QTo
50.58%
Wins 50.00%, ties 1.16%
22
49.42%
Wins 48.84%, ties 1.16%
QTo against 22: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| QTo | 50.002 | 1.155 | 48.843 | 50.579 |
| 22 | 48.843 | 1.155 | 50.002 | 49.421 |
The first hand is an offsuit hand; the second is a pocket pair. A pair against two higher cards is the classic race: the pair is usually a small favorite or close to even, and each overcard that pairs is a way to take the lead.
QTo leads by less than 2 points of equity, so the result of any one deal is close to a toss-up. Ties are part of the picture: 1.16% of boards end in a split pot, and each side counts that as half a win.
By strength against a random hand, QTo holds place 47 of 169 and 22 holds place 87.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| QTo | 61,645,000 | 1,424,000 | 60,217,000 |
| 22 | 60,217,000 | 1,424,000 | 61,645,000 |
Exact total: 72 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) |
|---|---|---|---|---|
| QTo | 1.023 | 2.000 | 2.047 | 0.977 |
| 22 | 0.977 | 2.047 | 2.000 | 1.023 |
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. QTo does best on rainbow flops topped by a ten or better, at 56.77%, and worst on low rainbow flops (nine high or lower), at 25.68%. Watch for low rainbow flops (nine high or lower): on those flops 22 holds the better equity.
| Flop | Share of flops | QTo wins | Ties | 22 wins | QTo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 56.475 | 0.579 | 42.946 | 56.765 |
| Rainbow, nine or lower | 6.314 | 25.144 | 1.065 | 73.791 | 25.677 |
| Two-tone | 46.485 | 50.307 | 0.661 | 49.032 | 50.637 |
| Monotone | 5.151 | 51.214 | 2.905 | 45.881 | 52.666 |
| Paired | 17.333 | 48.647 | 2.813 | 48.540 | 50.054 |
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
A random hand would give QTo 57.29% and 22 50.33%. Against each other the change is -6.71 points for QTo and -0.91 for 22.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QTo, all flops | 50.579 | 57.291 | -6.712 | 0.88284 |
| QTo, rainbow, ten or higher | 56.765 | 57.291 | -0.526 | 0.99082 |
| QTo, rainbow, nine or lower | 25.677 | 57.291 | -31.614 | 0.44819 |
| QTo, two-tone | 50.637 | 57.291 | -6.654 | 0.88386 |
| QTo, monotone | 52.666 | 57.291 | -4.625 | 0.91927 |
| QTo, paired | 50.054 | 57.291 | -7.237 | 0.87368 |
| 22, all flops | 49.421 | 50.334 | -0.913 | 0.98186 |
| 22, rainbow, ten or higher | 43.235 | 50.334 | -7.099 | 0.85896 |
| 22, rainbow, nine or lower | 74.323 | 50.334 | +23.989 | 1.47660 |
| 22, two-tone | 49.363 | 50.334 | -0.971 | 0.98071 |
| 22, monotone | 47.334 | 50.334 | -3.000 | 0.94040 |
| 22, paired | 49.946 | 50.334 | -0.388 | 0.99229 |
Does a shared suit matter?
Does suit overlap move the numbers? QTo has 50.67% when the hands share a suit and 50.14% when they do not. QTo does better with a shared suit, by 0.53 points.
| Deals | Specific deals | Share of deals | QTo wins | Ties | 22 wins | QTo equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 50.086 | 1.162 | 48.752 | 50.667 |
| No shared suit | 12 | 16.67 | 49.581 | 1.119 | 49.300 | 50.140 |
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
With $100 from each side, the $200 pot is split on average as $101.16 for QTo and $98.84 for 22; the first side gains $1.16 per all-in and the second gives up $1.16.
Think in thousands: about 500 of 1,000 go to QTo, about 488 go to 22, and about 12 are chopped.
The same matchup from the other side
If you came looking for 22 against QTo, the numbers are the same with the hands swapped: 49.42% and 50.58%.
Keep exploring
QsTh against 2d2c 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
Each figure is a complete count over boards. Take the 72 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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