19 Nov 2024 Intermediate This material is for medium-skilled players combinatorics equity outs probabilities Probabilities are one of the most important and fascinating aspects of the game. Many poker situations occur frequently, making it essential to memorize key poker probabilities. These probabilities are calculated using basic probability theory, which many people are familiar with from school and college. While you can calculate probabilities on your own, it is usually unnecessary, as specialized software and probability calculators have already done the work. Understanding and memorizing these probabilities, or at least most of them, is crucial for success in poker. What Are Probabilities in Poker? In poker, probability measures how often a specific event will occur, expressed as a percentage between 0 and 100%. Understanding these probabilities allows you to evaluate and analyze the profitability of various decisions in a given situation. This article contains tables with poker probabilities to help you make better decisions during the game. Note for Beginners: If you are new to poker, start by learning the rules of Texas Hold'em and poker hand rankings. Hand Combination Example Probability Pocket Aces AA 0.45% Any Pocket Pair 22-AA 0.9% Suited Ace-King AKs 0.3% Offsuit Ace-King AKo 0.9% Any Ace-King AK 1.2% Any Suited Cards XXs 24% Aces, Kings, or Ace-King KK-AA, AK 2.1% Probabilities in Typical Preflop All-Ins The table below shows your chances of winning in preflop all-in situations with different hands. Preflop Scenario Example Win Probability Pocket Pair vs Two Overcards 55 vs AK 54% Pocket Pair vs Lower Pocket Pair TT vs 88 81% Pair vs One Overcard KK vs AQ 71% Two Lower Cards vs Two Overcards JT vs AK 37% Two Cards vs One Overcard JT vs A9 45% Two Overcards (one matching) AK vs AQ 74% First and Third Card vs Second and Fourth AQ vs KJ 63% Probability of Making a Hand with a Pocket Pair The table below shows the probabilities of improving a pocket pair on the preflop to a specific hand on the post-flop. Hand Hand and Board Example Probability Set on the Flop on 10.8% Full House on the Flop on 0.7% Four of a Kind on the Flop on 0.2% Set or Better by the River on 19% Probability of Making a Hand with Suited Cards on the Flop The table below shows the probabilities of improving suited starting cards from the preflop to specific hands on the post-flop. Hand Hand and Board Example Probability Flush on the Flop on 0.84% Flush Draw on the Flop on 10.94% Backdoor Flush Draw on the Flop on 41.6% Made Straight on the Flop on 1.31% OESD or Better on the Flop on 10.45% Two Pair or Better on the Flop on 3.47% Flush by the River on 6.4% Probability of Making a Hand with Offsuit Cards on the Flop The table below shows the probabilities of improving offsuit starting cards from the preflop to specific hands on the post-flop. Hand Hand and Board Example Probability Flush Draw on the Flop on 1.1% Backdoor Flush Draw on the Flop on 12.8% OESD on the Flop on 9.71% Flush by the River on 1.8% Probabilities to Hit a Hand on the Flop The table below shows the probabilities (equity) of different types of starting hands hitting specific hands or draws on the flop. Starting Hand Example Straight Flush Two Pair+ OESD FD Total Equity Suited Connector (SC) 1.31% 0.84% 3.49% 9.71% 10.13% 25.5% SC with 1 Gap 0.96% 0.84% 3.49% 7.58% 10.13% 23% SC with 2 Gaps 0.64% 0.84% 3.49% 4.59% 10.13% 19.69% SC with 3 Gaps 0.32% 0.84% 3.49% 1.93% 10.13% 16.71% Offsuit Connector (OC) 1.31% - 3.49% 9.71% - 14.51% OС with 1 Gap 0.98% - 3.49% 7.67% - 12.14% OС with 2 Gap 0.65% - 3.49% 4.98% - 9.12% OС with 3 Gap 0.33% - 3.49% 2.61% - 6.43% Random Suited Hand - 0.84% 3.49% - 10.13% 14.46% Random Offsuit Hand - - 3.49% - - 3.49% Pocket Pair - - 11.75% - - 11.75% Probability of Making a Hand with Two Unpaired Cards on the Flop The table below shows the probabilities of improving two unpaired starting cards from the preflop to specific hands on the flop. Hand Hand and Board Example Probability Pair or Better on 32.5% Pair on 29% Two Pair (with both cards) on 2% Any Two Pair on 4% Trips on 1.35% Full House (with both cards) on 0.09% Four of a Kind on 0.01% Probability of Different Flop Textures This table shows the probabilities of flops having specific textures. Flop Texture Flop Example Probability Three of a Kind (Trips) 0.24% Paired 17% Three Cards of the Same Suit 5.2% Two Cards of the Same Suit 55% Rainbow (All Different Suits) 40% Three Consecutive Ranks 3.5% Two Consecutive Ranks 40% No Consecutive Ranks 56% Probability of No Overcards on the Flop When holding a pocket pair preflop, it is useful to know the likelihood of no overcards appearing on the flop, turn, or river, as overcards can weaken the strength of our hand. The table below shows these probabilities. Flop Turn River 77.45% 70.86% 64.7% 58.57% 48.6% 40.15% 43.04% 32.05% 23.69% 30.53% 20.14% 13.13% 20.71% 11.9% 6.73% 13.27% 6.49% 3.1% 7.86% 3.18% 1.24% 4.16% 1.33% 0.4% 1.86% 0.43% 0.09% 0.61% 0.09% 0.01% 0.1% 0.01% <0.01% Probability of Improving a Hand from the Flop to the Turn The table below shows the probabilities of improving specific hands from the flop to the turn. Hand Improvement Hand and Board Example Probability Set to Full House+ on 15% Two Pair to Full House on 8.5% Flush Draw to Flush on 19% OESD to Straight on 17% Gutshot to Straight on 8.5% Pair to Trips on 4.3% Pair to One of Two Overcards on 12.8% Probability of Improving a Hand from the Flop to the River This table shows the chances of improving a hand from the flop to the river. The probabilities for the turn and river can be combined to understand your odds better in post-flop situations. Hand Improvement Hand and Board Example Probability Set to Full House+ on 33% Two Pair to Full House+ on 17% Flush Draw to Flush on 35% Backdoor Flush Draw to Flush on 4.2% OESD to Straight on 32% Gutshot to Straight on 17% Pair to One of Two Overcards on 24% Probability of Facing a Dominating Ace Preflop The table below shows the chances of encountering a dominating Ace when you hold an Ace in your hand. The percentages represent the likelihood that your opponent(s) will have a better Ace (a higher kicker). These calculations apply to preflop situations. Your Hand 1 Opponent 2 Opponents 3 Opponents 4 Opponents 5 Opponents AQ 1.22% 2.43% 3.63% 4.81% 5.97% AJ 2.20% 4.36% 6.47% 8.53% 10.55% AT 3.18% 6.27% 9.25% 12.14% 14.94% A9 4.16% 8.15% 11.98% 15.64% 19.15% A8 5.14% 10.02% 14.65% 19.04% 23.20% A7 6.12% 11.87% 17.27% 22.33% 27.09% A6 7.10% 13.70% 19.83% 25.52% 30.81% A5 8.08% 15.51% 22.34% 28.62% 34.38% A4 9.06% 17.30% 24.79% 31.61% 37.81% A3 10.04% 19.07% 27.20% 34.51% 41.08% A2 11.02% 20.83% 9.55% 37.31% 44.22% Probability of Facing a Higher Pocket Pair Preflop Here is the table showing the probability of facing a higher pocket pair than yours preflop, based on the number of opponents. Your Hand 1 Opponent 2 Opponents 3 Opponents 4 Opponents 5 Opponents KK 0.49% 0.97% 1.47% 1.96% 2.44% QQ 0.98% 1.95% 2.92% 3.90% 4.84% JJ 1.47% 2.92% 4.37% 5.77% 7.18% TT 1.96% 3.89% 5.78% 7.64% 9.46% 99 2.45% 4.84% 7.19% 9.46% 11.68% 88 2.94% 5.80% 8.57% 11.25% 13.85% 77 3.43% 6.74% 9.95% 13.01% 15.95% 66 3.92% 7.68% 11.30% 14.74% 18.00% 55 4.41% 8.62% 12.63% 16.42% 19.95% 44 4.91% 9.57% 13.95% 18.05% 21.86% 33 5.38% 10.49% 15.27% 19.66% 23.71% 22 5.88% 11.42% 16.53% 21.24% 25.45%