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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Home » Featured, Theoretical

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%

Click here to download an Excel file with both tables (WestonPoker’s and mine).

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