AQs
61.42%
Wins 61.14%, ties 0.55%
54s
38.58%
Wins 38.31%, ties 0.55%
AQs against 54s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQs | 61.143 | 0.554 | 38.303 | 61.420 |
| 54s | 38.303 | 0.554 | 61.143 | 38.580 |
Here suited hands face each other, AQs on one side and 54s on the other. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
A 22.84 point lead is real, and 54s still takes about 383 of every 1,000 deals outright. Ties are part of the picture: 0.55% of boards end in a split pot, and each side counts that as half a win.
For context, AQs sits at number 10 of 169 starting hands and 54s at number 136 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQs | 16,751,000 | 152,000 | 10,494,000 |
| 54s | 10,494,000 | 152,000 | 16,751,000 |
Exact total: 16 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) |
|---|---|---|---|---|
| AQs | 1.592 | 1.636 | 2.611 | 0.628 |
| 54s | 0.628 | 2.611 | 1.636 | 1.592 |
The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.
Who is ahead on which flops
Across the five flop textures AQs' equity moves by 33.05 points, from 34.98% on low rainbow flops (nine high or lower) to 68.03% on rainbow flops topped by a ten or better. Watch for low rainbow flops (nine high or lower): on those flops 54s holds the better equity.
| Flop | Share of flops | AQs wins | Ties | 54s wins | AQs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 67.938 | 0.182 | 31.880 | 68.029 |
| Rainbow, nine or lower | 6.314 | 34.484 | 0.982 | 64.534 | 34.975 |
| Two-tone | 46.727 | 60.398 | 0.314 | 39.288 | 60.555 |
| Monotone | 5.273 | 57.048 | 3.554 | 39.398 | 58.825 |
| Paired | 17.091 | 64.513 | 0.661 | 34.826 | 64.843 |
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 AQs 66.21% and 54s 41.45%. Against each other the change is -4.79 points for AQs and -2.87 for 54s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQs, all flops | 61.420 | 66.209 | -4.789 | 0.92767 |
| AQs, rainbow, ten or higher | 68.029 | 66.209 | +1.820 | 1.02749 |
| AQs, rainbow, nine or lower | 34.975 | 66.209 | -31.234 | 0.52825 |
| AQs, two-tone | 60.555 | 66.209 | -5.654 | 0.91460 |
| AQs, monotone | 58.825 | 66.209 | -7.384 | 0.88847 |
| AQs, paired | 64.843 | 66.209 | -1.366 | 0.97937 |
| 54s, all flops | 38.580 | 41.453 | -2.873 | 0.93069 |
| 54s, rainbow, ten or higher | 31.971 | 41.453 | -9.482 | 0.77126 |
| 54s, rainbow, nine or lower | 65.025 | 41.453 | +23.572 | 1.56864 |
| 54s, two-tone | 39.445 | 41.453 | -2.008 | 0.95156 |
| 54s, monotone | 41.175 | 41.453 | -0.278 | 0.99329 |
| 54s, paired | 35.157 | 41.453 | -6.296 | 0.84812 |
Does a shared suit matter?
Two kinds of deal exist here. In 4 of them the hands share a suit and AQs holds 63.57%. In 12 they do not, and it holds 60.70%. AQs does better with a shared suit, by 2.87 points.
| Deals | Specific deals | Share of deals | AQs wins | Ties | 54s wins | AQs equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 63.255 | 0.633 | 36.112 | 63.571 |
| No shared suit | 12 | 75.00 | 60.439 | 0.527 | 39.034 | 60.703 |
How often this matchup comes up
Exactly 16 specific deals fit this matchup in one seat order, which is 0.0010% of 1,624,350; both orders together give 32, or 0.0020%.
A worked example
With $100 from each side, the $200 pot is split on average as $122.84 for AQs and $77.16 for 54s; the first side gains $22.84 per all-in and the second gives up $22.84.
Out of 1,000 deals you should see around 611 outright wins for AQs, 383 for 54s, and 6 split pots.
The same matchup from the other side
54s against AQs adds nothing new: it is 38.58% for 54s and 61.42% for AQs, the same figures reversed.
Keep exploring
Open the calculator with AsQs against 5h4h 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 16 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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