PAIRS AND OVERCARDS
When you're holding a pocket pair, the most common cause for concern is an overcard to your pair coming in the community cards. The table below shows how likely this is to happen!
Some interesting results include the percentages for an overcard on the flop when holding 88 or 77, common thinking is that is about 50% for these mid-pairs, but in actual fact an overcard will flop 86.73% and 92.14% of the time respectively.
When you see the whole board all the way through to the river holding KK, a third of the time there will be an Ace on the board. Holding QQ, by the river, almost 60% of boards will have an Ace or a King!
Obviously if your opponent holds one of the overcards to your pair, then the odds of one of them appearing decreases, these percentages are only correct if we don't know our opponent's hole cards.
| Pair | % flops with OC | % f+t with OC | % boards with OC |
| 2 2 | 100.00% | 100.00% | 100.00% |
| 3 3 | 99.90% | 99.99% | 100.00% |
| 4 4 | 99.39% | 99.91% | 99.99% |
| 5 5 | 98.14% | 99.57% | 99.91% |
| 6 6 | 95.84% | 98.67% | 99.60% |
| 7 7 | 92.14% | 96.82% | 98.76% |
| 8 8 | 86.73% | 93.51% | 96.90% |
| 9 9 | 79.29% | 88.10% | 93.27% |
| 10 10 | 69.47% | 79.86% | 86.87% |
| J J | 56.96% | 67.95% | 76.31% |
| Q Q | 41.43% | 51.40% | 59.85% |
| K K | 22.55% | 29.14% | 35.30% |
| A A | 0.00% | 0.00% | 0.00% |
To create this table, first find the total possible number of flops, flops and turns, and full boards possible, without including youre own cards. Using the choose function (See our Hold'em starting hands page for more information), we can find these to be;
for the flop: 50 C 3 = 19600
for flop + turn : 50 C 4 = 230300
for board : 50 C 5 = 2118760
Now we need to know how many of each are possible without using any overcards to your pair.
If r represents the rank of your pair from 1-13, 22 being 1 and AA being 13, then (13-r)*4 will give the number of overcards to your pair.
Repeating the choose function calculations from above, replacing 50 with (50-k), where k represents the number of overcards, gives the number of each (flop, flop+turn, and board) possible without an overcard.
Dividing this number by the corresponding number available including overcards, and you have the probability of flop, flop+turn or board without an overcard. Subtract this from one and mulitply by 100 to give the percentage of each with an overcard. Phew!
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