A3s
37.40%
Wins 36.44%, ties 1.91%
33
62.60%
Wins 61.65%, ties 1.91%
A3s against 33: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A3s | 36.441 | 1.909 | 61.650 | 37.395 |
| 33 | 61.650 | 1.909 | 36.441 | 62.605 |
We compare a suited hand with a pocket pair. The pair already holds one of the other hand's ranks, and that overlap cuts down the cards the other hand can pair with.
That is a modest edge, the kind that shows up over many hands and is easy to miss in one. 1.91% of boards are ties, so the equity of each hand is its win rate plus half of that.
In the ranking of all 169 starting hands, A3s is number 38 and 33 is number 66.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A3s | 7,488,000 | 392,000 | 12,668,000 |
| 33 | 12,668,000 | 392,000 | 7,488,000 |
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) |
|---|---|---|---|---|
| A3s | 0.597 | 2.744 | 1.622 | 1.674 |
| 33 | 1.674 | 1.622 | 2.744 | 0.597 |
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
By flop texture, 33's equity runs from 59.60% on monotone flops up to 76.62% on low rainbow flops (nine high or lower). 33 stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | A3s wins | Ties | 33 wins | A3s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.197 | 36.714 | 1.192 | 62.094 | 37.310 |
| Rainbow, nine or lower | 5.585 | 20.572 | 5.617 | 73.811 | 23.380 |
| Two-tone | 46.236 | 37.220 | 1.801 | 60.979 | 38.121 |
| Monotone | 5.151 | 38.564 | 3.670 | 57.766 | 40.399 |
| Paired | 17.831 | 38.391 | 1.533 | 60.076 | 39.158 |
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
Start from the random-hand figures, 58.22% for A3s and 53.69% for 33. This opponent changes them by -20.82 and +8.91 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A3s, all flops | 37.395 | 58.220 | -20.825 | 0.64231 |
| A3s, rainbow, ten or higher | 37.310 | 58.220 | -20.910 | 0.64085 |
| A3s, rainbow, nine or lower | 23.380 | 58.220 | -34.840 | 0.40158 |
| A3s, two-tone | 38.121 | 58.220 | -20.099 | 0.65477 |
| A3s, monotone | 40.399 | 58.220 | -17.821 | 0.69390 |
| A3s, paired | 39.158 | 58.220 | -19.062 | 0.67259 |
| 33, all flops | 62.605 | 53.693 | +8.912 | 1.16598 |
| 33, rainbow, ten or higher | 62.690 | 53.693 | +8.997 | 1.16756 |
| 33, rainbow, nine or lower | 76.620 | 53.693 | +22.927 | 1.42700 |
| 33, two-tone | 61.879 | 53.693 | +8.186 | 1.15246 |
| 33, monotone | 59.601 | 53.693 | +5.908 | 1.11003 |
| 33, paired | 60.842 | 53.693 | +7.149 | 1.13315 |
Does a shared suit matter?
A3s and 33 never overlap in suit in a legal deal, so the whole matchup sits in the no-shared-suit row.
| Deals | Specific deals | Share of deals | A3s wins | Ties | 33 wins | A3s equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 36.441 | 1.909 | 61.650 | 37.395 |
How often this matchup comes up
Exactly 12 specific deals fit this matchup in one seat order, which is 0.0007% of 1,624,350; both orders together give 24, or 0.0015%.
A worked example
With $100 from each side, the $200 pot is split on average as $125.20 for 33 and $74.80 for A3s; the first side gains $25.20 per all-in and the second gives up $25.20.
Run 1,000 deals and the tally comes out near 617 for 33, 364 for A3s and 19 ties.
The same matchup from the other side
33 against A3s adds nothing new: it is 62.60% for 33 and 37.40% for A3s, the same figures reversed.
Keep exploring
The calculator link fills in As3s against 3h3d, 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
Nothing here is simulated. The 12 deals of A3s against 33 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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