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Poker Probabilities
Poker Probabilities

Poker Probabilities

After 2.6 million hands the following statistics arose:

Poker Probabilities I


combinations numbers probability in percent ...
Royal Flush 4 0,00015 %
Straight Flush 36 0,00135 %
Four of A Kind 624 0,02 %
Full House 3744 0,14 %
Flush 5108 0,20 %
Straight 10200 0,39 %
Three of A Kind 54912 2,11 %
Two Pair 123552 4,75 %
Pair 1098240 42,25 %
High Card 1302540 50,13 %


Poker Probabilities II - Head's Up


Favorite-to-underdog matchup Probability Odds for
Pair vs. 2 undercards 0.83 4.9 : 1
Pair vs. lower pair 0.82 4.5 : 1
Pair vs. 1 overcard, 1 undercard 0.71 2.5 : 1
2 overcards vs. 2 undercards 0.63 1.7 : 1
Pair vs. 2 overcards 0.55 1.2 : 1


Poker Probabilities III - PocketPairs


Probability of facing a
larger pair when holding
Against 1 Against 2 Against 3 Against 4 Against 5 Against 6 Against 7 Against 8 Against 9
KK 0.0049 0.0098 0.0147 0.0196 0.0244 0.0293 0.0342 0.0391 0.0439
QQ 0.0098 0.0195 0.0292 0.0388 0.0484 0.0579 0.0673 0.0766 0.0859
JJ 0.0147 0.0292 0.0436 0.0577 0.0717 0.0856 0.0992 0.1127 0.1259
TT 0.0196 0.0389 0.0578 0.0764 0.0946 0.1124 0.1299 0.1470 0.1637
99 0.0245 0.0484 0.0718 0.0946 0.1168 0.1384 0.1593 0.1795 0.1990
88 0.0294 0.0580 0.0857 0.1125 0.1384 0.1634 0.1873 0.2101 0.2318
77 0.0343 0.0674 0.0994 0.1301 0.1595 0.1874 0.2138 0.2387 0.2619
66 0.0392 0.0769 0.1130 0.1473 0.1799 0.2104 0.2389 0.2651 0.2890
55 0.0441 0.0862 0.1263 0.1642 0.1996 0.2324 0.2623 0.2892 0.3129
44 0.0490 0.0956 0.1395 0.1806 0.2186 0.2532 0.2841 0.3109 0.3334
33 0.0539 0.1048 0.1526 0.1967 0.2370 0.2729 0.3040 0.3300 0.3503
22 0.0588 0.1141 0.1654 0.2124 0.2546 0.2914 0.3222 0.3464 0.3633


Poker Probabilities IV - Board


Board consisting of Making on flop Making by turn Making by river
Prob. Odds Prob. Odds Prob. Odds
Three or more of same suit 0.05177 18.3 : 1 0.13522 6.40 : 1 0.23589 3.24 : 1
Four or more of same suit 0.01056 93.7 : 1 0.03394 28.5 : 1
Rainbow flop (all different suits) 0.39765 1.51 : 1 0.10550 8.48 : 1
Three cards of consecutive rank (but not four consecutive) 0.03475 27.8 : 1 0.11820 7.46 : 1 0.25068 2.99 : 1
Four cards to a straight (but not five) 0.03877 24.8 : 1 0.18991 4.27 : 1
Three or more cards of consecutive rank and same suit 0.00217 459 : 1 0.00869 114 : 1 0.02172 45.0 : 1
Three of a kind (but not a full house or four of a kind) 0.00235 424 : 1 0.00935 106 : 1 0.02128 46 : 1
A pair (but not two pair or three or four of a kind) 0.16941 4.90 : 1 0.30417 2.29 : 1 0.42450 1.36 : 1
Two pair (but not a full house) 0.01037 95.4 : 1 0.04716 20.2 : 1


Poker Probabilities V - Flopping overcards when holding a pocket pair


Holding pocket pair no Overcard on flop no Overcard by turn no Overcard by river
Prob. Odds Prob. Odds Prob. Odds
KK 0.7745 0.29 : 1 0.7086 0.41 : 1 0.6470 0.55 : 1
QQ 0.5857 0.71 : 1 0.4860 1.06 : 1 0.4015 1.49 : 1
JJ 0.4304 1.32 : 1 0.3205 2.12 : 1 0.2369 3.22 : 1
TT 0.3053 2.28 : 1 0.2014 3.97 : 1 0.1313 6.61 : 1
99 0.2071 3.83 : 1 0.1190 7.40 : 1 0.0673 13.87 : 1
88 0.1327 6.54 : 1 0.0649 14.40 : 1 0.0310 31.21 : 1
77 0.0786 11.73 : 1 0.0318 30.48 : 1 0.0124 79.46 : 1
66 0.0416 23.02 : 1 0.0133 74.26 : 1 0.0040 246.29 : 1
55 0.0186 52.85 : 1 0.0043 229.07 : 1 0.0009 1057.32 : 1
44 0.0061 162.33 : 1 0.0009 1095.67 : 1 0.0001 8406.78 : 1
33 0.0010 979.00 : 1 0.0001 15352.33 : 1 0.0000 353125.67 : 1