AA
78.91%
Wins 78.68%, ties 0.45%
54s
21.09%
Wins 20.87%, ties 0.45%
AA against 54s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 78.679 | 0.454 | 20.867 | 78.906 |
| 54s | 20.867 | 0.454 | 78.679 | 21.094 |
The first hand is a pocket pair; the second is a suited hand. The pair outranks both of the other hand's cards, which is why the pair is a strong favorite.
AA is the clear favorite, though 54s gets there on roughly one board in 5. The tie share is 0.45%: on those boards the pot is chopped and neither hand wins outright.
Place 1 of 169 belongs to AA and place 136 belongs to 54s in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 32,333,000 | 187,000 | 8,575,000 |
| 54s | 8,575,000 | 187,000 | 32,333,000 |
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) |
|---|---|---|---|---|
| AA | 3.741 | 1.271 | 4.792 | 0.267 |
| 54s | 0.267 | 4.792 | 1.271 | 3.741 |
The final column gives the least the pot must offer for each unit called for a call to break even at this equity.
Who is ahead on which flops
Split by what the flop looks like, AA peaks at 84.31% on rainbow flops topped by a ten or better and bottoms out at 64.96% on low rainbow flops (nine high or lower). AA 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 | AA wins | Ties | 54s wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 84.171 | 0.276 | 15.553 | 84.309 |
| Rainbow, nine or lower | 6.314 | 64.440 | 1.041 | 34.519 | 64.961 |
| Two-tone | 46.545 | 76.719 | 0.402 | 22.879 | 76.920 |
| Monotone | 5.212 | 72.289 | 2.532 | 25.179 | 73.555 |
| Paired | 17.334 | 83.260 | 0.007 | 16.733 | 83.263 |
A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.
Compared with a random hand
Start from the random-hand figures, 85.20% for AA and 41.45% for 54s. This opponent changes them by -6.29 and -20.36 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 78.906 | 85.204 | -6.298 | 0.92608 |
| AA, rainbow, ten or higher | 84.309 | 85.204 | -0.895 | 0.98950 |
| AA, rainbow, nine or lower | 64.961 | 85.204 | -20.243 | 0.76242 |
| AA, two-tone | 76.920 | 85.204 | -8.284 | 0.90277 |
| AA, monotone | 73.555 | 85.204 | -11.649 | 0.86328 |
| AA, paired | 83.263 | 85.204 | -1.941 | 0.97722 |
| 54s, all flops | 21.094 | 41.453 | -20.359 | 0.50887 |
| 54s, rainbow, ten or higher | 15.691 | 41.453 | -25.762 | 0.37853 |
| 54s, rainbow, nine or lower | 35.039 | 41.453 | -6.414 | 0.84527 |
| 54s, two-tone | 23.080 | 41.453 | -18.373 | 0.55678 |
| 54s, monotone | 26.445 | 41.453 | -15.008 | 0.63795 |
| 54s, paired | 16.737 | 41.453 | -24.716 | 0.40376 |
Does a shared suit matter?
Split by suits, the deals give AA 79.46% when the hands overlap in a suit and 78.35% when they do not. AA does better with a shared suit, by 1.11 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | 54s wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 79.215 | 0.493 | 20.292 | 79.462 |
| No shared suit | 12 | 50.00 | 78.144 | 0.415 | 21.441 | 78.351 |
How often this matchup comes up
This page stands for 24 specific-card matchups (0.0015% of 1,624,350 ordered deals), or 48 once you count the seats both ways (0.0030%).
A worked example
Take a $200 pot built from $100 each. AA's equity of 78.91% is worth $157.82, a $57.82 edge, and 54s' 21.09% is worth $42.18, which is $57.82 under its stake.
Think in thousands: about 787 of 1,000 go to AA, about 209 go to 54s, and about 4 are chopped.
The same matchup from the other side
The mirror image, 54s against AA, is 21.09% to 78.91%, and its address redirects to this page.
Keep exploring
The calculator link fills in AsAh against 5d4d, 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
We counted every case. Each suit pattern of the 24 specific AA against 54s 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.
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