AA
87.09%
Wins 86.45%, ties 1.29%
A4s
12.91%
Wins 12.26%, ties 1.29%
AA against A4s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 86.450 | 1.286 | 12.264 | 87.093 |
| A4s | 12.264 | 1.286 | 86.450 | 12.907 |
Here a pocket pair (AA) meets a suited hand (A4s). One hand holds a card of the same rank as the pair, which removes a card the pair needs and makes the pair a bigger favorite.
This is one of the lopsided matchups: A4s wins only 12.26% of the boards outright. About 1.29% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
Place 1 of 169 belongs to AA and place 35 belongs to A4s in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 17,763,000 | 264,000 | 2,520,000 |
| A4s | 2,520,000 | 264,000 | 17,763,000 |
12 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, 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 | 6.748 | 1.157 | 8.154 | 0.148 |
| A4s | 0.148 | 8.154 | 1.157 | 6.748 |
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 92.38% on rainbow flops topped by a ten or better and bottoms out at 77.11% on monotone flops. 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 | A4s wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.740 | 91.774 | 1.220 | 7.006 | 92.384 |
| Rainbow, nine or lower | 7.042 | 83.043 | 2.474 | 14.483 | 84.280 |
| Two-tone | 46.236 | 84.908 | 1.362 | 13.730 | 85.589 |
| Monotone | 5.151 | 75.929 | 2.365 | 21.706 | 77.112 |
| Paired | 17.831 | 87.748 | 0.393 | 11.859 | 87.944 |
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
A random hand would give AA 85.20% and A4s 59.03%. Against each other the change is +1.89 points for AA and -46.12 for A4s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 87.093 | 85.204 | +1.889 | 1.02217 |
| AA, rainbow, ten or higher | 92.384 | 85.204 | +7.180 | 1.08427 |
| AA, rainbow, nine or lower | 84.280 | 85.204 | -0.924 | 0.98916 |
| AA, two-tone | 85.589 | 85.204 | +0.385 | 1.00452 |
| AA, monotone | 77.112 | 85.204 | -8.092 | 0.90503 |
| AA, paired | 87.944 | 85.204 | +2.740 | 1.03216 |
| A4s, all flops | 12.907 | 59.034 | -46.127 | 0.21864 |
| A4s, rainbow, ten or higher | 7.616 | 59.034 | -51.418 | 0.12901 |
| A4s, rainbow, nine or lower | 15.720 | 59.034 | -43.314 | 0.26629 |
| A4s, two-tone | 14.411 | 59.034 | -44.623 | 0.24411 |
| A4s, monotone | 22.888 | 59.034 | -36.146 | 0.38771 |
| A4s, paired | 12.056 | 59.034 | -46.978 | 0.20422 |
Does a shared suit matter?
For this pair the shared-suit row is empty: the two hands cannot both own a card of one suit without reusing a card.
| Deals | Specific deals | Share of deals | AA wins | Ties | A4s wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 86.450 | 1.286 | 12.264 | 87.093 |
How often this matchup comes up
AA against A4s is made up of 12 specific-card matchups in one seat order, 0.0007% of the 1,624,350 ordered deals, and 24 counting both seat orders, 0.0015%.
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. AA averages $174.18 from the $200, up $74.18; A4s averages $25.82, down $74.18.
A thousand deals look like this: AA takes 864, A4s takes 123, 13 are ties.
The same matchup from the other side
One page covers both views. From A4s' side the equity is 12.91%, and from AA's side it is 87.09%.
Keep exploring
Try AsAh 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 12 deals of AA 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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