QTo
59.91%
Wins 59.44%, ties 0.93%
54s
40.09%
Wins 39.63%, ties 0.93%
QTo against 54s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| QTo | 59.440 | 0.929 | 39.631 | 59.905 |
| 54s | 39.631 | 0.929 | 59.440 | 40.095 |
QTo, an offsuit hand, plays 54s, a suited hand. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
A 19.82 point lead is real, and 54s still takes about 396 of every 1,000 deals outright. Ties are 0.93% of the outcomes here; each tied board gives both hands half the pot.
In the ranking of all 169 starting hands, QTo is number 47 and 54s is number 136.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| QTo | 48,854,000 | 764,000 | 32,573,000 |
| 54s | 32,573,000 | 764,000 | 48,854,000 |
Exact total: 48 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 | 1.494 | 1.682 | 2.523 | 0.669 |
| 54s | 0.669 | 2.523 | 1.682 | 1.494 |
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
By flop texture, QTo's equity runs from 35.10% on low rainbow flops (nine high or lower) up to 67.86% on rainbow flops topped by a ten or better. QTo is the favorite overall but falls behind on low rainbow flops (nine high or lower).
| Flop | Share of flops | QTo wins | Ties | 54s wins | QTo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 67.620 | 0.488 | 31.892 | 67.864 |
| Rainbow, nine or lower | 6.313 | 34.722 | 0.750 | 64.528 | 35.097 |
| Two-tone | 46.667 | 58.156 | 0.514 | 41.330 | 58.413 |
| Monotone | 5.212 | 57.019 | 2.634 | 40.347 | 58.336 |
| Paired | 17.091 | 60.986 | 2.247 | 36.767 | 62.110 |
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
Start from the random-hand figures, 57.29% for QTo and 41.45% for 54s. This opponent changes them by +2.62 and -1.36 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QTo, all flops | 59.905 | 57.291 | +2.614 | 1.04563 |
| QTo, rainbow, ten or higher | 67.864 | 57.291 | +10.573 | 1.18455 |
| QTo, rainbow, nine or lower | 35.097 | 57.291 | -22.194 | 0.61261 |
| QTo, two-tone | 58.413 | 57.291 | +1.122 | 1.01958 |
| QTo, monotone | 58.336 | 57.291 | +1.045 | 1.01824 |
| QTo, paired | 62.110 | 57.291 | +4.819 | 1.08411 |
| 54s, all flops | 40.095 | 41.453 | -1.358 | 0.96724 |
| 54s, rainbow, ten or higher | 32.136 | 41.453 | -9.317 | 0.77524 |
| 54s, rainbow, nine or lower | 64.903 | 41.453 | +23.450 | 1.56570 |
| 54s, two-tone | 41.587 | 41.453 | +0.134 | 1.00323 |
| 54s, monotone | 41.664 | 41.453 | +0.211 | 1.00509 |
| 54s, paired | 37.890 | 41.453 | -3.563 | 0.91405 |
Does a shared suit matter?
When the hands share a suit, QTo holds 60.60%; when they do not, it holds 59.21%. QTo does better with a shared suit, by 1.39 points.
| Deals | Specific deals | Share of deals | QTo wins | Ties | 54s wins | QTo equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 60.116 | 0.970 | 38.914 | 60.601 |
| No shared suit | 24 | 50.00 | 58.764 | 0.888 | 40.348 | 59.208 |
How often this matchup comes up
QTo against 54s is made up of 48 specific-card matchups in one seat order, 0.0030% of the 1,624,350 ordered deals, and 96 counting both seat orders, 0.0059%.
A worked example
With $100 from each side, the $200 pot is split on average as $119.82 for QTo and $80.18 for 54s; the first side gains $19.82 per all-in and the second gives up $19.82.
Over a long run, 1,000 deals split into about 595 for QTo, 396 for 54s and 9 tied.
The same matchup from the other side
Swap the hands and you get 54s with 40.09% against QTo with 59.91%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
Open the calculator with QsTh against 5d4d already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.
How this was computed
Method: exact enumeration. The 48 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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