AQo
62.53%
Wins 62.30%, ties 0.46%
KTo
37.47%
Wins 37.24%, ties 0.46%
AQo against KTo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQo | 62.302 | 0.455 | 37.243 | 62.529 |
| KTo | 37.243 | 0.455 | 62.302 | 37.471 |
AQo and KTo are both offsuit hands. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
A 25.06 point lead is real, and KTo still takes about 372 of every 1,000 deals outright. 0.46% of boards are ties, so the equity of each hand is its win rate plus half of that.
For context, AQo sits at number 14 of 169 starting hands and KTo at number 33 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQo | 153,619,000 | 1,122,000 | 91,831,000 |
| KTo | 91,831,000 | 1,122,000 | 153,619,000 |
The board total is exact, 144 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) |
|---|---|---|---|---|
| AQo | 1.669 | 1.605 | 2.685 | 0.599 |
| KTo | 0.599 | 2.685 | 1.605 | 1.669 |
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
If you know the kind of flop that came, the numbers shift: AQo holds 74.69% on low rainbow flops (nine high or lower) and 57.67% on rainbow flops topped by a ten or better. AQo 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 | AQo wins | Ties | KTo wins | AQo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.381 | 57.613 | 0.117 | 42.270 | 57.671 |
| Rainbow, nine or lower | 7.771 | 74.167 | 1.039 | 24.794 | 74.686 |
| Two-tone | 46.606 | 61.617 | 0.332 | 38.051 | 61.783 |
| Monotone | 5.151 | 59.594 | 1.712 | 38.694 | 60.450 |
| Paired | 17.091 | 66.008 | 0.604 | 33.388 | 66.310 |
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
A random hand would give AQo 64.43% and KTo 59.74%. Against each other the change is -1.90 points for AQo and -22.27 for KTo.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQo, all flops | 62.529 | 64.432 | -1.903 | 0.97046 |
| AQo, rainbow, ten or higher | 57.671 | 64.432 | -6.761 | 0.89507 |
| AQo, rainbow, nine or lower | 74.686 | 64.432 | +10.254 | 1.15914 |
| AQo, two-tone | 61.783 | 64.432 | -2.649 | 0.95889 |
| AQo, monotone | 60.450 | 64.432 | -3.982 | 0.93820 |
| AQo, paired | 66.310 | 64.432 | +1.878 | 1.02915 |
| KTo, all flops | 37.471 | 59.739 | -22.268 | 0.62725 |
| KTo, rainbow, ten or higher | 42.329 | 59.739 | -17.410 | 0.70857 |
| KTo, rainbow, nine or lower | 25.314 | 59.739 | -34.425 | 0.42374 |
| KTo, two-tone | 38.217 | 59.739 | -21.522 | 0.63973 |
| KTo, monotone | 39.550 | 59.739 | -20.189 | 0.66205 |
| KTo, paired | 33.690 | 59.739 | -26.049 | 0.56395 |
Does a shared suit matter?
When the hands share a suit, AQo holds 62.59%; when they do not, it holds 62.22%. AQo does better with a shared suit, by 0.37 points.
| Deals | Specific deals | Share of deals | AQo wins | Ties | KTo wins | AQo equity |
|---|---|---|---|---|---|---|
| Share a suit | 120 | 83.33 | 62.357 | 0.470 | 37.173 | 62.592 |
| No shared suit | 24 | 16.67 | 62.029 | 0.375 | 37.596 | 62.216 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 144 are AQo in one seat and KTo in the other (0.0089%); with the seats swapped too, 288 (0.0177%).
A worked example
Take a $200 pot built from $100 each. AQo's equity of 62.53% is worth $125.06, a $25.06 edge, and KTo's 37.47% is worth $74.94, which is $25.06 under its stake.
Think in thousands: about 623 of 1,000 go to AQo, about 372 go to KTo, and about 5 are chopped.
The same matchup from the other side
The reversed view, KTo against AQo, shows 37.47% for KTo and 62.53% for AQo. It is the same count, so it redirects here.
Keep exploring
AsQh against KdTc 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 144 specific deals of AQo against KTo, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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