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 |
