The probability of many events in Poker can be determined by direct calculation. For example, there are 1,326 (52 × 51) / 2) distinct possible combinations of two hole cards from a standard 52-card deck, but since suits have no hierarchy value in poker, many of the hands are identical in value before the flop. For example, K?Q? and K?Q? are identical.
Of the 1,326 combinations, there are 169 distinct starting hands grouped into three categories,13 pocket pairs (13 × 12 / 2 = 78), 78 suited hands and 78 unsuited hands (13 + 78 + 78 = 169).
The relative probability of being dealt a starting hand of each given category is calculated as follows:
| Category | Hands | Suited combination | Combinations | Probability |
|---|---|---|---|---|
| Pocket Pair | 13 | 6 | 13 x 6 = 78 | 6 / 1326 = 0.00453 |
| Suited Cards | 78 | 4 | 78 x 4 = 312 | 4 / 1326 = 0.00302 |
| Unsuited/ non-paired | 78 | 12 | 78 x 12 = 936 | 12 / 1326 = 0.00905 |
| Hand (non suit specific) | Probability | Odds |
|---|---|---|
| AKs (or any specific suited cards) | 0.00302 | 331 :1 |
| AA (or any specific pair) | 0.00453 | 220 :1 |
| AK, KK, QJ or J10 (suited) | 0.0121 | 81.9 :1 |
| AK (any non-pair incl. suited) | 0.0121 | 81.9 :1 |
| AA, KK, QQ | 0.0136 | 72.7 :1 |
| AA, KK, QQ or JJ | 0.0181 | 54.3 :1 |
| Suited cards, J or better | 0.0181 | 54.3 :1 |
| AA, KK, QQ, JJ or 1010 | 0.0226 | 43.2 :1 |
| Suited cards, 10 or better | 0.0302 | 32.2 :1 |
| Suited connectors | 0.0392 | 24.5 :1 |
| Connected cards, 10 or better | 0.0483 | 19.7 :1 |
| Any 2 cards with rank at least Q | 0.0498 | 19.1 :1 |
| Any 2 cards with rank at least J | 0.0905 | 10.1 :1 |
| Any 2 cards with rank at least 10 | 0.143 | 5.98 :1 |
| Connected cards (consecutive) | 0.157 | 5.38 :1 |
| Any 2 cards with rank at least 9 | 0.208 | 3.81 :1 |
| Not connected nor suited, 2-9 | 0.534 | 0.873 :1 |
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