Poker Math Cheatsheet

Tournament math

Essential mathematical reference for optimal poker decisions

Poker Math Cheatsheet

Essential mathematical reference for optimal poker decisions

×2

outs × 2 your % to hit on the next card

×4

outs × 4 your % to hit by the river once the money is in on the flop

call ÷ (pot + call) the equity a call needs to break even

Bet Sizing

defender: pot odds · MDF — aggressor: α fold equity · value : bluff

Bet Size Pot Odds MDF α fold eq Value : bluff

10% 8.33% 91% 9%

91.67%

25% 16.67% 80% 20%

83.33%

16.67%

33% 19.88% 75% 25%

80.12%

19.88%

50% 25.00% 67% 33%

75.00%

25.00%

66% 28.45% 60% 40%

71.55%

28.45%

75% 30.00% 57% 43%

70.00%

30.00%

100% 33.33% 50% 50%

66.67%

33.33%

125% 35.71% 44% 56%

64.29%

35.71%

150% 37.50% 40% 60%

62.50%

37.50%

200% 40.00% 33% 67%

60.00%

40.00%

300% 42.86% 25% 75%

57.14%

42.86%

400% 44.44% 20% 80%

55.56%

44.44%

500% 45.45% 17% 83%

54.55%

45.45%

Pot Odds: The price you're getting to call
MDF: Minimum Defense Frequency to prevent exploitation
Fold Equity (α): Required fold frequency for profitable bluffs
Value/Bluff %: Optimal range composition

Outs

pale bar is the second card

1 Set to Quads 45:1 · 22.5:1 4% 2%

2 Pair to Set (Poker Pair) 22:1 · 10.9:1 8% 4%

3 Single Overcard 14:1 · 7:1 13% 7%

4 Two Pair to Full House or Gutshot 10:1 · 5:1 17% 9%

5 One Pair, Two Pair or Set 8:1 · 4:1 20% 11%

6 No Pair to Pair or Two Overcards 6.7:1 · 3.2:1 24% 13%

7 Set to Full House or Quads 5.6:1 · 2.6:1 28% 15%

8 Open Straight 4.7:1 · 2.2:1 32% 17%

9 Flush 4.1:1 · 1.9:1 35% 20%

10 Gutshot and Two Overcards 3.6:1 · 1.6:1 38% 22%

11 Open Straight and One Overcard 3.2:1 · 1.4:1 42% 24%

12 Flush and Gutshot 2.8:1 · 1.2:1 45% 26%

13 Flush and Two Overcards 2.5:1 · 1.1:1 48% 28%

14 Flush, Gutshot and One Overcard 2.3:1 · 0.95:1 51% 30%

15 Flush and Open Straight 2.1:1 · 0.85:1 54% 33%

16 Flush and Open Straight, Overcard (shared out) 1.9:1 · 0.75:1 57% 35%

17 Flush, Open Straight and One Overcard 1.7:1 · 0.67:1 60% 37%

One Card %: Probability of hitting your draw on the next card
Two Cards %: Probability of hitting your draw by the river (2 cards remaining)
Odds: Ratio format showing likelihood against hitting your draw
Usage: Count your outs and find the corresponding winning probability

Hand Matchups

equity split — hand A : hand B

Overpair vs Underpair

AA vs QQ

80.9%

19.1%

AA vs 55

80.2%

19.8%

AA vs KQo

86.3%

13.6%

AA vs 76o

80.1%

19.3%

AA vs 87s

77%

23%

Pair vs Two overcards

JJ vs KQo

56.9%

43.1%

22 vs KQo

51.6%

48.3%

Pair vs One overcard

99 vs A2o

70.3%

29.7%

Pair vs One overcard (Suited)

99 vs A2s

66.6%

33.8%

Dominated

AKo vs AJo

73.7%

26.3%

AKo vs A2s

69.4%

30.6%

AKo vs K2s

72.6%

27.4%

Two overcards vs Non Pair

AKo vs JTo

62.6%

37.4%

AKo vs JTs

58.8%

41.2%

One overcard vs Non Pair

A5o vs 87o

56.2%

43.9%

A5o vs 87s

52.6%

47.4%

Percentages: Preflop equity values for common hand matchups
All values calculated for preflop all-in situations
Use these equities to understand hand strength relationships

Poker Probability

every bar on one absolute 0–100% scale

Preflop

Pocket A 0.45%

Pocket A or K 0.91%

Pocket Pair 5.88%

AKs 0.30%

AKo 0.90%

AK 1.21%

Suited 23.53%

AA + KK + AK 2.11%

Pocket Pairs

Flop set 10.80%

Flop full house 0.73%

Flop Quad 0.25%

Suited

Flop flush 0.84%

Flop flush draw 10.90%

Flop BD flush draw 41.60%

Flush by the river 6.40%

Offsuited

Flop flush draw (Monotone) 2.24%

Flop BD flush draw 25.59%

Flush by the river 1.85%

Non Pair

Flop a pair+ 32.40%

Flop one pair 29.00%

Two pair 2.02%

Trip 1.35%

Fullhouse 0.09%

Quad 0.01%

Flop Types

Three of a kind 0.24%

A pair 16.94%

Monotone 5.18%

Two tone 55.10%

Rainbow 39.80%

3 connected 3.50%

2+ connected 40.50%

Non connected 59.50%

Flop high card

A 21.74%

K 18.33%

Q 15.22%

J 12.40%

T 9.86%

9 7.62%

8 5.66%

7 4.00%

6 2.62%

5 1.54%

4 0.74%

3 0.24%

2 0.02%

Turn

Full house+ from a set 14.89%

Full house from two pair 8.51%

Flush from four flush 19.15%

Straight from OESD 17.02%

Straight from a gut shot 8.51%

A pair from two overcard 12.77%

Flop to River

Full house+ from a set 33.40%

Full house+ from two pair 16.50%

Flush from four flush 35%

Backdoor flush 4%

Straight from OESD 31.45%

Straight from gutshot 16.47%

Pair from two overcards 24.14%

Turn to River

Fullhouse+ from a set 21.70%

Fullhouse+ from two pair 8.70%

Flush from four flush 19.60%

OESD 17.40%

Pair from two overcards 13%

Percentages: Statistical likelihood of events occurring
Calculations: Based on combinatorial analysis and card removal
Usage: Use these probabilities to make informed decisions

Hand Combinations

combos, and how many are left once one card is seen

1 Pair

6 3 left with one card seen

1 Suit

4 3 left with one card seen

1 Offsuit

12 6 left with one card seen

Premium (QQ+,AKs,AKo)

34 combos

Small Pairs (22-66)

30 combos

Medium Pairs (77-JJ)

30 combos

All Broadway

190 combos

All of Any card (eg. All A)

198 combos

Combos: Total number of possible combinations
Combos - 1: Combinations when one card is already visible
Examples: AA has 6 combos total, 3 when one A is seen