AJo
68.33%
Wins 64.57%, ties 7.52%
A7s
31.67%
Wins 27.91%, ties 7.52%
AJo against A7s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AJo | 64.565 | 7.522 | 27.913 | 68.326 |
| A7s | 27.913 | 7.522 | 64.565 | 31.674 |
AJo, an offsuit hand, plays A7s, a suited hand. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
AJo is the clear favorite, though A7s gets there on roughly one board in 3. A split pot comes up on 7.52% of boards, so the wins and the equity differ by half of that.
The hand ranking puts AJo at 15 and A7s at 24 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AJo | 39,800,000 | 4,637,000 | 17,206,000 |
| A7s | 17,206,000 | 4,637,000 | 39,800,000 |
36 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, 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 | 2.157 | 1.549 | 3.583 | 0.464 |
| A7s | 0.464 | 3.583 | 1.549 | 2.157 |
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
Across the five flop textures AJo's equity moves by 19.18 points, from 56.40% on low rainbow flops (nine high or lower) to 75.58% 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 | A7s wins | AJo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.905 | 72.781 | 5.605 | 21.614 | 75.583 |
| Rainbow, nine or lower | 7.042 | 54.275 | 4.240 | 41.485 | 56.395 |
| Two-tone | 46.527 | 64.972 | 5.003 | 30.025 | 67.474 |
| Monotone | 5.192 | 60.573 | 5.895 | 33.532 | 63.521 |
| Paired | 17.334 | 57.517 | 18.747 | 23.736 | 66.891 |
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
How much does the opponent matter? Compared with its random-hand 63.56%, AJo changes by +4.77 points, and A7s, from 60.98%, by -29.31.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AJo, all flops | 68.326 | 63.563 | +4.763 | 1.07493 |
| AJo, rainbow, ten or higher | 75.583 | 63.563 | +12.020 | 1.18910 |
| AJo, rainbow, nine or lower | 56.395 | 63.563 | -7.168 | 0.88723 |
| AJo, two-tone | 67.474 | 63.563 | +3.911 | 1.06153 |
| AJo, monotone | 63.521 | 63.563 | -0.042 | 0.99934 |
| AJo, paired | 66.891 | 63.563 | +3.328 | 1.05236 |
| A7s, all flops | 31.674 | 60.984 | -29.310 | 0.51938 |
| A7s, rainbow, ten or higher | 24.417 | 60.984 | -36.567 | 0.40038 |
| A7s, rainbow, nine or lower | 43.605 | 60.984 | -17.379 | 0.71502 |
| A7s, two-tone | 32.526 | 60.984 | -28.458 | 0.53335 |
| A7s, monotone | 36.479 | 60.984 | -24.505 | 0.59817 |
| A7s, paired | 33.109 | 60.984 | -27.875 | 0.54291 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common AJo has 69.14% equity, and with none in common it has 67.92%. AJo does better with a shared suit, by 1.22 points.
| Deals | Specific deals | Share of deals | AJo wins | Ties | A7s wins | AJo equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 65.325 | 7.630 | 27.045 | 69.140 |
| No shared suit | 24 | 66.67 | 64.185 | 7.468 | 28.347 | 67.919 |
How often this matchup comes up
How often does it happen? 36 of the 1,624,350 ordered deals (0.0022%) are AJo against A7s, and 72 (0.0044%) if either hand may sit in either seat.
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says AJo gets $136.66 of it on average and A7s gets $63.34.
Over a long run, 1,000 deals split into about 646 for AJo, 279 for A7s and 75 tied.
The same matchup from the other side
If you came looking for A7s against AJo, the numbers are the same with the hands swapped: 31.67% and 68.33%.
Keep exploring
Try AsJh against Ad7d 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
This is an exact count with no sampling. For the 36 ways to deal one AJo and one A7s without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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