AJs
49.23%
Wins 48.98%, ties 0.51%
44
50.77%
Wins 50.51%, ties 0.51%
AJs against 44: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AJs | 48.976 | 0.506 | 50.518 | 49.229 |
| 44 | 50.518 | 0.506 | 48.976 | 50.771 |
We compare a suited hand with a pocket pair. A pair against two higher cards is the classic race: the pair is usually a small favorite or close to even, and each overcard that pairs is a way to take the lead.
That is a slim edge: neither hand is far ahead. A split pot comes up on 0.51% of boards, so the wins and the equity differ by half of that.
The hand ranking puts AJs at 11 and 44 at 48 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AJs | 20,127,000 | 208,000 | 20,761,000 |
| 44 | 20,761,000 | 208,000 | 20,127,000 |
Exact total: 24 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AJs | 0.970 | 2.042 | 1.979 | 1.031 |
| 44 | 1.031 | 1.979 | 2.042 | 0.970 |
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
Low rainbow flops (nine high or lower) are the best for 44 (76.83%); rainbow flops topped by a ten or better are the worst (45.28%). On rainbow flops topped by a ten or better and two-tone flops the numbers flip and AJs is the one ahead.
| Flop | Share of flops | AJs wins | Ties | 44 wins | AJs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 54.619 | 0.195 | 45.186 | 54.716 |
| Rainbow, nine or lower | 6.314 | 22.709 | 0.926 | 76.365 | 23.172 |
| Two-tone | 46.545 | 50.310 | 0.318 | 49.372 | 50.469 |
| Monotone | 5.212 | 47.981 | 2.816 | 49.203 | 49.389 |
| Paired | 17.334 | 47.257 | 0.600 | 52.143 | 47.557 |
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
Each hand has a baseline against a random hand: 65.39% for AJs, 57.02% for 44. Here the change is -16.16 and -6.25 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AJs, all flops | 49.229 | 65.393 | -16.164 | 0.75282 |
| AJs, rainbow, ten or higher | 54.716 | 65.393 | -10.677 | 0.83673 |
| AJs, rainbow, nine or lower | 23.172 | 65.393 | -42.221 | 0.35435 |
| AJs, two-tone | 50.469 | 65.393 | -14.924 | 0.77178 |
| AJs, monotone | 49.389 | 65.393 | -16.004 | 0.75526 |
| AJs, paired | 47.557 | 65.393 | -17.836 | 0.72725 |
| 44, all flops | 50.771 | 57.023 | -6.252 | 0.89036 |
| 44, rainbow, ten or higher | 45.284 | 57.023 | -11.739 | 0.79414 |
| 44, rainbow, nine or lower | 76.828 | 57.023 | +19.805 | 1.34732 |
| 44, two-tone | 49.531 | 57.023 | -7.492 | 0.86861 |
| 44, monotone | 50.611 | 57.023 | -6.412 | 0.88755 |
| 44, paired | 52.443 | 57.023 | -4.580 | 0.91968 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common 44 has 50.95% equity, and with none in common it has 50.59%. 44 does better with a shared suit, by 0.36 points.
| Deals | Specific deals | Share of deals | AJs wins | Ties | 44 wins | AJs equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 48.779 | 0.543 | 50.678 | 49.050 |
| No shared suit | 12 | 50.00 | 49.174 | 0.468 | 50.358 | 49.408 |
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
Say each player puts $100 in before the flop, making a $200 pot. On average 44 takes back $101.54 of it, which is $1.54 more than it put in, and AJs takes back $98.46, $1.54 less than it put in.
Scaled to 1,000 deals, that is roughly 505 wins for 44, 490 for AJs and 5 chopped pots.
The same matchup from the other side
44 against AJs adds nothing new: it is 50.77% for 44 and 49.23% for AJs, the same figures reversed.
Keep exploring
Try AsJs against 4h4d 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 24 deals of AJs against 44 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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