33
60.86%
Wins 58.57%, ties 4.57%
53s
39.14%
Wins 36.86%, ties 4.57%
33 against 53s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 33 | 58.571 | 4.569 | 36.860 | 60.856 |
| 53s | 36.860 | 4.569 | 58.571 | 39.144 |
33, a pocket pair, plays 53s, a suited hand. One hand holds a card of the same rank as the pair, which removes a card the pair needs and makes the pair a bigger favorite.
A 21.72 point lead is real, and 53s still takes about 368 of every 1,000 deals outright. A split pot comes up on 4.57% of boards, so the wins and the equity differ by half of that.
33 ranks number 66 of 169 starting hands, and 53s ranks number 146, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 33 | 12,035,000 | 939,000 | 7,574,000 |
| 53s | 7,574,000 | 939,000 | 12,035,000 |
The total is exact: 12 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 | 1.555 | 1.707 | 2.713 | 0.643 |
| 53s | 0.643 | 2.713 | 1.707 | 1.555 |
In the last column, a pot-to-call ratio at or above the figure makes a call break even or better at this equity.
Who is ahead on which flops
The flop changes the picture. 33 does best on rainbow flops topped by a ten or better, at 65.03%, and worst on low rainbow flops (nine high or lower), at 47.38%. 53s is ahead on low rainbow flops (nine high or lower), even though it trails 33 when every flop is counted.
| Flop | Share of flops | 33 wins | Ties | 53s wins | 33 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.786 | 63.665 | 2.724 | 33.611 | 65.027 |
| Rainbow, nine or lower | 4.995 | 44.564 | 5.626 | 49.810 | 47.377 |
| Two-tone | 46.236 | 57.694 | 3.001 | 39.305 | 59.195 |
| Monotone | 5.152 | 55.634 | 4.859 | 39.507 | 58.064 |
| Paired | 17.831 | 58.254 | 10.920 | 30.826 | 63.714 |
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
Each hand has a baseline against a random hand: 53.69% for 33, 39.69% for 53s. Here the change is +7.17 and -0.55 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 33, all flops | 60.856 | 53.693 | +7.163 | 1.13341 |
| 33, rainbow, ten or higher | 65.027 | 53.693 | +11.334 | 1.21109 |
| 33, rainbow, nine or lower | 47.377 | 53.693 | -6.316 | 0.88237 |
| 33, two-tone | 59.195 | 53.693 | +5.502 | 1.10247 |
| 33, monotone | 58.064 | 53.693 | +4.371 | 1.08141 |
| 33, paired | 63.714 | 53.693 | +10.021 | 1.18664 |
| 53s, all flops | 39.144 | 39.693 | -0.549 | 0.98617 |
| 53s, rainbow, ten or higher | 34.973 | 39.693 | -4.720 | 0.88109 |
| 53s, rainbow, nine or lower | 52.623 | 39.693 | +12.930 | 1.32575 |
| 53s, two-tone | 40.805 | 39.693 | +1.112 | 1.02802 |
| 53s, monotone | 41.936 | 39.693 | +2.243 | 1.05651 |
| 53s, paired | 36.286 | 39.693 | -3.407 | 0.91417 |
Does a shared suit matter?
Every legal deal of 33 against 53s leaves the hands with no suit in common, so the suit split does not apply here.
| Deals | Specific deals | Share of deals | 33 wins | Ties | 53s wins | 33 equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 58.571 | 4.569 | 36.860 | 60.856 |
How often this matchup comes up
The class pair covers 12 combinations of specific cards in a fixed seat order, 0.0007% of 1,624,350, and 24 (0.0015%) in either order.
A worked example
With $100 from each side, the $200 pot is split on average as $121.72 for 33 and $78.28 for 53s; the first side gains $21.72 per all-in and the second gives up $21.72.
Out of 1,000 deals you should see around 586 outright wins for 33, 368 for 53s, and 46 split pots.
The same matchup from the other side
53s against 33 adds nothing new: it is 39.14% for 53s and 60.86% for 33, the same figures reversed.
Keep exploring
Try 3s3h against 5d3d 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
We counted every case. Each suit pattern of the 12 specific 33 against 53s deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
Bring your own hands to a session
Review the spots you actually play against these numbers in a Game Assessment, and leave with a one-page written plan.
Book a session