AA
79.02%
Wins 78.83%, ties 0.39%
75s
20.98%
Wins 20.78%, ties 0.39%
AA against 75s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 78.826 | 0.392 | 20.782 | 79.022 |
| 75s | 20.782 | 0.392 | 78.826 | 20.978 |
AA and 75s are a pocket pair and a suited hand, in that order. Here a pair faces two cards that are both smaller, so the other hand needs to pair up and still be behind.
That is a clear edge, 79.02% to 20.98%, but 75s still wins often enough that one hand proves nothing. Ties are 0.39% of the outcomes here; each tied board gives both hands half the pot.
Among the 169 starting hands, AA is number 1 and 75s is number 124 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 32,394,000 | 161,000 | 8,540,000 |
| 75s | 8,540,000 | 161,000 | 32,394,000 |
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) |
|---|---|---|---|---|
| AA | 3.767 | 1.269 | 4.812 | 0.265 |
| 75s | 0.265 | 4.812 | 1.269 | 3.767 |
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
AA prefers rainbow flops topped by a ten or better, where it holds 84.62%, and likes low rainbow flops (nine high or lower) least, where it holds 64.62%. 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 | 75s wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 84.489 | 0.251 | 15.260 | 84.615 |
| Rainbow, nine or lower | 6.314 | 64.240 | 0.755 | 35.005 | 64.618 |
| Two-tone | 46.545 | 76.914 | 0.333 | 22.753 | 77.080 |
| Monotone | 5.212 | 72.491 | 2.436 | 25.073 | 73.709 |
| Paired | 17.334 | 83.142 | 0.007 | 16.851 | 83.146 |
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
Compared with a random opponent, this matchup shifts AA from 85.20% by -6.18 points and 75s from 43.68% by -22.70 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 79.022 | 85.204 | -6.182 | 0.92744 |
| AA, rainbow, ten or higher | 84.615 | 85.204 | -0.589 | 0.99309 |
| AA, rainbow, nine or lower | 64.618 | 85.204 | -20.586 | 0.75839 |
| AA, two-tone | 77.080 | 85.204 | -8.124 | 0.90465 |
| AA, monotone | 73.709 | 85.204 | -11.495 | 0.86509 |
| AA, paired | 83.146 | 85.204 | -2.058 | 0.97585 |
| 75s, all flops | 20.978 | 43.676 | -22.698 | 0.48031 |
| 75s, rainbow, ten or higher | 15.385 | 43.676 | -28.291 | 0.35225 |
| 75s, rainbow, nine or lower | 35.382 | 43.676 | -8.294 | 0.81010 |
| 75s, two-tone | 22.920 | 43.676 | -20.756 | 0.52477 |
| 75s, monotone | 26.291 | 43.676 | -17.385 | 0.60196 |
| 75s, paired | 16.854 | 43.676 | -26.822 | 0.38589 |
Does a shared suit matter?
Of the deals of this matchup, 12 share a suit (AA at 79.60%) and 12 do not (78.45%). AA does better with a shared suit, by 1.15 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | 75s wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 79.379 | 0.434 | 20.187 | 79.596 |
| No shared suit | 12 | 50.00 | 78.273 | 0.351 | 21.376 | 78.448 |
How often this matchup comes up
Exactly 24 specific deals fit this matchup in one seat order, which is 0.0015% of 1,624,350; both orders together give 48, or 0.0030%.
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. AA averages $158.04 from the $200, up $58.04; 75s averages $41.96, down $58.04.
Over a long run, 1,000 deals split into about 788 for AA, 208 for 75s and 4 tied.
The same matchup from the other side
One page covers both views. From 75s' side the equity is 20.98%, and from AA's side it is 79.02%.
Keep exploring
The calculator link fills in AsAh against 7d5d, 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
The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 24 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.
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