AKs
70.24%
Wins 68.06%, ties 4.36%
A4s
29.76%
Wins 27.58%, ties 4.36%
AKs against A4s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AKs | 68.061 | 4.364 | 27.575 | 70.243 |
| A4s | 27.575 | 4.364 | 68.061 | 29.757 |
Both hands are suited hands: AKs and A4s. The two hands share a rank, and the one with the better other card dominates: it wins most kicker battles when that shared rank hits.
AKs is well ahead, and A4s needs a specific kind of board to catch up. Ties are part of the picture: 4.36% of boards end in a split pot, and each side counts that as half a win.
Place 8 of 169 belongs to AKs and place 35 belongs to A4s in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AKs | 13,985,000 | 897,000 | 5,666,000 |
| A4s | 5,666,000 | 897,000 | 13,985,000 |
The total is exact: 12 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) |
|---|---|---|---|---|
| AKs | 2.361 | 1.469 | 3.626 | 0.424 |
| A4s | 0.424 | 3.626 | 1.469 | 2.361 |
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
The flop changes the picture. AKs does best on rainbow flops topped by a ten or better, at 77.01%, and worst on low rainbow flops (nine high or lower), at 55.55%. AKs 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 | AKs wins | Ties | A4s wins | AKs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 75.803 | 2.404 | 21.793 | 77.005 |
| Rainbow, nine or lower | 7.042 | 53.450 | 4.204 | 42.346 | 55.552 |
| Two-tone | 46.543 | 68.124 | 2.530 | 29.346 | 69.389 |
| Monotone | 5.215 | 61.789 | 4.558 | 33.653 | 64.068 |
| Paired | 17.333 | 65.055 | 11.993 | 22.952 | 71.052 |
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
A random hand would give AKs 67.05% and A4s 59.03%. Against each other the change is +3.19 points for AKs and -29.27 for A4s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AKs, all flops | 70.243 | 67.045 | +3.198 | 1.04770 |
| AKs, rainbow, ten or higher | 77.005 | 67.045 | +9.960 | 1.14856 |
| AKs, rainbow, nine or lower | 55.552 | 67.045 | -11.493 | 0.82858 |
| AKs, two-tone | 69.389 | 67.045 | +2.344 | 1.03496 |
| AKs, monotone | 64.068 | 67.045 | -2.977 | 0.95560 |
| AKs, paired | 71.052 | 67.045 | +4.007 | 1.05977 |
| A4s, all flops | 29.757 | 59.034 | -29.277 | 0.50407 |
| A4s, rainbow, ten or higher | 22.995 | 59.034 | -36.039 | 0.38952 |
| A4s, rainbow, nine or lower | 44.448 | 59.034 | -14.586 | 0.75292 |
| A4s, two-tone | 30.611 | 59.034 | -28.423 | 0.51853 |
| A4s, monotone | 35.932 | 59.034 | -23.102 | 0.60867 |
| A4s, paired | 28.948 | 59.034 | -30.086 | 0.49036 |
Does a shared suit matter?
Suits do not split this matchup, because no legal deal has the hands holding the same suit.
| Deals | Specific deals | Share of deals | AKs wins | Ties | A4s wins | AKs equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 68.061 | 4.364 | 27.575 | 70.243 |
How often this matchup comes up
Exactly 12 specific deals fit this matchup in one seat order, which is 0.0007% of 1,624,350; both orders together give 24, or 0.0015%.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. AKs is worth $140.48 on average (+$40.48); A4s is worth $59.52 (-$40.48).
Over a long run, 1,000 deals split into about 680 for AKs, 276 for A4s and 44 tied.
The same matchup from the other side
One page covers both views. From A4s' side the equity is 29.76%, and from AKs' side it is 70.24%.
Keep exploring
AsKs against Ah4h 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 12 specific AKs 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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