KK
81.37%
Wins 81.12%, ties 0.49%
33
18.63%
Wins 18.39%, ties 0.49%
KK against 33: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KK | 81.121 | 0.492 | 18.387 | 81.367 |
| 33 | 18.387 | 0.492 | 81.121 | 18.633 |
The matchup is pocket pairs on both sides, KK against 33. Both hands are pairs, so the bigger pair is ahead on every board that does not pair a card below it.
That is a heavy lead: 33 needs the board to help it on most runouts and still falls behind far more often than not. A split pot comes up on 0.49% of boards, so the wins and the equity differ by half of that.
The hand ranking puts KK at 2 and 33 at 66 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KK | 50,005,000 | 303,000 | 11,334,000 |
| 33 | 11,334,000 | 303,000 | 50,005,000 |
Exact total: 36 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| KK | 4.367 | 1.233 | 5.439 | 0.229 |
| 33 | 0.229 | 5.439 | 1.233 | 4.367 |
The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.
Who is ahead on which flops
By flop texture, KK's equity runs from 68.26% on low rainbow flops (nine high or lower) up to 86.97% on paired flops. KK stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | KK wins | Ties | 33 wins | KK equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 83.903 | 0.255 | 15.842 | 84.031 |
| Rainbow, nine or lower | 6.314 | 67.598 | 1.314 | 31.088 | 68.255 |
| Two-tone | 46.363 | 80.000 | 0.451 | 19.549 | 80.225 |
| Monotone | 5.152 | 74.720 | 2.310 | 22.970 | 75.875 |
| Paired | 17.576 | 86.920 | 0.100 | 12.980 | 86.970 |
Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.
Compared with a random hand
A random hand would give KK 82.40% and 33 53.69%. Against each other the change is -1.03 points for KK and -35.06 for 33.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KK, all flops | 81.367 | 82.396 | -1.029 | 0.98751 |
| KK, rainbow, ten or higher | 84.031 | 82.396 | +1.635 | 1.01984 |
| KK, rainbow, nine or lower | 68.255 | 82.396 | -14.141 | 0.82838 |
| KK, two-tone | 80.225 | 82.396 | -2.171 | 0.97365 |
| KK, monotone | 75.875 | 82.396 | -6.521 | 0.92086 |
| KK, paired | 86.970 | 82.396 | +4.574 | 1.05551 |
| 33, all flops | 18.633 | 53.693 | -35.060 | 0.34703 |
| 33, rainbow, ten or higher | 15.969 | 53.693 | -37.724 | 0.29741 |
| 33, rainbow, nine or lower | 31.745 | 53.693 | -21.948 | 0.59123 |
| 33, two-tone | 19.775 | 53.693 | -33.918 | 0.36830 |
| 33, monotone | 24.125 | 53.693 | -29.568 | 0.44931 |
| 33, paired | 13.030 | 53.693 | -40.663 | 0.24268 |
Does a shared suit matter?
The suit split reads 81.50% for KK with a shared suit and 80.71% without one. KK does better with a shared suit, by 0.79 points.
| Deals | Specific deals | Share of deals | KK wins | Ties | 33 wins | KK equity |
|---|---|---|---|---|---|---|
| Share a suit | 30 | 83.33 | 81.248 | 0.503 | 18.249 | 81.499 |
| No shared suit | 6 | 16.67 | 80.487 | 0.436 | 19.077 | 80.705 |
How often this matchup comes up
Counting specific cards, KK against 33 appears in 36 of the 1,624,350 ordered heads-up deals (0.0022%), and in 72 when the seats are swapped too (0.0044%).
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. KK averages $162.74 from the $200, up $62.74; 33 averages $37.26, down $62.74.
Out of 1,000 deals you should see around 811 outright wins for KK, 184 for 33, and 5 split pots.
The same matchup from the other side
33 versus KK is this same page seen from the other hand: 18.63% for 33, 81.37% for KK.
Keep exploring
Open the calculator with KsKh 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
We counted every case. Each suit pattern of the 36 specific KK against 33 deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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