A3s
34.13%
Wins 33.84%, ties 0.59%
44
65.87%
Wins 65.57%, ties 0.59%
A3s against 44: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A3s | 33.839 | 0.585 | 65.576 | 34.131 |
| 44 | 65.576 | 0.585 | 33.839 | 65.869 |
A3s and 44 are a suited hand and a pocket pair, in that order. The pair is ahead of one card and behind the other, so the board decides how that plays out.
That is a clear edge, 65.87% to 34.13%, but A3s still wins often enough that one hand proves nothing. 0.59% of boards are ties, so the equity of each hand is its win rate plus half of that.
Among the 169 starting hands, A3s is number 38 and 44 is number 48 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A3s | 13,906,000 | 240,000 | 26,949,000 |
| 44 | 26,949,000 | 240,000 | 13,906,000 |
The board total is exact, 24 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| A3s | 0.518 | 2.955 | 1.525 | 1.930 |
| 44 | 1.930 | 1.525 | 2.955 | 0.518 |
In the last column, a pot-to-call ratio at or above the figure makes a call break even or better at this equity.
Who is ahead on which flops
Split by what the flop looks like, 44 peaks at 80.77% on low rainbow flops (nine high or lower) and bottoms out at 62.41% on monotone flops. 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 | A3s wins | Ties | 44 wins | A3s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 33.901 | 0.291 | 65.808 | 34.047 |
| Rainbow, nine or lower | 5.689 | 18.690 | 1.084 | 80.226 | 19.232 |
| Two-tone | 46.545 | 34.407 | 0.397 | 65.196 | 34.605 |
| Monotone | 5.212 | 36.153 | 2.865 | 60.982 | 37.586 |
| Paired | 17.334 | 36.502 | 0.665 | 62.833 | 36.834 |
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
A random hand would give A3s 58.22% and 44 57.02%. Against each other the change is -24.09 points for A3s and +8.85 for 44.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A3s, all flops | 34.131 | 58.220 | -24.089 | 0.58624 |
| A3s, rainbow, ten or higher | 34.047 | 58.220 | -24.173 | 0.58480 |
| A3s, rainbow, nine or lower | 19.232 | 58.220 | -38.988 | 0.33033 |
| A3s, two-tone | 34.605 | 58.220 | -23.615 | 0.59438 |
| A3s, monotone | 37.586 | 58.220 | -20.634 | 0.64559 |
| A3s, paired | 36.834 | 58.220 | -21.386 | 0.63267 |
| 44, all flops | 65.869 | 57.023 | +8.846 | 1.15513 |
| 44, rainbow, ten or higher | 65.953 | 57.023 | +8.930 | 1.15660 |
| 44, rainbow, nine or lower | 80.768 | 57.023 | +23.745 | 1.41641 |
| 44, two-tone | 65.395 | 57.023 | +8.372 | 1.14682 |
| 44, monotone | 62.414 | 57.023 | +5.391 | 1.09454 |
| 44, paired | 63.166 | 57.023 | +6.143 | 1.10773 |
Does a shared suit matter?
When the hands share a suit, 44 holds 66.14%; when they do not, it holds 65.59%. 44 does better with a shared suit, by 0.55 points.
| Deals | Specific deals | Share of deals | A3s wins | Ties | 44 wins | A3s equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 33.547 | 0.621 | 65.832 | 33.857 |
| No shared suit | 12 | 50.00 | 34.131 | 0.549 | 65.320 | 34.406 |
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
A $100 all-in from each player makes a $200 pot, and the exact equity says 44 gets $131.74 of it on average and A3s gets $68.26.
A thousand deals look like this: 44 takes 656, A3s takes 338, 6 are ties.
The same matchup from the other side
One page covers both views. From 44's side the equity is 65.87%, and from A3s' side it is 34.13%.
Keep exploring
Open the calculator with As3s against 4h4d already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.
How this was computed
The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 24 specific deals, both seven-card hands evaluated. A tie is worth half a win to each hand, and a board is tallied under each of its ten possible flops for the texture rows.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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