AJo
67.93%
Wins 64.08%, ties 7.72%
A3s
32.07%
Wins 28.20%, ties 7.72%
AJo against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AJo | 64.076 | 7.716 | 28.208 | 67.934 |
| A3s | 28.208 | 7.716 | 64.076 | 32.066 |
AJo, an offsuit hand, plays A3s, a suited hand. 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.
AJo is well ahead, and A3s needs a specific kind of board to catch up. Ties are 7.72% of the outcomes here; each tied board gives both hands half the pot.
AJo ranks number 15 of 169 starting hands, and A3s ranks number 38, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AJo | 39,498,000 | 4,756,000 | 17,388,000 |
| A3s | 17,388,000 | 4,756,000 | 39,498,000 |
The total is exact: 36 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) |
|---|---|---|---|---|
| AJo | 2.119 | 1.561 | 3.545 | 0.472 |
| A3s | 0.472 | 3.545 | 1.561 | 2.119 |
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
Across the five flop textures AJo's equity moves by 19.84 points, from 55.34% on low rainbow flops (nine high or lower) to 75.18% on rainbow flops topped by a ten or better. AJo 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 | AJo wins | Ties | A3s wins | AJo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.905 | 72.338 | 5.685 | 21.977 | 75.180 |
| Rainbow, nine or lower | 7.042 | 53.143 | 4.394 | 42.463 | 55.340 |
| Two-tone | 46.527 | 64.440 | 5.118 | 30.442 | 66.999 |
| Monotone | 5.192 | 60.250 | 6.039 | 33.711 | 63.270 |
| Paired | 17.334 | 57.292 | 19.341 | 23.367 | 66.963 |
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
Relative to a random opponent, AJo changes by +4.37 points (baseline 63.56%) and A3s by -26.15 points (baseline 58.22%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AJo, all flops | 67.934 | 63.563 | +4.371 | 1.06877 |
| AJo, rainbow, ten or higher | 75.180 | 63.563 | +11.617 | 1.18276 |
| AJo, rainbow, nine or lower | 55.340 | 63.563 | -8.223 | 0.87063 |
| AJo, two-tone | 66.999 | 63.563 | +3.436 | 1.05406 |
| AJo, monotone | 63.270 | 63.563 | -0.293 | 0.99539 |
| AJo, paired | 66.963 | 63.563 | +3.400 | 1.05349 |
| A3s, all flops | 32.066 | 58.220 | -26.154 | 0.55077 |
| A3s, rainbow, ten or higher | 24.820 | 58.220 | -33.400 | 0.42631 |
| A3s, rainbow, nine or lower | 44.660 | 58.220 | -13.560 | 0.76709 |
| A3s, two-tone | 33.001 | 58.220 | -25.219 | 0.56683 |
| A3s, monotone | 36.730 | 58.220 | -21.490 | 0.63088 |
| A3s, paired | 33.037 | 58.220 | -25.183 | 0.56745 |
Does a shared suit matter?
Does suit overlap move the numbers? AJo has 68.75% when the hands share a suit and 67.53% when they do not. AJo does better with a shared suit, by 1.22 points.
| Deals | Specific deals | Share of deals | AJo wins | Ties | A3s wins | AJo equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 64.835 | 7.825 | 27.340 | 68.748 |
| No shared suit | 24 | 66.67 | 63.696 | 7.661 | 28.643 | 67.527 |
How often this matchup comes up
AJo against A3s is made up of 36 specific-card matchups in one seat order, 0.0022% of the 1,624,350 ordered deals, and 72 counting both seat orders, 0.0044%.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. AJo is worth $135.86 on average (+$35.86); A3s is worth $64.14 (-$35.86).
A thousand deals look like this: AJo takes 641, A3s takes 282, 77 are ties.
The same matchup from the other side
A3s versus AJo is this same page seen from the other hand: 32.07% for A3s, 67.93% for AJo.
Keep exploring
Try AsJh against Ad3d 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
The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 36 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
Bring your own hands to a session
Review the spots you actually play against these numbers in a Game Assessment, and leave with a one-page written plan.
Book a session