A9o
56.96%
Wins 56.75%, ties 0.42%
QTo
43.04%
Wins 42.83%, ties 0.42%
A9o against QTo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A9o | 56.749 | 0.420 | 42.831 | 56.959 |
| QTo | 42.831 | 0.420 | 56.749 | 43.041 |
A9o meets QTo, and both are offsuit hands. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
A 13.92 point lead is real, and QTo still takes about 428 of every 1,000 deals outright. 0.42% of boards are ties, so the equity of each hand is its win rate plus half of that.
A9o ranks number 25 of 169 starting hands, and QTo ranks number 47, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A9o | 139,927,000 | 1,036,000 | 105,609,000 |
| QTo | 105,609,000 | 1,036,000 | 139,927,000 |
144 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) |
|---|---|---|---|---|
| A9o | 1.323 | 1.762 | 2.335 | 0.756 |
| QTo | 0.756 | 2.335 | 1.762 | 1.323 |
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 A9o is strongest on low rainbow flops (nine high or lower) (73.87%) and weakest on rainbow flops topped by a ten or better (50.53%). A9o 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 | A9o wins | Ties | QTo wins | A9o equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.110 | 50.458 | 0.153 | 49.389 | 50.534 |
| Rainbow, nine or lower | 7.042 | 73.465 | 0.804 | 25.731 | 73.867 |
| Two-tone | 46.606 | 55.530 | 0.287 | 44.183 | 55.673 |
| Monotone | 5.151 | 53.612 | 1.681 | 44.707 | 54.453 |
| Paired | 17.091 | 63.007 | 0.620 | 36.373 | 63.317 |
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
Each hand has a baseline against a random hand: 60.77% for A9o, 57.29% for QTo. Here the change is -3.81 and -14.25 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A9o, all flops | 56.959 | 60.773 | -3.814 | 0.93724 |
| A9o, rainbow, ten or higher | 50.534 | 60.773 | -10.239 | 0.83152 |
| A9o, rainbow, nine or lower | 73.867 | 60.773 | +13.094 | 1.21546 |
| A9o, two-tone | 55.673 | 60.773 | -5.100 | 0.91608 |
| A9o, monotone | 54.453 | 60.773 | -6.320 | 0.89601 |
| A9o, paired | 63.317 | 60.773 | +2.544 | 1.04186 |
| QTo, all flops | 43.041 | 57.291 | -14.250 | 0.75127 |
| QTo, rainbow, ten or higher | 49.466 | 57.291 | -7.825 | 0.86342 |
| QTo, rainbow, nine or lower | 26.133 | 57.291 | -31.158 | 0.45614 |
| QTo, two-tone | 44.327 | 57.291 | -12.964 | 0.77372 |
| QTo, monotone | 45.547 | 57.291 | -11.744 | 0.79501 |
| QTo, paired | 36.683 | 57.291 | -20.608 | 0.64029 |
Does a shared suit matter?
Of the deals of this matchup, 120 share a suit (A9o at 56.97%) and 24 do not (56.92%). The two rows differ by only 0.05 points, so suits barely change this matchup.
| Deals | Specific deals | Share of deals | A9o wins | Ties | QTo wins | A9o equity |
|---|---|---|---|---|---|---|
| Share a suit | 120 | 83.33 | 56.748 | 0.436 | 42.816 | 56.966 |
| No shared suit | 24 | 16.67 | 56.752 | 0.341 | 42.907 | 56.922 |
How often this matchup comes up
Counting specific cards, A9o against QTo appears in 144 of the 1,624,350 ordered heads-up deals (0.0089%), and in 288 when the seats are swapped too (0.0177%).
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. A9o is worth $113.92 on average (+$13.92); QTo is worth $86.08 (-$13.92).
In 1,000 deals of exactly this matchup, expect about 568 won outright by A9o, about 428 won outright by QTo and about 4 split.
The same matchup from the other side
QTo against A9o adds nothing new: it is 43.04% for QTo and 56.96% for A9o, the same figures reversed.
Keep exploring
Try As9h against QdTc 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
Each figure is a complete count over boards. Take the 144 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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