33
49.80%
Wins 48.36%, ties 2.88%
54s
50.20%
Wins 48.76%, ties 2.88%
33 against 54s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 33 | 48.362 | 2.879 | 48.759 | 49.801 |
| 54s | 48.759 | 2.879 | 48.362 | 50.199 |
Here a pocket pair (33) meets a suited hand (54s). This is a pair against two overcards, a matchup that stays close because the other hand only needs one of its ranks to appear.
54s leads by less than 1 points of equity, so the result of any one deal is close to a toss-up. Ties are 2.88% of the outcomes here; each tied board gives both hands half the pot.
Among the 169 starting hands, 33 is number 66 and 54s is number 136 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 33 | 19,875,000 | 1,183,000 | 20,038,000 |
| 54s | 20,038,000 | 1,183,000 | 19,875,000 |
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 | 0.992 | 2.068 | 2.051 | 1.008 |
| 54s | 1.008 | 2.051 | 2.068 | 0.992 |
The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.
Who is ahead on which flops
Across the five flop textures 54s' equity moves by 15.80 points, from 45.22% on paired flops to 61.02% on low rainbow flops (nine high or lower). The lead reverses on rainbow flops topped by a ten or better and paired flops: there 33 is the favorite even though 54s is ahead overall.
| Flop | Share of flops | 33 wins | Ties | 54s wins | 33 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.844 | 51.290 | 1.635 | 47.075 | 52.108 |
| Rainbow, nine or lower | 5.065 | 38.290 | 1.389 | 60.321 | 38.985 |
| Two-tone | 46.545 | 47.165 | 1.512 | 51.323 | 47.921 |
| Monotone | 5.212 | 46.994 | 4.242 | 48.764 | 49.115 |
| Paired | 17.334 | 50.565 | 8.428 | 41.007 | 54.779 |
Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.
Compared with a random hand
How much does the opponent matter? Compared with its random-hand 53.69%, 33 changes by -3.89 points, and 54s, from 41.45%, by +8.75.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 33, all flops | 49.801 | 53.693 | -3.892 | 0.92751 |
| 33, rainbow, ten or higher | 52.108 | 53.693 | -1.585 | 0.97048 |
| 33, rainbow, nine or lower | 38.985 | 53.693 | -14.708 | 0.72607 |
| 33, two-tone | 47.921 | 53.693 | -5.772 | 0.89250 |
| 33, monotone | 49.115 | 53.693 | -4.578 | 0.91474 |
| 33, paired | 54.779 | 53.693 | +1.086 | 1.02023 |
| 54s, all flops | 50.199 | 41.453 | +8.746 | 1.21099 |
| 54s, rainbow, ten or higher | 47.892 | 41.453 | +6.439 | 1.15533 |
| 54s, rainbow, nine or lower | 61.015 | 41.453 | +19.562 | 1.47191 |
| 54s, two-tone | 52.079 | 41.453 | +10.626 | 1.25634 |
| 54s, monotone | 50.885 | 41.453 | +9.432 | 1.22753 |
| 54s, paired | 45.221 | 41.453 | +3.768 | 1.09090 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and 54s holds 50.10%. In 12 they do not, and it holds 50.29%. The two rows differ by only 0.19 points, so suits barely change this matchup.
| Deals | Specific deals | Share of deals | 33 wins | Ties | 54s wins | 33 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 48.442 | 2.907 | 48.651 | 49.896 |
| No shared suit | 12 | 50.00 | 48.282 | 2.851 | 48.867 | 49.707 |
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 54s takes back $100.40 of it, which is $0.40 more than it put in, and 33 takes back $99.60, $0.40 less than it put in.
Over a long run, 1,000 deals split into about 487 for 54s, 484 for 33 and 29 tied.
The same matchup from the other side
Read it from the other side: 54s against 33 is the same matchup with the numbers swapped, so 54s holds 50.20% and 33 holds 49.80%. That address sends you back to this page.
Keep exploring
The calculator link fills in 3s3h against 5d4d, 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 24 specific deals of 33 against 54s, 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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