33
49.47%
Wins 48.33%, ties 2.29%
75s
50.53%
Wins 49.38%, ties 2.29%
33 against 75s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 33 | 48.330 | 2.288 | 49.382 | 49.474 |
| 75s | 49.382 | 2.288 | 48.330 | 50.526 |
One side is a pocket pair, the other 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.
This is close to even money, with 75s a little ahead. Ties are part of the picture: 2.29% of boards end in a split pot, and each side counts that as half a win.
33 ranks number 66 of 169 starting hands, and 75s ranks number 124, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 33 | 19,861,000 | 940,000 | 20,294,000 |
| 75s | 20,294,000 | 940,000 | 19,861,000 |
The total is exact: 24 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and 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 | 0.979 | 2.069 | 2.025 | 1.021 |
| 75s | 1.021 | 2.025 | 2.069 | 0.979 |
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
Across the five flop textures 75s' equity moves by 13.80 points, from 47.00% on paired flops to 60.80% on low rainbow flops (nine high or lower). Rainbow flops topped by a ten or better and paired flops favor 33, the hand that is behind overall.
| Flop | Share of flops | 33 wins | Ties | 75s wins | 33 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.844 | 51.338 | 1.338 | 47.324 | 52.007 |
| Rainbow, nine or lower | 5.065 | 38.749 | 0.913 | 60.338 | 39.205 |
| Two-tone | 46.545 | 47.298 | 1.204 | 51.498 | 47.900 |
| Monotone | 5.212 | 47.278 | 3.893 | 48.829 | 49.225 |
| Paired | 17.334 | 49.733 | 6.536 | 43.731 | 53.001 |
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
Start from the random-hand figures, 53.69% for 33 and 43.68% for 75s. This opponent changes them by -4.22 and +6.85 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 33, all flops | 49.474 | 53.693 | -4.219 | 0.92142 |
| 33, rainbow, ten or higher | 52.007 | 53.693 | -1.686 | 0.96860 |
| 33, rainbow, nine or lower | 39.205 | 53.693 | -14.488 | 0.73017 |
| 33, two-tone | 47.900 | 53.693 | -5.793 | 0.89211 |
| 33, monotone | 49.225 | 53.693 | -4.468 | 0.91679 |
| 33, paired | 53.001 | 53.693 | -0.692 | 0.98711 |
| 75s, all flops | 50.526 | 43.676 | +6.850 | 1.15684 |
| 75s, rainbow, ten or higher | 47.993 | 43.676 | +4.317 | 1.09884 |
| 75s, rainbow, nine or lower | 60.795 | 43.676 | +17.119 | 1.39195 |
| 75s, two-tone | 52.100 | 43.676 | +8.424 | 1.19287 |
| 75s, monotone | 50.775 | 43.676 | +7.099 | 1.16254 |
| 75s, paired | 46.999 | 43.676 | +3.323 | 1.07608 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, 75s has 50.39%; looking only at deals where they do not, 50.66%. 75s does better with no shared suit, by 0.27 points.
| Deals | Specific deals | Share of deals | 33 wins | Ties | 75s wins | 33 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 48.448 | 2.316 | 49.236 | 49.606 |
| No shared suit | 12 | 50.00 | 48.212 | 2.260 | 49.528 | 49.342 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 24 are 33 in one seat and 75s in the other (0.0015%); with the seats swapped too, 48 (0.0030%).
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says 75s gets $101.06 of it on average and 33 gets $98.94.
Out of 1,000 deals you should see around 494 outright wins for 75s, 483 for 33, and 23 split pots.
The same matchup from the other side
75s against 33 adds nothing new: it is 50.53% for 75s and 49.47% for 33, the same figures reversed.
Keep exploring
Try 3s3h against 7d5d 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 33 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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