55
66.31%
Wins 66.05%, ties 0.53%
A4s
33.69%
Wins 33.42%, ties 0.53%
55 against A4s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 55 | 66.049 | 0.530 | 33.421 | 66.314 |
| A4s | 33.421 | 0.530 | 66.049 | 33.686 |
55, a pocket pair, plays A4s, a suited hand. One of the other hand's cards outranks the pair and one is below it, which makes this a closer race than a pair against two small cards.
55 is well ahead, and A4s needs a specific kind of board to catch up. Of every 100 boards, about 0.53 are split pots, and the equity figures already include them.
55 ranks number 27 of 169 starting hands, and A4s ranks number 35, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 55 | 27,143,000 | 218,000 | 13,734,000 |
| A4s | 13,734,000 | 218,000 | 27,143,000 |
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 | 1.969 | 1.514 | 2.992 | 0.508 |
| A4s | 0.508 | 2.992 | 1.514 | 1.969 |
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 55's equity moves by 18.08 points, from 62.62% on monotone flops to 80.70% on low rainbow flops (nine high or lower). 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 | A4s wins | 55 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 65.964 | 0.291 | 33.745 | 66.110 |
| Rainbow, nine or lower | 5.689 | 80.274 | 0.853 | 18.873 | 80.701 |
| Two-tone | 46.545 | 65.335 | 0.361 | 34.304 | 65.516 |
| Monotone | 5.212 | 61.302 | 2.635 | 36.063 | 62.619 |
| Paired | 17.334 | 64.847 | 0.592 | 34.561 | 65.143 |
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
Each hand has a baseline against a random hand: 60.33% for 55, 59.03% for A4s. Here the change is +5.98 and -25.34 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 55, all flops | 66.314 | 60.325 | +5.989 | 1.09928 |
| 55, rainbow, ten or higher | 66.110 | 60.325 | +5.785 | 1.09590 |
| 55, rainbow, nine or lower | 80.701 | 60.325 | +20.376 | 1.33777 |
| 55, two-tone | 65.516 | 60.325 | +5.191 | 1.08605 |
| 55, monotone | 62.619 | 60.325 | +2.294 | 1.03803 |
| 55, paired | 65.143 | 60.325 | +4.818 | 1.07987 |
| A4s, all flops | 33.686 | 59.034 | -25.348 | 0.57062 |
| A4s, rainbow, ten or higher | 33.890 | 59.034 | -25.144 | 0.57408 |
| A4s, rainbow, nine or lower | 19.299 | 59.034 | -39.735 | 0.32691 |
| A4s, two-tone | 34.484 | 59.034 | -24.550 | 0.58414 |
| A4s, monotone | 37.381 | 59.034 | -21.653 | 0.63321 |
| A4s, paired | 34.857 | 59.034 | -24.177 | 0.59046 |
Does a shared suit matter?
The suit split reads 66.58% for 55 with a shared suit and 66.05% without one. 55 does better with a shared suit, by 0.53 points.
| Deals | Specific deals | Share of deals | 55 wins | Ties | A4s wins | 55 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 66.291 | 0.570 | 33.139 | 66.576 |
| No shared suit | 12 | 50.00 | 65.806 | 0.490 | 33.704 | 66.051 |
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
Put $100 each into a $200 pot and deal every board once: 55 averages $132.62 back, ahead of its $100 by $32.62, while A4s averages $67.38, short of its $100 by $32.62.
Per 1,000 deals: 55 wins about 661, A4s wins about 334, and about 5 end in a split pot.
The same matchup from the other side
A4s versus 55 is this same page seen from the other hand: 33.69% for A4s, 66.31% for 55.
Keep exploring
Try 5s5h against Ad4d 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
Nothing here is simulated. The 24 deals of 55 against A4s 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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