A4s
36.90%
Wins 35.77%, ties 2.26%
44
63.10%
Wins 61.97%, ties 2.26%
A4s against 44: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A4s | 35.769 | 2.255 | 61.976 | 36.896 |
| 44 | 61.976 | 2.255 | 35.769 | 63.104 |
We compare a suited hand with a pocket pair. The pair already holds one of the other hand's ranks, and that overlap cuts down the cards the other hand can pair with.
44 is ahead, but A4s is far from dead: it takes 358 of every 1,000 deals outright. The tie share is 2.26%: on those boards the pot is chopped and neither hand wins outright.
The hand ranking puts A4s at 35 and 44 at 48 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A4s | 7,350,000 | 463,000 | 12,735,000 |
| 44 | 12,735,000 | 463,000 | 7,350,000 |
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) |
|---|---|---|---|---|
| A4s | 0.585 | 2.796 | 1.614 | 1.710 |
| 44 | 1.710 | 1.614 | 2.796 | 0.585 |
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
Across the five flop textures 44's equity moves by 16.48 points, from 59.98% on monotone flops to 76.46% on low rainbow flops (nine high or lower). 44 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 | A4s wins | Ties | 44 wins | A4s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.197 | 36.402 | 1.433 | 62.165 | 37.119 |
| Rainbow, nine or lower | 5.585 | 19.924 | 7.226 | 72.850 | 23.537 |
| Two-tone | 46.236 | 36.865 | 2.238 | 60.897 | 37.984 |
| Monotone | 5.151 | 38.287 | 3.472 | 58.241 | 40.023 |
| Paired | 17.831 | 36.266 | 1.554 | 62.180 | 37.043 |
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 A4s 59.03% and 44 57.02%. Against each other the change is -22.13 points for A4s and +6.08 for 44.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A4s, all flops | 36.896 | 59.034 | -22.138 | 0.62500 |
| A4s, rainbow, ten or higher | 37.119 | 59.034 | -21.915 | 0.62877 |
| A4s, rainbow, nine or lower | 23.537 | 59.034 | -35.497 | 0.39870 |
| A4s, two-tone | 37.984 | 59.034 | -21.050 | 0.64343 |
| A4s, monotone | 40.023 | 59.034 | -19.011 | 0.67797 |
| A4s, paired | 37.043 | 59.034 | -21.991 | 0.62749 |
| 44, all flops | 63.104 | 57.023 | +6.081 | 1.10664 |
| 44, rainbow, ten or higher | 62.881 | 57.023 | +5.858 | 1.10273 |
| 44, rainbow, nine or lower | 76.463 | 57.023 | +19.440 | 1.34092 |
| 44, two-tone | 62.016 | 57.023 | +4.993 | 1.08756 |
| 44, monotone | 59.977 | 57.023 | +2.954 | 1.05180 |
| 44, paired | 62.957 | 57.023 | +5.934 | 1.10406 |
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 | A4s wins | Ties | 44 wins | A4s equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 35.769 | 2.255 | 61.976 | 36.896 |
How often this matchup comes up
You will meet this exact matchup 0.0015% of the time in a random heads-up deal: 24 of 1,624,350, counting either seat order.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. 44 is worth $126.20 on average (+$26.20); A4s is worth $73.80 (-$26.20).
Run 1,000 deals and the tally comes out near 620 for 44, 358 for A4s and 22 ties.
The same matchup from the other side
44 against A4s adds nothing new: it is 63.10% for 44 and 36.90% for A4s, the same figures reversed.
Keep exploring
The calculator link fills in As4s against 4h4d, 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 12 specific A4s against 44 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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