A4s
58.33%
Wins 58.09%, ties 0.47%
QTo
41.67%
Wins 41.44%, ties 0.47%
A4s against QTo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A4s | 58.093 | 0.471 | 41.436 | 58.329 |
| QTo | 41.436 | 0.471 | 58.093 | 41.671 |
A4s, a suited hand, plays QTo, an offsuit hand. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.
A4s is ahead, but QTo is far from dead: it takes 414 of every 1,000 deals outright. Ties are part of the picture: 0.47% of boards end in a split pot, and each side counts that as half a win.
Ranked by equity against a random hand, A4s is number 35 of the 169 starting hands and QTo is number 47.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A4s | 47,747,000 | 387,000 | 34,056,000 |
| QTo | 34,056,000 | 387,000 | 47,747,000 |
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) |
|---|---|---|---|---|
| A4s | 1.400 | 1.721 | 2.413 | 0.714 |
| QTo | 0.714 | 2.413 | 1.721 | 1.400 |
In the last column, a pot-to-call ratio at or above the figure makes a call break even or better at this equity.
Who is ahead on which flops
If you know the kind of flop that came, the numbers shift: A4s holds 74.52% on low rainbow flops (nine high or lower) and 50.80% on rainbow flops topped by a ten or better. A4s 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 | A4s wins | Ties | QTo wins | A4s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.988 | 50.722 | 0.159 | 49.119 | 50.802 |
| Rainbow, nine or lower | 7.042 | 74.093 | 0.861 | 25.046 | 74.524 |
| Two-tone | 46.667 | 57.782 | 0.296 | 41.922 | 57.930 |
| Monotone | 5.212 | 54.163 | 2.393 | 43.444 | 55.359 |
| Paired | 17.091 | 63.892 | 0.641 | 35.467 | 64.213 |
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, 59.03% for A4s and 57.29% for QTo. This opponent changes them by -0.70 and -15.62 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A4s, all flops | 58.329 | 59.034 | -0.705 | 0.98806 |
| A4s, rainbow, ten or higher | 50.802 | 59.034 | -8.232 | 0.86055 |
| A4s, rainbow, nine or lower | 74.524 | 59.034 | +15.490 | 1.26239 |
| A4s, two-tone | 57.930 | 59.034 | -1.104 | 0.98130 |
| A4s, monotone | 55.359 | 59.034 | -3.675 | 0.93775 |
| A4s, paired | 64.213 | 59.034 | +5.179 | 1.08773 |
| QTo, all flops | 41.671 | 57.291 | -15.620 | 0.72736 |
| QTo, rainbow, ten or higher | 49.198 | 57.291 | -8.093 | 0.85874 |
| QTo, rainbow, nine or lower | 25.476 | 57.291 | -31.815 | 0.44468 |
| QTo, two-tone | 42.070 | 57.291 | -15.221 | 0.73432 |
| QTo, monotone | 44.641 | 57.291 | -12.650 | 0.77920 |
| QTo, paired | 35.787 | 57.291 | -21.504 | 0.62465 |
Does a shared suit matter?
Of the deals of this matchup, 24 share a suit (A4s at 57.98%) and 24 do not (58.68%). A4s does better with no shared suit, by 0.70 points.
| Deals | Specific deals | Share of deals | A4s wins | Ties | QTo wins | A4s equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 57.723 | 0.513 | 41.764 | 57.979 |
| No shared suit | 24 | 50.00 | 58.464 | 0.429 | 41.107 | 58.678 |
How often this matchup comes up
A4s against QTo 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
Take a $200 pot built from $100 each. A4s' equity of 58.33% is worth $116.66, a $16.66 edge, and QTo's 41.67% is worth $83.34, which is $16.66 under its stake.
In 1,000 deals of exactly this matchup, expect about 581 won outright by A4s, about 414 won outright by QTo and about 5 split.
The same matchup from the other side
Swap the hands and you get QTo with 41.67% against A4s with 58.33%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
Open the calculator with As4s against QhTd 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
We counted every case. Each suit pattern of the 48 specific A4s against QTo deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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