33
48.27%
Wins 47.28%, ties 1.99%
86s
51.73%
Wins 50.73%, ties 1.99%
33 against 86s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 33 | 47.278 | 1.989 | 50.733 | 48.273 |
| 86s | 50.733 | 1.989 | 47.278 | 51.727 |
Here a pocket pair (33) meets a suited hand (86s). One hand holds a pair and the other holds two cards that both outrank it, which keeps the equity closer than most people expect.
With only 3.46 points between them, the board decides this matchup far more than the cards in hand. A split pot comes up on 1.99% of boards, so the wins and the equity differ by half of that.
For context, 33 sits at number 66 of 169 starting hands and 86s at number 110 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 33 | 19,429,000 | 817,000 | 20,849,000 |
| 86s | 20,849,000 | 817,000 | 19,429,000 |
The board total is exact, 24 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| 33 | 0.933 | 2.115 | 1.971 | 1.072 |
| 86s | 1.072 | 1.971 | 2.115 | 0.933 |
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
86s prefers low rainbow flops (nine high or lower), where it holds 61.00%, and likes paired flops least, where it holds 48.43%. 33 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 | 33 wins | Ties | 86s wins | 33 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.844 | 49.979 | 1.143 | 48.878 | 50.551 |
| Rainbow, nine or lower | 5.065 | 38.598 | 0.812 | 60.590 | 39.004 |
| Two-tone | 46.545 | 46.244 | 1.036 | 52.720 | 46.762 |
| Monotone | 5.212 | 46.630 | 3.746 | 49.624 | 48.503 |
| Paired | 17.334 | 48.761 | 5.621 | 45.618 | 51.572 |
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
Compared with a random opponent, this matchup shifts 33 from 53.69% by -5.42 points and 86s from 46.24% by +5.49 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 33, all flops | 48.273 | 53.693 | -5.420 | 0.89906 |
| 33, rainbow, ten or higher | 50.551 | 53.693 | -3.142 | 0.94148 |
| 33, rainbow, nine or lower | 39.004 | 53.693 | -14.689 | 0.72643 |
| 33, two-tone | 46.762 | 53.693 | -6.931 | 0.87091 |
| 33, monotone | 48.503 | 53.693 | -5.190 | 0.90334 |
| 33, paired | 51.572 | 53.693 | -2.121 | 0.96050 |
| 86s, all flops | 51.727 | 46.243 | +5.484 | 1.11859 |
| 86s, rainbow, ten or higher | 49.449 | 46.243 | +3.206 | 1.06933 |
| 86s, rainbow, nine or lower | 60.996 | 46.243 | +14.753 | 1.31903 |
| 86s, two-tone | 53.238 | 46.243 | +6.995 | 1.15127 |
| 86s, monotone | 51.497 | 46.243 | +5.254 | 1.11362 |
| 86s, paired | 48.428 | 46.243 | +2.185 | 1.04725 |
Does a shared suit matter?
The suit split reads 51.58% for 86s with a shared suit and 51.87% without one. 86s does better with no shared suit, by 0.29 points.
| Deals | Specific deals | Share of deals | 33 wins | Ties | 86s wins | 33 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 47.409 | 2.016 | 50.575 | 48.417 |
| No shared suit | 12 | 50.00 | 47.148 | 1.960 | 50.892 | 48.128 |
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
With $100 from each side, the $200 pot is split on average as $103.46 for 86s and $96.54 for 33; the first side gains $3.46 per all-in and the second gives up $3.46.
A thousand deals look like this: 86s takes 507, 33 takes 473, 20 are ties.
The same matchup from the other side
86s versus 33 is this same page seen from the other hand: 51.73% for 86s, 48.27% for 33.
Keep exploring
The calculator link fills in 3s3h against 8d6d, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.
How this was computed
This is an exact count with no sampling. For the 24 ways to deal one 33 and one 86s without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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