AA
87.06%
Wins 86.45%, ties 1.23%
AJs
12.94%
Wins 12.32%, ties 1.23%
AA against AJs: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 86.445 | 1.234 | 12.321 | 87.062 |
| AJs | 12.321 | 1.234 | 86.445 | 12.938 |
AA, a pocket pair, plays AJs, a suited hand. The pair already holds one of the other hand's ranks, and that overlap cuts down the cards the other hand can pair with.
That is a heavy lead: AJs needs the board to help it on most runouts and still falls behind far more often than not. Ties are part of the picture: 1.23% of boards end in a split pot, and each side counts that as half a win.
Among the 169 starting hands, AA is number 1 and AJs is number 11 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 17,762,000 | 254,000 | 2,532,000 |
| AJs | 2,532,000 | 254,000 | 17,762,000 |
12 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) |
|---|---|---|---|---|
| AA | 6.729 | 1.157 | 8.116 | 0.149 |
| AJs | 0.149 | 8.116 | 1.157 | 6.729 |
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
Split by what the flop looks like, AA peaks at 94.12% on low rainbow flops (nine high or lower) and bottoms out at 77.09% on monotone flops. AA 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 | AA wins | Ties | AJs wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.011 | 88.762 | 1.016 | 10.222 | 89.270 |
| Rainbow, nine or lower | 7.771 | 92.780 | 2.685 | 4.535 | 94.122 |
| Two-tone | 46.236 | 84.908 | 1.301 | 13.791 | 85.558 |
| Monotone | 5.151 | 75.930 | 2.327 | 21.743 | 77.093 |
| Paired | 17.831 | 87.720 | 0.393 | 11.887 | 87.917 |
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: 85.20% for AA, 65.39% for AJs. Here the change is +1.86 and -52.45 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 87.062 | 85.204 | +1.858 | 1.02181 |
| AA, rainbow, ten or higher | 89.270 | 85.204 | +4.066 | 1.04772 |
| AA, rainbow, nine or lower | 94.122 | 85.204 | +8.918 | 1.10467 |
| AA, two-tone | 85.558 | 85.204 | +0.354 | 1.00415 |
| AA, monotone | 77.093 | 85.204 | -8.111 | 0.90480 |
| AA, paired | 87.917 | 85.204 | +2.713 | 1.03184 |
| AJs, all flops | 12.938 | 65.393 | -52.455 | 0.19785 |
| AJs, rainbow, ten or higher | 10.730 | 65.393 | -54.663 | 0.16408 |
| AJs, rainbow, nine or lower | 5.878 | 65.393 | -59.515 | 0.08989 |
| AJs, two-tone | 14.442 | 65.393 | -50.951 | 0.22085 |
| AJs, monotone | 22.907 | 65.393 | -42.486 | 0.35030 |
| AJs, paired | 12.083 | 65.393 | -53.310 | 0.18478 |
Does a shared suit matter?
AA and AJs never overlap in suit in a legal deal, so the whole matchup sits in the no-shared-suit row.
| Deals | Specific deals | Share of deals | AA wins | Ties | AJs wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 86.445 | 1.234 | 12.321 | 87.062 |
How often this matchup comes up
Counting specific cards, AA against AJs appears in 12 of the 1,624,350 ordered heads-up deals (0.0007%), and in 24 when the seats are swapped too (0.0015%).
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. AA averages $174.12 from the $200, up $74.12; AJs averages $25.88, down $74.12.
Over a long run, 1,000 deals split into about 865 for AA, 123 for AJs and 12 tied.
The same matchup from the other side
AJs versus AA is this same page seen from the other hand: 12.94% for AJs, 87.06% for AA.
Keep exploring
AsAh against AdJd is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.
How this was computed
The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 12 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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