April 3, 2010 – 10:41 am | 7 Comments

I’ve compiled a short (just 7-pages) e-book, an introduction to the mathematics of poker. It’s basically covers how to calculate your expected value in a certain spot – starting with explaining what EV is, all …

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## Pre-Flop Odds Charts

Submitted by on December 27, 2009 – 8:43 pmOne Comment

This post has been in the works for a while now, it’s just taken me longer than I expected to run the calculations on PokerStove. What is it I’ve done? A preflop odds chart.

WestonPoker has a very good odds chart showing the odds each hand has of winning, against anywhere from 1 to 9 opponents on any random hand. While useful, it has its drawbacks in real play. Your opponents are never going to be on a random hand. There are certain hands which your opponent will never call with, for example.

So I created my own odds chart, against the following range:

• Any pocket pair,
• Any Broadway (AT+, KT+, QT+ JT)
• A7+

It’s a relatively arbitrary range, but I think it’s a decent semi-tight range. I’ve only created the chart for up to 3 opponents, however, mainly because it’s been taking too long. All percentages were generated by PokerStove, either with full enumeration or with a Monte Carlo Simulation of at least 50 million hands.

So without further ado, here is the percentage equity that every hand has against the afore-mentioned range, against 1 to 3 opponents.

 Opponents: 1 2 3 Hand AA 84.98% 73.34% 63.60% AKs 62.78% 44.32% 33.64% AKo 60.97% 41.57% 30.36% AQs 59.76% 40.76% 30.23% AQo 57.74% 37.74% 26.68% AJs 56.76% 37.56% 27.40% AJo 54.52% 34.29% 23.61% ATs 53.84% 34.72% 25.05% ATo 51.40% 31.23% 21.07% A9s 48.79% 31.10% 22.91% A9o 45.96% 27.37% 18.84% A8s 46.61% 29.72% 21.88% A8o 43.62% 25.90% 17.74% A7s 44.73% 28.42% 20.92% A7o 41.60% 24.40% 16.72% A6s 43.72% 27.76% 20.49% A6o 40.49% 23.79% 16.30% A5s 44.38% 28.77% 21.68% A5o 41.22% 24.85% 17.57% A4s 43.86% 28.17% 21.18% A4o 40.65% 24.29% 17.04% A3s 43.29% 27.49% 20.53% A3o 40.04% 23.50% 16.34% A2s 42.70% 26.71% 19.86% A2o 39.40% 22.82% 15.60% KK 76.48% 62.28% 52.79% KQs 50.08% 34.57% 27.18% KQo 47.42% 31.20% 23.64% KJs 47.30% 32.26% 25.09% KJo 44.44% 28.66% 21.36% KTs 44.67% 30.15% 23.37% KTo 41.62% 26.52% 19.53% K9s 41.37% 28.43% 22.15% K9o 38.04% 24.58% 18.25% K8s 39.97% 27.17% 21.11% K8o 36.56% 23.26% 17.11% K7s 39.62% 26.93% 20.88% K7o 36.17% 22.94% 16.84% K6s 39.83% 27.32% 21.46% K6o 36.39% 23.51% 17.53% K5s 39.42% 27.05% 21.17% K5o 35.97% 23.12% 17.19% K4s 38.88% 26.52% 20.73% K4o 35.38% 22.56% 16.69% K3s 38.29% 25.89% 20.12% K3o 34.75% 21.83% 16.00% K2s 37.68% 25.18% 19.43% K2o 34.09% 21.14% 15.34% QQ 71.48% 55.21% 44.81% QJs 44.12% 30.46% 23.80% QJo 41.08% 26.79% 20.03% QTs 41.52% 28.76% 22.38% QTo 38.30% 25.10% 18.51% Q9s 39.13% 27.73% 21.77% Q9o 35.70% 23.97% 17.86% Q8s 37.77% 26.43% 20.63% Q8o 34.23% 22.56% 16.63% Q7s 36.38% 25.14% 19.57% Q7o 32.75% 21.17% 15.46% Q6s 36.88% 25.77% 20.19% Q6o 33.28% 21.90% 16.26% Q5s 36.50% 25.44% 19.94% Q5o 32.89% 21.51% 15.92% Q4s 35.94% 24.92% 19.45% Q4o 32.28% 20.95% 15.41% Q3s 35.32% 24.27% 18.84% Q3o 31.61% 20.23% 14.76% Q2s 34.67% 23.58% 18.18% Q2o 30.91% 19.53% 14.08% JJ 66.41% 48.70% 18.18% JTs 39.67% 28.20% 22.03% JTo 36.34% 24.53% 18.21% J9s 38.13% 27.72% 21.90% J9o 34.65% 24.01% 18.09% J8s 36.78% 26.42% 20.72% J8o 33.21% 22.61% 16.83% J7s 35.37% 25.04% 19.51% J7o 31.71% 21.13% 15.53% J6s 34.75% 24.63% 19.30% J6o 31.04% 20.73% 15.36% J5s 34.62% 24.44% 19.08% J5o 30.91% 20.51% 15.11% J4s 34.05% 23.92% 18.62% J4o 30.30% 19.94% 14.61% J3s 33.41% 23.27% 18.01% J3o 29.60% 19.22% 13.94% J2s 32.74% 22.57% 17.36% J2o 28.89% 18.51% 13.25% TT 61.42% 42.89% 32.43% T9s 38.35% 28.13% 22.48% T9o 34.92% 24.47% 18.75% T8s 37.02% 26.83% 21.32% T8o 33.50% 23.08% 17.49% T7s 35.60% 25.42% 20.05% T7o 31.98% 21.56% 16.12% T6s 34.90% 24.85% 19.51% T6o 31.22% 21.00% 15.69% T5s 33.54% 23.54% 18.39% T5o 29.78% 19.56% 14.40% T4s 33.21% 23.18% 18.05% T4o 29.43% 19.19% 14.02% T3s 32.57% 22.52% 17.43% T3o 28.73% 18.47% 13.34% T2s 31.90% 21.84% 16.78% T2o 28.01% 17.75% 12.67% 99 56.91% 39.01% 30.03% 98s 38.21% 28.41% 23.10% 98o 34.91% 24.82% 19.49% 97s 37.02% 27.35% 22.35% 97o 33.52% 23.68% 18.67% 96s 36.29% 26.81% 21.99% 96o 32.74% 23.15% 18.34% 95s 34.91% 25.48% 20.77% 95o 31.28% 21.70% 17.02% 94s 33.33% 23.86% 19.18% 94o 29.58% 19.97% 15.34% 93s 32.99% 23.54% 18.90% 93o 29.22% 19.62% 15.01% 92s 32.35% 22.91% 18.32% 92o 28.53% 38.55% 14.40% 88 54.28% 36.66% 28.24% 87s 37.64% 28.08% 23.15% 87o 34.19% 24.46% 19.49% 86s 36.99% 27.66% 22.94% 86o 33.49% 24.04% 19.33% 85s 35.63% 26.40% 21.80% 85o 32.05% 22.67% 18.11% 84s 34.04% 24.77% 20.21% 84o 30.34% 20.93% 16.40% 83s 32.42% 23.10% 18.56% 83o 28.61% 19.13% 14.62% 82s 32.07% 22.77% 18.25% 82o 28.23% 18.78% 14.32% 77 51.65% 34.41% 26.50% 76s 37.49% 28.28% 23.61% 76o 34.03% 24.69% 20.06% 75s 36.21% 27.16% 22.75% 75o 32.67% 23.47% 19.09% 74s 34.64% 25.58% 21.25% 74o 30.99% 21.81% 17.49% 73s 33.01% 23.89% 19.53% 73o 29.25% 19.99% 15.65% 72s 31.36% 22.15% 17.80% 72o 27.49% 18.16% 13.84% 66 49.79% 33.13% 25.92% 65s 37.31% 28.43% 24.05% 65o 33.85% 24.86% 20.55% 64s 35.84% 27.07% 22.88% 64o 32.28% 23.42% 19.29% 63s 34.22% 25.41% 21.25% 63o 30.56% 21.64% 17.55% 62s 32.59% 23.69% 19.55% 62o 28.81% 19.84% 15.76% 55 48.07% 31.72% 24.72% 54s 36.73% 27.92% 23.66% 54o 33.25% 24.32% 20.11% 53s 35.14% 26.32% 22.12% 53o 31.54% 22.60% 18.45% 52s 33.50% 24.64% 20.44% 52o 29.79% 20.82% 16.70% 44 46.18% 30.21% 23.50% 43s 34.50% 25.75% 21.60% 43o 34.50% 22.02% 17.89% 42s 32.89% 24.12% 20.00% 42o 29.15% 20.27% 16.21% 33 44.28% 28.69% 22.20% 32s 32.19% 23.46% 1933.60% 32o 28.40% 19.57% 15.53% 22 42.37% 27.23% 20.97%