55
66.49%
Wins 66.23%, ties 0.54%
A3s
33.51%
Wins 33.23%, ties 0.54%
55 against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 55 | 66.225 | 0.535 | 33.240 | 66.492 |
| A3s | 33.240 | 0.535 | 66.225 | 33.508 |
55 and A3s are a pocket pair and a suited hand, in that order. The pair sits between the other hand's two cards: one is higher and one is lower, so the pair is exposed to the higher card.
55 is well ahead, and A3s needs a specific kind of board to catch up. Of every 100 boards, about 0.54 are split pots, and the equity figures already include them.
The hand ranking puts 55 at 27 and A3s at 38 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 55 | 27,215,000 | 220,000 | 13,660,000 |
| A3s | 13,660,000 | 220,000 | 27,215,000 |
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) |
|---|---|---|---|---|
| 55 | 1.984 | 1.510 | 3.008 | 0.504 |
| A3s | 0.504 | 3.008 | 1.510 | 1.984 |
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
Split by what the flop looks like, 55 peaks at 81.39% on low rainbow flops (nine high or lower) and bottoms out at 62.79% on monotone flops. 55 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 | 55 wins | Ties | A3s wins | 55 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 66.095 | 0.291 | 33.614 | 66.241 |
| Rainbow, nine or lower | 5.689 | 80.944 | 0.896 | 18.160 | 81.392 |
| Two-tone | 46.545 | 65.545 | 0.367 | 34.088 | 65.729 |
| Monotone | 5.212 | 61.474 | 2.638 | 35.888 | 62.793 |
| Paired | 17.334 | 64.833 | 0.592 | 34.575 | 65.129 |
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, 60.33% for 55 and 58.22% for A3s. This opponent changes them by +6.16 and -24.71 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 55, all flops | 66.492 | 60.325 | +6.167 | 1.10223 |
| 55, rainbow, ten or higher | 66.241 | 60.325 | +5.916 | 1.09807 |
| 55, rainbow, nine or lower | 81.392 | 60.325 | +21.067 | 1.34923 |
| 55, two-tone | 65.729 | 60.325 | +5.404 | 1.08958 |
| 55, monotone | 62.793 | 60.325 | +2.468 | 1.04091 |
| 55, paired | 65.129 | 60.325 | +4.804 | 1.07964 |
| A3s, all flops | 33.508 | 58.220 | -24.712 | 0.57554 |
| A3s, rainbow, ten or higher | 33.759 | 58.220 | -24.461 | 0.57985 |
| A3s, rainbow, nine or lower | 18.608 | 58.220 | -39.612 | 0.31962 |
| A3s, two-tone | 34.271 | 58.220 | -23.949 | 0.58865 |
| A3s, monotone | 37.207 | 58.220 | -21.013 | 0.63908 |
| A3s, paired | 34.871 | 58.220 | -23.349 | 0.59895 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, 55 has 66.77%; looking only at deals where they do not, 66.22%. 55 does better with a shared suit, by 0.55 points.
| Deals | Specific deals | Share of deals | 55 wins | Ties | A3s wins | 55 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 66.477 | 0.576 | 32.947 | 66.765 |
| No shared suit | 12 | 50.00 | 65.971 | 0.495 | 33.534 | 66.219 |
How often this matchup comes up
Exactly 24 specific deals fit this matchup in one seat order, which is 0.0015% of 1,624,350; both orders together give 48, or 0.0030%.
A worked example
With $100 from each side, the $200 pot is split on average as $132.98 for 55 and $67.02 for A3s; the first side gains $32.98 per all-in and the second gives up $32.98.
Run 1,000 deals and the tally comes out near 662 for 55, 333 for A3s and 5 ties.
The same matchup from the other side
Swap the hands and you get A3s with 33.51% against 55 with 66.49%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
Try 5s5h against Ad3d 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
Each figure is a complete count over boards. Take the 24 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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