AQs
69.73%
Wins 67.00%, ties 5.46%
A4s
30.27%
Wins 27.54%, ties 5.46%
AQs against A4s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQs | 66.999 | 5.463 | 27.538 | 69.730 |
| A4s | 27.538 | 5.463 | 66.999 | 30.270 |
Here suited hands face each other, AQs on one side and A4s on the other. The two hands share a rank, and the one with the better other card dominates: it wins most kicker battles when that shared rank hits.
That is a clear edge, 69.73% to 30.27%, but A4s still wins often enough that one hand proves nothing. The tie share is 5.46%: on those boards the pot is chopped and neither hand wins outright.
Place 10 of 169 belongs to AQs and place 35 belongs to A4s in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQs | 13,767,000 | 1,123,000 | 5,658,000 |
| A4s | 5,658,000 | 1,123,000 | 13,767,000 |
12 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, rounded to the nearest thousand.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AQs | 2.304 | 1.493 | 3.631 | 0.434 |
| A4s | 0.434 | 3.631 | 1.493 | 2.304 |
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
AQs prefers rainbow flops topped by a ten or better, where it holds 76.52%, and likes low rainbow flops (nine high or lower) least, where it holds 55.59%. AQs 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 | AQs wins | Ties | A4s wins | AQs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 74.769 | 3.497 | 21.734 | 76.518 |
| Rainbow, nine or lower | 7.042 | 53.501 | 4.175 | 42.324 | 55.588 |
| Two-tone | 46.543 | 67.363 | 3.334 | 29.303 | 69.030 |
| Monotone | 5.215 | 61.086 | 5.291 | 33.623 | 63.731 |
| Paired | 17.333 | 62.582 | 14.466 | 22.952 | 69.815 |
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
Relative to a random opponent, AQs changes by +3.52 points (baseline 66.21%) and A4s by -28.76 points (baseline 59.03%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQs, all flops | 69.730 | 66.209 | +3.521 | 1.05318 |
| AQs, rainbow, ten or higher | 76.518 | 66.209 | +10.309 | 1.15570 |
| AQs, rainbow, nine or lower | 55.588 | 66.209 | -10.621 | 0.83958 |
| AQs, two-tone | 69.030 | 66.209 | +2.821 | 1.04261 |
| AQs, monotone | 63.731 | 66.209 | -2.478 | 0.96257 |
| AQs, paired | 69.815 | 66.209 | +3.606 | 1.05446 |
| A4s, all flops | 30.270 | 59.034 | -28.764 | 0.51276 |
| A4s, rainbow, ten or higher | 23.482 | 59.034 | -35.552 | 0.39777 |
| A4s, rainbow, nine or lower | 44.412 | 59.034 | -14.622 | 0.75231 |
| A4s, two-tone | 30.970 | 59.034 | -28.064 | 0.52461 |
| A4s, monotone | 36.269 | 59.034 | -22.765 | 0.61437 |
| A4s, paired | 30.185 | 59.034 | -28.849 | 0.51132 |
Does a shared suit matter?
There is no shared-suit case for this pair, since the cards they would need are already in the other hand. Every deal is a no-shared-suit deal.
| Deals | Specific deals | Share of deals | AQs wins | Ties | A4s wins | AQs equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 66.999 | 5.463 | 27.538 | 69.730 |
How often this matchup comes up
Counting specific cards, AQs against A4s appears in 12 of the 1,624,350 ordered heads-up deals (0.0007%), and in 24 when the seats are swapped too (0.0015%).
A worked example
Worked example: both players commit $100, so $200 sits in the middle. Over every board, AQs' average share is $139.46 (a gain of $39.46) and A4s' is $60.54 (a loss of $39.46).
Scaled to 1,000 deals, that is roughly 670 wins for AQs, 275 for A4s and 55 chopped pots.
The same matchup from the other side
One page covers both views. From A4s' side the equity is 30.27%, and from AQs' side it is 69.73%.
Keep exploring
AsQs against Ah4h 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
This is an exact count with no sampling. For the 12 ways to deal one AQs and one A4s without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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