22
47.87%
Wins 46.67%, ties 2.41%
86s
52.13%
Wins 50.92%, ties 2.41%
22 against 86s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 22 | 46.667 | 2.408 | 50.925 | 47.871 |
| 86s | 50.925 | 2.408 | 46.667 | 52.129 |
We compare a pocket pair with a suited hand. One hand holds a pair and the other holds two cards that both outrank it, which keeps the equity closer than most people expect.
86s leads by less than 5 points of equity, so the result of any one deal is close to a toss-up. Split pots make up 2.41% of the boards, and both equity figures count them as half a win each.
By strength against a random hand, 22 holds place 87 of 169 and 86s holds place 110.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 22 | 19,178,000 | 990,000 | 20,928,000 |
| 86s | 20,928,000 | 990,000 | 19,178,000 |
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 | 0.918 | 2.143 | 1.964 | 1.089 |
| 86s | 1.089 | 1.964 | 2.143 | 0.918 |
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, 86s peaks at 61.26% on low rainbow flops (nine high or lower) and bottoms out at 49.63% on rainbow flops topped by a ten or better. 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 | 86s wins | 22 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.844 | 49.694 | 1.357 | 48.949 | 50.373 |
| Rainbow, nine or lower | 5.065 | 38.301 | 0.885 | 60.814 | 38.744 |
| Two-tone | 46.545 | 45.969 | 1.219 | 52.812 | 46.578 |
| Monotone | 5.212 | 45.870 | 4.433 | 49.697 | 48.086 |
| Paired | 17.334 | 46.712 | 7.004 | 46.284 | 50.214 |
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
How much does the opponent matter? Compared with its random-hand 50.33%, 22 changes by -2.46 points, and 86s, from 46.24%, by +5.89.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 22, all flops | 47.871 | 50.334 | -2.463 | 0.95107 |
| 22, rainbow, ten or higher | 50.373 | 50.334 | +0.039 | 1.00077 |
| 22, rainbow, nine or lower | 38.744 | 50.334 | -11.590 | 0.76974 |
| 22, two-tone | 46.578 | 50.334 | -3.756 | 0.92538 |
| 22, monotone | 48.086 | 50.334 | -2.248 | 0.95534 |
| 22, paired | 50.214 | 50.334 | -0.120 | 0.99762 |
| 86s, all flops | 52.129 | 46.243 | +5.886 | 1.12728 |
| 86s, rainbow, ten or higher | 49.627 | 46.243 | +3.384 | 1.07318 |
| 86s, rainbow, nine or lower | 61.256 | 46.243 | +15.013 | 1.32465 |
| 86s, two-tone | 53.422 | 46.243 | +7.179 | 1.15525 |
| 86s, monotone | 51.914 | 46.243 | +5.671 | 1.12263 |
| 86s, paired | 49.786 | 46.243 | +3.543 | 1.07662 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common 86s has 51.98% equity, and with none in common it has 52.28%. 86s does better with no shared suit, by 0.30 points.
| Deals | Specific deals | Share of deals | 22 wins | Ties | 86s wins | 22 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 46.807 | 2.426 | 50.767 | 48.020 |
| No shared suit | 12 | 50.00 | 46.527 | 2.389 | 51.084 | 47.722 |
How often this matchup comes up
How often does it happen? 24 of the 1,624,350 ordered deals (0.0015%) are 22 against 86s, and 48 (0.0030%) if either hand may sit in either seat.
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average 86s takes back $104.26 of it, which is $4.26 more than it put in, and 22 takes back $95.74, $4.26 less than it put in.
Over a long run, 1,000 deals split into about 509 for 86s, 467 for 22 and 24 tied.
The same matchup from the other side
If you came looking for 86s against 22, the numbers are the same with the hands swapped: 52.13% and 47.87%.
Keep exploring
Try 2s2h against 8d6d in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.
How this was computed
Nothing here is simulated. The 24 deals of 22 against 86s 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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