AQs
62.65%
Wins 62.39%, ties 0.51%
75s
37.35%
Wins 37.10%, ties 0.51%
AQs against 75s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQs | 62.393 | 0.506 | 37.101 | 62.646 |
| 75s | 37.101 | 0.506 | 62.393 | 37.354 |
The matchup is suited hands on both sides, AQs against 75s. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
The lead is steady rather than large, and the flop still has plenty of say in who wins. 0.51% of boards are ties, so the equity of each hand is its win rate plus half of that.
The hand ranking puts AQs at 10 and 75s at 124 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQs | 17,094,000 | 139,000 | 10,165,000 |
| 75s | 10,165,000 | 139,000 | 17,094,000 |
Exact total: 16 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AQs | 1.677 | 1.603 | 2.695 | 0.596 |
| 75s | 0.596 | 2.695 | 1.603 | 1.677 |
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
The flop changes the picture. AQs does best on rainbow flops topped by a ten or better, at 69.68%, and worst on low rainbow flops (nine high or lower), at 36.01%. On low rainbow flops (nine high or lower) the numbers flip and 75s is the one ahead.
| Flop | Share of flops | AQs wins | Ties | 75s wins | AQs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 69.591 | 0.178 | 30.231 | 69.680 |
| Rainbow, nine or lower | 6.314 | 35.651 | 0.723 | 63.626 | 36.013 |
| Two-tone | 46.727 | 61.789 | 0.265 | 37.946 | 61.922 |
| Monotone | 5.273 | 58.140 | 3.442 | 38.418 | 59.861 |
| Paired | 17.091 | 64.875 | 0.649 | 34.476 | 65.199 |
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, AQs changes by -3.56 points (baseline 66.21%) and 75s by -6.33 points (baseline 43.68%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQs, all flops | 62.646 | 66.209 | -3.563 | 0.94619 |
| AQs, rainbow, ten or higher | 69.680 | 66.209 | +3.471 | 1.05242 |
| AQs, rainbow, nine or lower | 36.013 | 66.209 | -30.196 | 0.54393 |
| AQs, two-tone | 61.922 | 66.209 | -4.287 | 0.93525 |
| AQs, monotone | 59.861 | 66.209 | -6.348 | 0.90412 |
| AQs, paired | 65.199 | 66.209 | -1.010 | 0.98475 |
| 75s, all flops | 37.354 | 43.676 | -6.322 | 0.85525 |
| 75s, rainbow, ten or higher | 30.320 | 43.676 | -13.356 | 0.69420 |
| 75s, rainbow, nine or lower | 63.987 | 43.676 | +20.311 | 1.46504 |
| 75s, two-tone | 38.078 | 43.676 | -5.598 | 0.87183 |
| 75s, monotone | 40.139 | 43.676 | -3.537 | 0.91902 |
| 75s, paired | 34.801 | 43.676 | -8.875 | 0.79680 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common AQs has 64.92% equity, and with none in common it has 61.89%. AQs does better with a shared suit, by 3.03 points.
| Deals | Specific deals | Share of deals | AQs wins | Ties | 75s wins | AQs equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 64.624 | 0.586 | 34.790 | 64.917 |
| No shared suit | 12 | 75.00 | 61.649 | 0.479 | 37.872 | 61.889 |
How often this matchup comes up
The class pair covers 16 combinations of specific cards in a fixed seat order, 0.0010% of 1,624,350, and 32 (0.0020%) in either order.
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. AQs averages $125.30 from the $200, up $25.30; 75s averages $74.70, down $25.30.
A thousand deals look like this: AQs takes 624, 75s takes 371, 5 are ties.
The same matchup from the other side
Swap the hands and you get 75s with 37.35% against AQs with 62.65%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
Try AsQs against 7h5h 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 16 ways to deal one AQs and one 75s 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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