AA
81.61%
Wins 81.44%, ties 0.34%
T9o
18.39%
Wins 18.22%, ties 0.34%
AA against T9o: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 81.441 | 0.339 | 18.220 | 81.610 |
| T9o | 18.220 | 0.339 | 81.441 | 18.390 |
AA and T9o are a pocket pair and an offsuit hand, in that order. A pair against two lower cards is a lopsided matchup: the pair is ahead and the other hand has no overcard to catch.
This is one of the lopsided matchups: T9o wins only 18.22% of the boards outright. 0.34% of boards are ties, so the equity of each hand is its win rate plus half of that.
By strength against a random hand, AA holds place 1 of 169 and T9o holds place 78.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 100,405,000 | 418,000 | 22,463,000 |
| T9o | 22,463,000 | 418,000 | 100,405,000 |
The board total is exact, 72 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) |
|---|---|---|---|---|
| AA | 4.438 | 1.228 | 5.488 | 0.225 |
| T9o | 0.225 | 5.488 | 1.228 | 4.438 |
The final column gives the least the pot must offer for each unit called for a call to break even at this equity.
Who is ahead on which flops
Break the boards down by their first three cards and AA is strongest on paired flops (85.57%) and weakest on monotone flops (77.28%). AA stays ahead on all five textures.
| Flop | Share of flops | AA wins | Ties | T9o wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.988 | 80.642 | 0.196 | 19.162 | 80.740 |
| Rainbow, nine or lower | 7.042 | 82.635 | 0.790 | 16.575 | 83.030 |
| Two-tone | 46.485 | 80.690 | 0.317 | 18.993 | 80.848 |
| Monotone | 5.151 | 76.431 | 1.702 | 21.867 | 77.282 |
| Paired | 17.334 | 85.563 | 0.007 | 14.430 | 85.567 |
Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.
Compared with a random hand
How much does the opponent matter? Compared with its random-hand 85.20%, AA changes by -3.59 points, and T9o, from 51.53%, by -33.14.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 81.610 | 85.204 | -3.594 | 0.95782 |
| AA, rainbow, ten or higher | 80.740 | 85.204 | -4.464 | 0.94761 |
| AA, rainbow, nine or lower | 83.030 | 85.204 | -2.174 | 0.97448 |
| AA, two-tone | 80.848 | 85.204 | -4.356 | 0.94888 |
| AA, monotone | 77.282 | 85.204 | -7.922 | 0.90702 |
| AA, paired | 85.567 | 85.204 | +0.363 | 1.00426 |
| T9o, all flops | 18.390 | 51.532 | -33.142 | 0.35687 |
| T9o, rainbow, ten or higher | 19.260 | 51.532 | -32.272 | 0.37375 |
| T9o, rainbow, nine or lower | 16.970 | 51.532 | -34.562 | 0.32931 |
| T9o, two-tone | 19.152 | 51.532 | -32.380 | 0.37165 |
| T9o, monotone | 22.718 | 51.532 | -28.814 | 0.44085 |
| T9o, paired | 14.433 | 51.532 | -37.099 | 0.28008 |
Does a shared suit matter?
Does suit overlap move the numbers? AA has 81.75% when the hands share a suit and 80.92% when they do not. AA does better with a shared suit, by 0.83 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | T9o wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 81.571 | 0.355 | 18.074 | 81.748 |
| No shared suit | 12 | 16.67 | 80.790 | 0.259 | 18.951 | 80.919 |
How often this matchup comes up
Exactly 72 specific deals fit this matchup in one seat order, which is 0.0044% of 1,624,350; both orders together give 144, or 0.0089%.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. AA is worth $163.22 on average (+$63.22); T9o is worth $36.78 (-$63.22).
Think in thousands: about 815 of 1,000 go to AA, about 182 go to T9o, and about 3 are chopped.
The same matchup from the other side
One page covers both views. From T9o's side the equity is 18.39%, and from AA's side it is 81.61%.
Keep exploring
The calculator link fills in AsAh against Td9c, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.
How this was computed
We counted every case. Each suit pattern of the 72 specific AA against T9o deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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