33
47.04%
Wins 46.06%, ties 1.96%
87s
52.96%
Wins 51.98%, ties 1.96%
33 against 87s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 33 | 46.055 | 1.960 | 51.985 | 47.035 |
| 87s | 51.985 | 1.960 | 46.055 | 52.965 |
The first hand is a pocket pair; the second is a suited hand. This is a pair against two overcards, a matchup that stays close because the other hand only needs one of its ranks to appear.
That is a slim edge: neither hand is far ahead. A split pot comes up on 1.96% of boards, so the wins and the equity differ by half of that.
33 ranks number 66 of 169 starting hands, and 87s ranks number 100, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 33 | 18,926,000 | 805,000 | 21,363,000 |
| 87s | 21,363,000 | 805,000 | 18,926,000 |
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) |
|---|---|---|---|---|
| 33 | 0.888 | 2.171 | 1.924 | 1.126 |
| 87s | 1.126 | 1.924 | 2.171 | 0.888 |
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
Low rainbow flops (nine high or lower) are the best for 87s (61.78%); paired flops are the worst (49.28%). On paired flops the numbers flip and 33 is the one ahead.
| Flop | Share of flops | 33 wins | Ties | 87s wins | 33 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.844 | 48.432 | 1.139 | 50.429 | 49.001 |
| Rainbow, nine or lower | 5.065 | 37.856 | 0.725 | 61.419 | 38.218 |
| Two-tone | 46.545 | 44.954 | 1.021 | 54.025 | 45.465 |
| Monotone | 5.212 | 45.732 | 3.735 | 50.533 | 47.599 |
| Paired | 17.334 | 47.955 | 5.535 | 46.510 | 50.723 |
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 33 53.69% and 87s 47.94%. Against each other the change is -6.65 points for 33 and +5.02 for 87s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 33, all flops | 47.035 | 53.693 | -6.658 | 0.87600 |
| 33, rainbow, ten or higher | 49.001 | 53.693 | -4.692 | 0.91261 |
| 33, rainbow, nine or lower | 38.218 | 53.693 | -15.475 | 0.71179 |
| 33, two-tone | 45.465 | 53.693 | -8.228 | 0.84676 |
| 33, monotone | 47.599 | 53.693 | -6.094 | 0.88650 |
| 33, paired | 50.723 | 53.693 | -2.970 | 0.94469 |
| 87s, all flops | 52.965 | 47.936 | +5.029 | 1.10491 |
| 87s, rainbow, ten or higher | 50.999 | 47.936 | +3.063 | 1.06390 |
| 87s, rainbow, nine or lower | 61.782 | 47.936 | +13.846 | 1.28884 |
| 87s, two-tone | 54.535 | 47.936 | +6.599 | 1.13766 |
| 87s, monotone | 52.401 | 47.936 | +4.465 | 1.09315 |
| 87s, paired | 49.277 | 47.936 | +1.341 | 1.02797 |
Does a shared suit matter?
Split by suits, the deals give 87s 52.83% when the hands overlap in a suit and 53.10% when they do not. 87s does better with no shared suit, by 0.27 points.
| Deals | Specific deals | Share of deals | 33 wins | Ties | 87s wins | 33 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 46.176 | 1.989 | 51.835 | 47.170 |
| No shared suit | 12 | 50.00 | 45.933 | 1.932 | 52.135 | 46.899 |
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
Say each player puts $100 in before the flop, making a $200 pot. On average 87s takes back $105.92 of it, which is $5.92 more than it put in, and 33 takes back $94.08, $5.92 less than it put in.
In 1,000 deals of exactly this matchup, expect about 520 won outright by 87s, about 460 won outright by 33 and about 20 split.
The same matchup from the other side
If you came looking for 87s against 33, the numbers are the same with the hands swapped: 52.96% and 47.04%.
Keep exploring
3s3h against 8d7d is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.
How this was computed
The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 24 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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