websites allow you to play free online poker games in India. Free poker games online are good training grounds for novices to master poker winning strategies.

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