A9s
61.67%
Wins 61.39%, ties 0.56%
54s
38.33%
Wins 38.05%, ties 0.56%
A9s against 54s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A9s | 61.390 | 0.555 | 38.055 | 61.667 |
| 54s | 38.055 | 0.555 | 61.390 | 38.333 |
A9s meets 54s, and both are suited hands. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.
That is a modest edge, the kind that shows up over many hands and is easy to miss in one. 0.56% of boards are ties, so the equity of each hand is its win rate plus half of that.
The hand ranking puts A9s at 18 and 54s at 136 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A9s | 16,819,000 | 152,000 | 10,426,000 |
| 54s | 10,426,000 | 152,000 | 16,819,000 |
The board total is exact, 16 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) |
|---|---|---|---|---|
| A9s | 1.609 | 1.629 | 2.628 | 0.622 |
| 54s | 0.622 | 2.628 | 1.629 | 1.609 |
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
Break the boards down by their first three cards and A9s is strongest on rainbow flops topped by a ten or better (65.05%) and weakest on low rainbow flops (nine high or lower) (46.36%). 54s is ahead on low rainbow flops (nine high or lower), even though it trails A9s when every flop is counted.
| Flop | Share of flops | A9s wins | Ties | 54s wins | A9s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 64.925 | 0.239 | 34.836 | 65.045 |
| Rainbow, nine or lower | 5.689 | 45.952 | 0.815 | 53.233 | 46.359 |
| Two-tone | 46.727 | 60.678 | 0.313 | 39.009 | 60.834 |
| Monotone | 5.273 | 57.242 | 3.551 | 39.207 | 59.017 |
| Paired | 17.091 | 64.538 | 0.673 | 34.789 | 64.874 |
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
Against one random hand instead, A9s holds 62.78% and 54s holds 41.45%. Facing each other changes that by -1.11 points for A9s and -3.12 points for 54s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A9s, all flops | 61.667 | 62.781 | -1.114 | 0.98226 |
| A9s, rainbow, ten or higher | 65.045 | 62.781 | +2.264 | 1.03606 |
| A9s, rainbow, nine or lower | 46.359 | 62.781 | -16.422 | 0.73842 |
| A9s, two-tone | 60.834 | 62.781 | -1.947 | 0.96899 |
| A9s, monotone | 59.017 | 62.781 | -3.764 | 0.94005 |
| A9s, paired | 64.874 | 62.781 | +2.093 | 1.03334 |
| 54s, all flops | 38.333 | 41.453 | -3.120 | 0.92473 |
| 54s, rainbow, ten or higher | 34.955 | 41.453 | -6.498 | 0.84324 |
| 54s, rainbow, nine or lower | 53.641 | 41.453 | +12.188 | 1.29402 |
| 54s, two-tone | 39.166 | 41.453 | -2.287 | 0.94483 |
| 54s, monotone | 40.983 | 41.453 | -0.470 | 0.98866 |
| 54s, paired | 35.126 | 41.453 | -6.327 | 0.84737 |
Does a shared suit matter?
Split by suits, the deals give A9s 63.84% when the hands overlap in a suit and 60.94% when they do not. A9s does better with a shared suit, by 2.90 points.
| Deals | Specific deals | Share of deals | A9s wins | Ties | 54s wins | A9s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 63.525 | 0.634 | 35.841 | 63.842 |
| No shared suit | 12 | 75.00 | 60.678 | 0.529 | 38.793 | 60.942 |
How often this matchup comes up
This page stands for 16 specific-card matchups (0.0010% of 1,624,350 ordered deals), or 32 once you count the seats both ways (0.0020%).
A worked example
With $100 from each side, the $200 pot is split on average as $123.34 for A9s and $76.66 for 54s; the first side gains $23.34 per all-in and the second gives up $23.34.
Think in thousands: about 614 of 1,000 go to A9s, about 381 go to 54s, and about 5 are chopped.
The same matchup from the other side
One page covers both views. From 54s' side the equity is 38.33%, and from A9s' side it is 61.67%.
Keep exploring
Open the calculator with As9s against 5h4h already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.
How this was computed
Method: exact enumeration. The 16 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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