33
48.24%
Wins 47.39%, ties 1.71%
97s
51.76%
Wins 50.90%, ties 1.71%
33 against 97s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 33 | 47.387 | 1.707 | 50.906 | 48.241 |
| 97s | 50.906 | 1.707 | 47.387 | 51.759 |
Here a pocket pair (33) meets a suited hand (97s). This is a pair against two overcards, a matchup that stays close because the other hand only needs one of its ranks to appear.
With only 3.52 points between them, the board decides this matchup far more than the cards in hand. Of every 100 boards, about 1.71 are split pots, and the equity figures already include them.
33 ranks number 66 of 169 starting hands, and 97s ranks number 94, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 33 | 19,474,000 | 701,000 | 20,920,000 |
| 97s | 20,920,000 | 701,000 | 19,474,000 |
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 | 0.932 | 2.110 | 1.964 | 1.073 |
| 97s | 1.073 | 1.964 | 2.110 | 0.932 |
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
Low rainbow flops (nine high or lower) are the best for 97s (57.72%); paired flops are the worst (48.87%). 33 is ahead on paired flops, even though it trails 97s when every flop is counted.
| Flop | Share of flops | 33 wins | Ties | 97s wins | 33 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.844 | 49.485 | 0.992 | 49.523 | 49.981 |
| Rainbow, nine or lower | 5.065 | 41.978 | 0.599 | 57.423 | 42.278 |
| Two-tone | 46.545 | 46.373 | 0.885 | 52.742 | 46.815 |
| Monotone | 5.212 | 46.729 | 3.626 | 49.645 | 48.542 |
| Paired | 17.334 | 48.762 | 4.727 | 46.511 | 51.126 |
Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.
Compared with a random hand
Each hand has a baseline against a random hand: 53.69% for 33, 49.12% for 97s. Here the change is -5.45 and +2.64 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 33, all flops | 48.241 | 53.693 | -5.452 | 0.89846 |
| 33, rainbow, ten or higher | 49.981 | 53.693 | -3.712 | 0.93087 |
| 33, rainbow, nine or lower | 42.278 | 53.693 | -11.415 | 0.78740 |
| 33, two-tone | 46.815 | 53.693 | -6.878 | 0.87190 |
| 33, monotone | 48.542 | 53.693 | -5.151 | 0.90407 |
| 33, paired | 51.126 | 53.693 | -2.567 | 0.95219 |
| 97s, all flops | 51.759 | 49.118 | +2.641 | 1.05377 |
| 97s, rainbow, ten or higher | 50.019 | 49.118 | +0.901 | 1.01834 |
| 97s, rainbow, nine or lower | 57.722 | 49.118 | +8.604 | 1.17517 |
| 97s, two-tone | 53.185 | 49.118 | +4.067 | 1.08280 |
| 97s, monotone | 51.458 | 49.118 | +2.340 | 1.04764 |
| 97s, paired | 48.874 | 49.118 | -0.244 | 0.99503 |
Does a shared suit matter?
Does suit overlap move the numbers? 97s has 51.61% when the hands share a suit and 51.91% when they do not. 97s does better with no shared suit, by 0.30 points.
| Deals | Specific deals | Share of deals | 33 wins | Ties | 97s wins | 33 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 47.519 | 1.736 | 50.745 | 48.387 |
| No shared suit | 12 | 50.00 | 47.256 | 1.678 | 51.066 | 48.095 |
How often this matchup comes up
You will meet this exact matchup 0.0030% of the time in a random heads-up deal: 48 of 1,624,350, counting either seat order.
A worked example
Put $100 each into a $200 pot and deal every board once: 97s averages $103.52 back, ahead of its $100 by $3.52, while 33 averages $96.48, short of its $100 by $3.52.
Over a long run, 1,000 deals split into about 509 for 97s, 474 for 33 and 17 tied.
The same matchup from the other side
If you came looking for 97s against 33, the numbers are the same with the hands swapped: 51.76% and 48.24%.
Keep exploring
3s3h against 9d7d 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 24 specific deals of 33 against 97s, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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