AA
80.55%
Wins 80.32%, ties 0.46%
53s
19.45%
Wins 19.22%, ties 0.46%
AA against 53s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 80.320 | 0.463 | 19.217 | 80.552 |
| 53s | 19.217 | 0.463 | 80.320 | 19.448 |
We compare a pocket pair with a suited hand. Here a pair faces two cards that are both smaller, so the other hand needs to pair up and still be behind.
That is a heavy lead: 53s needs the board to help it on most runouts and still falls behind far more often than not. The tie share is 0.46%: on those boards the pot is chopped and neither hand wins outright.
By strength against a random hand, AA holds place 1 of 169 and 53s holds place 146.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 33,008,000 | 190,000 | 7,897,000 |
| 53s | 7,897,000 | 190,000 | 33,008,000 |
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 | 4.142 | 1.245 | 5.204 | 0.241 |
| 53s | 0.241 | 5.204 | 1.245 | 4.142 |
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
The flop changes the picture. AA does best on rainbow flops topped by a ten or better, at 85.81%, and worst on low rainbow flops (nine high or lower), at 68.51%. 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 | 53s wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 85.670 | 0.276 | 14.054 | 85.808 |
| Rainbow, nine or lower | 6.314 | 67.960 | 1.109 | 30.931 | 68.514 |
| Two-tone | 46.545 | 78.472 | 0.412 | 21.116 | 78.678 |
| Monotone | 5.212 | 73.581 | 2.542 | 23.877 | 74.852 |
| Paired | 17.334 | 84.220 | 0.007 | 15.773 | 84.223 |
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, 85.20% for AA and 39.69% for 53s. This opponent changes them by -4.65 and -20.24 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 80.552 | 85.204 | -4.652 | 0.94540 |
| AA, rainbow, ten or higher | 85.808 | 85.204 | +0.604 | 1.00709 |
| AA, rainbow, nine or lower | 68.514 | 85.204 | -16.690 | 0.80412 |
| AA, two-tone | 78.678 | 85.204 | -6.526 | 0.92341 |
| AA, monotone | 74.852 | 85.204 | -10.352 | 0.87850 |
| AA, paired | 84.223 | 85.204 | -0.981 | 0.98849 |
| 53s, all flops | 19.448 | 39.693 | -20.245 | 0.48996 |
| 53s, rainbow, ten or higher | 14.192 | 39.693 | -25.501 | 0.35754 |
| 53s, rainbow, nine or lower | 31.486 | 39.693 | -8.207 | 0.79324 |
| 53s, two-tone | 21.322 | 39.693 | -18.371 | 0.53717 |
| 53s, monotone | 25.148 | 39.693 | -14.545 | 0.63356 |
| 53s, paired | 15.777 | 39.693 | -23.916 | 0.39748 |
Does a shared suit matter?
When the hands share a suit, AA holds 81.13%; when they do not, it holds 79.97%. AA does better with a shared suit, by 1.16 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | 53s wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 80.882 | 0.502 | 18.616 | 81.133 |
| No shared suit | 12 | 50.00 | 79.758 | 0.425 | 19.817 | 79.970 |
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
To see what the equity is worth, imagine $100 each in a $200 pot. AA is worth $161.10 on average (+$61.10); 53s is worth $38.90 (-$61.10).
Out of 1,000 deals you should see around 803 outright wins for AA, 192 for 53s, and 5 split pots.
The same matchup from the other side
Swap the hands and you get 53s with 19.45% against AA with 80.55%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
AsAh against 5d3d is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.
How this was computed
We counted every case. Each suit pattern of the 24 specific AA against 53s 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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