KQo
48.13%
Wins 47.75%, ties 0.77%
33
51.87%
Wins 51.48%, ties 0.77%
KQo against 33: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KQo | 47.747 | 0.770 | 51.483 | 48.132 |
| 33 | 51.483 | 0.770 | 47.747 | 51.868 |
The first hand is an offsuit hand; the second is a pocket pair. A pair against two higher cards is the classic race: the pair is usually a small favorite or close to even, and each overcard that pairs is a way to take the lead.
This is close to even money, with 33 a little ahead. The tie share is 0.77%: on those boards the pot is chopped and neither hand wins outright.
Place 23 of 169 belongs to KQo and place 66 belongs to 33 in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KQo | 58,865,000 | 949,000 | 63,471,000 |
| 33 | 63,471,000 | 949,000 | 58,865,000 |
The total is exact: 72 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and rounded to the nearest thousand.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| KQo | 0.928 | 2.094 | 1.942 | 1.078 |
| 33 | 1.078 | 1.942 | 2.094 | 0.928 |
The final column gives the least the pot must offer for each unit called for a call to break even at this equity.
Who is ahead on which flops
Split by what the flop looks like, 33 peaks at 79.29% on low rainbow flops (nine high or lower) and bottoms out at 45.10% on rainbow flops topped by a ten or better. On rainbow flops topped by a ten or better and monotone flops the numbers flip and KQo is the one ahead.
| Flop | Share of flops | KQo wins | Ties | 33 wins | KQo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 54.736 | 0.323 | 44.941 | 54.898 |
| Rainbow, nine or lower | 6.314 | 20.073 | 1.279 | 78.648 | 20.713 |
| Two-tone | 46.485 | 47.973 | 0.500 | 51.527 | 48.223 |
| Monotone | 5.151 | 49.462 | 2.376 | 48.162 | 50.650 |
| Paired | 17.333 | 46.747 | 1.471 | 51.782 | 47.482 |
Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.
Compared with a random hand
A random hand would give KQo 61.46% and 33 53.69%. Against each other the change is -13.33 points for KQo and -1.82 for 33.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KQo, all flops | 48.132 | 61.456 | -13.324 | 0.78319 |
| KQo, rainbow, ten or higher | 54.898 | 61.456 | -6.558 | 0.89329 |
| KQo, rainbow, nine or lower | 20.713 | 61.456 | -40.743 | 0.33704 |
| KQo, two-tone | 48.223 | 61.456 | -13.233 | 0.78468 |
| KQo, monotone | 50.650 | 61.456 | -10.806 | 0.82417 |
| KQo, paired | 47.482 | 61.456 | -13.974 | 0.77262 |
| 33, all flops | 51.868 | 53.693 | -1.825 | 0.96601 |
| 33, rainbow, ten or higher | 45.102 | 53.693 | -8.591 | 0.84000 |
| 33, rainbow, nine or lower | 79.287 | 53.693 | +25.594 | 1.47667 |
| 33, two-tone | 51.777 | 53.693 | -1.916 | 0.96432 |
| 33, monotone | 49.350 | 53.693 | -4.343 | 0.91911 |
| 33, paired | 52.518 | 53.693 | -1.175 | 0.97812 |
Does a shared suit matter?
The suit split reads 51.78% for 33 with a shared suit and 52.29% without one. 33 does better with no shared suit, by 0.51 points.
| Deals | Specific deals | Share of deals | KQo wins | Ties | 33 wins | KQo equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 47.825 | 0.781 | 51.394 | 48.216 |
| No shared suit | 12 | 16.67 | 47.357 | 0.716 | 51.927 | 47.715 |
How often this matchup comes up
Counting specific cards, KQo against 33 appears in 72 of the 1,624,350 ordered heads-up deals (0.0044%), and in 144 when the seats are swapped too (0.0089%).
A worked example
With $100 from each side, the $200 pot is split on average as $103.74 for 33 and $96.26 for KQo; the first side gains $3.74 per all-in and the second gives up $3.74.
Run 1,000 deals and the tally comes out near 515 for 33, 477 for KQo and 8 ties.
The same matchup from the other side
If you came looking for 33 against KQo, the numbers are the same with the hands swapped: 51.87% and 48.13%.
Keep exploring
Open the calculator with KsQh against 3d3c already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.
How this was computed
The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 72 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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