AKo
68.92%
Wins 66.62%, ties 4.59%
A4s
31.08%
Wins 28.79%, ties 4.59%
AKo against A4s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AKo | 66.620 | 4.594 | 28.786 | 68.917 |
| A4s | 28.786 | 4.594 | 66.620 | 31.083 |
AKo and A4s are an offsuit hand and a suited hand, in that order. Because the hands share one rank, the one with the higher kicker is ahead when that rank pairs and the other hand is mostly drawing.
AKo is well ahead, and A4s needs a specific kind of board to catch up. The tie share is 4.59%: on those boards the pot is chopped and neither hand wins outright.
By strength against a random hand, AKo holds place 12 of 169 and A4s holds place 35.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AKo | 41,067,000 | 2,832,000 | 17,745,000 |
| A4s | 17,745,000 | 2,832,000 | 41,067,000 |
36 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) |
|---|---|---|---|---|
| AKo | 2.217 | 1.501 | 3.474 | 0.451 |
| A4s | 0.451 | 3.474 | 1.501 | 2.217 |
The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.
Who is ahead on which flops
By flop texture, AKo's equity runs from 53.89% on low rainbow flops (nine high or lower) up to 76.38% on rainbow flops topped by a ten or better. AKo 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 | AKo wins | Ties | A4s wins | AKo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.905 | 75.137 | 2.479 | 22.384 | 76.376 |
| Rainbow, nine or lower | 7.042 | 51.699 | 4.385 | 43.916 | 53.892 |
| Two-tone | 46.527 | 66.214 | 2.750 | 31.036 | 67.589 |
| Monotone | 5.192 | 61.769 | 4.079 | 34.152 | 63.809 |
| Paired | 17.334 | 63.479 | 12.702 | 23.819 | 69.830 |
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, 65.32% for AKo and 59.03% for A4s. This opponent changes them by +3.60 and -27.95 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AKo, all flops | 68.917 | 65.320 | +3.597 | 1.05507 |
| AKo, rainbow, ten or higher | 76.376 | 65.320 | +11.056 | 1.16926 |
| AKo, rainbow, nine or lower | 53.892 | 65.320 | -11.428 | 0.82505 |
| AKo, two-tone | 67.589 | 65.320 | +2.269 | 1.03474 |
| AKo, monotone | 63.809 | 65.320 | -1.511 | 0.97687 |
| AKo, paired | 69.830 | 65.320 | +4.510 | 1.06904 |
| A4s, all flops | 31.083 | 59.034 | -27.951 | 0.52653 |
| A4s, rainbow, ten or higher | 23.624 | 59.034 | -35.410 | 0.40018 |
| A4s, rainbow, nine or lower | 46.108 | 59.034 | -12.926 | 0.78104 |
| A4s, two-tone | 32.411 | 59.034 | -26.623 | 0.54902 |
| A4s, monotone | 36.191 | 59.034 | -22.843 | 0.61305 |
| A4s, paired | 30.170 | 59.034 | -28.864 | 0.51106 |
Does a shared suit matter?
The suit split reads 69.74% for AKo with a shared suit and 68.51% without one. AKo does better with a shared suit, by 1.23 points.
| Deals | Specific deals | Share of deals | AKo wins | Ties | A4s wins | AKo equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 67.399 | 4.673 | 27.928 | 69.735 |
| No shared suit | 24 | 66.67 | 66.231 | 4.555 | 29.214 | 68.508 |
How often this matchup comes up
Exactly 36 specific deals fit this matchup in one seat order, which is 0.0022% of 1,624,350; both orders together give 72, or 0.0044%.
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. AKo averages $137.84 from the $200, up $37.84; A4s averages $62.16, down $37.84.
Think in thousands: about 666 of 1,000 go to AKo, about 288 go to A4s, and about 46 are chopped.
The same matchup from the other side
One page covers both views. From A4s' side the equity is 31.08%, and from AKo's side it is 68.92%.
Keep exploring
AsKh against Ad4d 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 36 specific AKo against A4s 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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