22
47.97%
Wins 46.57%, ties 2.79%
75s
52.03%
Wins 50.64%, ties 2.79%
22 against 75s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 22 | 46.572 | 2.786 | 50.642 | 47.965 |
| 75s | 50.642 | 2.786 | 46.572 | 52.035 |
Here a pocket pair (22) meets a suited hand (75s). 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.
That is a slim edge: neither hand is far ahead. The tie share is 2.79%: on those boards the pot is chopped and neither hand wins outright.
The hand ranking puts 22 at 87 and 75s at 124 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 22 | 19,139,000 | 1,145,000 | 20,811,000 |
| 75s | 20,811,000 | 1,145,000 | 19,139,000 |
24 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, 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) |
|---|---|---|---|---|
| 22 | 0.922 | 2.147 | 1.975 | 1.085 |
| 75s | 1.085 | 1.975 | 2.147 | 0.922 |
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
Break the boards down by their first three cards and 75s is strongest on low rainbow flops (nine high or lower) (63.86%) and weakest on rainbow flops topped by a ten or better (49.13%). 22 takes over on rainbow flops topped by a ten or better and paired flops, so the favorite before the flop is the underdog on those boards.
| Flop | Share of flops | 22 wins | Ties | 75s wins | 22 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.844 | 50.086 | 1.575 | 48.339 | 50.874 |
| Rainbow, nine or lower | 5.065 | 35.555 | 1.178 | 63.267 | 36.144 |
| Two-tone | 46.545 | 45.857 | 1.435 | 52.708 | 46.574 |
| Monotone | 5.212 | 45.783 | 4.616 | 49.601 | 48.091 |
| Paired | 17.334 | 46.712 | 8.137 | 45.151 | 50.781 |
A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.
Compared with a random hand
Start from the random-hand figures, 50.33% for 22 and 43.68% for 75s. This opponent changes them by -2.36 and +8.35 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 22, all flops | 47.965 | 50.334 | -2.369 | 0.95293 |
| 22, rainbow, ten or higher | 50.874 | 50.334 | +0.540 | 1.01073 |
| 22, rainbow, nine or lower | 36.144 | 50.334 | -14.190 | 0.71808 |
| 22, two-tone | 46.574 | 50.334 | -3.760 | 0.92530 |
| 22, monotone | 48.091 | 50.334 | -2.243 | 0.95544 |
| 22, paired | 50.781 | 50.334 | +0.447 | 1.00888 |
| 75s, all flops | 52.035 | 43.676 | +8.359 | 1.19139 |
| 75s, rainbow, ten or higher | 49.126 | 43.676 | +5.450 | 1.12478 |
| 75s, rainbow, nine or lower | 63.856 | 43.676 | +20.180 | 1.46204 |
| 75s, two-tone | 53.426 | 43.676 | +9.750 | 1.22323 |
| 75s, monotone | 51.909 | 43.676 | +8.233 | 1.18850 |
| 75s, paired | 49.219 | 43.676 | +5.543 | 1.12691 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and 75s holds 51.89%. In 12 they do not, and it holds 52.18%. 75s does better with no shared suit, by 0.29 points.
| Deals | Specific deals | Share of deals | 22 wins | Ties | 75s wins | 22 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 46.710 | 2.805 | 50.485 | 48.113 |
| No shared suit | 12 | 50.00 | 46.435 | 2.767 | 50.798 | 47.818 |
How often this matchup comes up
The class pair covers 24 combinations of specific cards in a fixed seat order, 0.0015% of 1,624,350, and 48 (0.0030%) in either order.
A worked example
Worked example: both players commit $100, so $200 sits in the middle. Over every board, 75s' average share is $104.06 (a gain of $4.06) and 22's is $95.94 (a loss of $4.06).
Out of 1,000 deals you should see around 506 outright wins for 75s, 466 for 22, and 28 split pots.
The same matchup from the other side
75s against 22 adds nothing new: it is 52.03% for 75s and 47.97% for 22, the same figures reversed.
Keep exploring
Open the calculator with 2s2h against 7d5d 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
Nothing here is simulated. The 24 deals of 22 against 75s fall into a few suit patterns, each dealt against all 1,712,304 boards, with both best five-card hands compared on every board. Ties give each hand half a win, and the flop rows count a board under each of its ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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