ATo
66.19%
Wins 61.05%, ties 10.29%
A4s
33.81%
Wins 28.66%, ties 10.29%
ATo against A4s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| ATo | 61.048 | 10.292 | 28.660 | 66.194 |
| A4s | 28.660 | 10.292 | 61.048 | 33.806 |
Here an offsuit hand (ATo) meets a suited hand (A4s). Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
A lead of 32.38 points is large but not decisive: A4s still takes about 287 of every 1,000 deals. Split pots make up 10.29% of the boards, and both equity figures count them as half a win each.
ATo ranks number 19 of 169 starting hands, and A4s ranks number 35, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| ATo | 37,632,000 | 6,344,000 | 17,667,000 |
| A4s | 17,667,000 | 6,344,000 | 37,632,000 |
Exact total: 36 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) |
|---|---|---|---|---|
| ATo | 1.958 | 1.638 | 3.489 | 0.511 |
| A4s | 0.511 | 3.489 | 1.638 | 1.958 |
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
By flop texture, ATo's equity runs from 54.41% on low rainbow flops (nine high or lower) up to 73.40% on rainbow flops topped by a ten or better. ATo 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 | ATo wins | Ties | A4s wins | ATo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.905 | 69.077 | 8.642 | 22.281 | 73.398 |
| Rainbow, nine or lower | 7.042 | 52.389 | 4.044 | 43.567 | 54.411 |
| Two-tone | 46.527 | 61.929 | 7.184 | 30.887 | 65.521 |
| Monotone | 5.192 | 58.353 | 7.621 | 34.026 | 62.163 |
| Paired | 17.334 | 51.932 | 24.250 | 23.818 | 64.057 |
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
Compared with a random opponent, this matchup shifts ATo from 62.72% by +3.47 points and A4s from 59.03% by -25.22 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| ATo, all flops | 66.194 | 62.722 | +3.472 | 1.05536 |
| ATo, rainbow, ten or higher | 73.398 | 62.722 | +10.676 | 1.17021 |
| ATo, rainbow, nine or lower | 54.411 | 62.722 | -8.311 | 0.86749 |
| ATo, two-tone | 65.521 | 62.722 | +2.799 | 1.04463 |
| ATo, monotone | 62.163 | 62.722 | -0.559 | 0.99109 |
| ATo, paired | 64.057 | 62.722 | +1.335 | 1.02128 |
| A4s, all flops | 33.806 | 59.034 | -25.228 | 0.57265 |
| A4s, rainbow, ten or higher | 26.602 | 59.034 | -32.432 | 0.45062 |
| A4s, rainbow, nine or lower | 45.589 | 59.034 | -13.445 | 0.77225 |
| A4s, two-tone | 34.479 | 59.034 | -24.555 | 0.58405 |
| A4s, monotone | 37.837 | 59.034 | -21.197 | 0.64094 |
| A4s, paired | 35.943 | 59.034 | -23.091 | 0.60885 |
Does a shared suit matter?
Of the deals of this matchup, 12 share a suit (ATo at 66.99%) and 24 do not (65.79%). ATo does better with a shared suit, by 1.20 points.
| Deals | Specific deals | Share of deals | ATo wins | Ties | A4s wins | ATo equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 61.781 | 10.423 | 27.796 | 66.992 |
| No shared suit | 24 | 66.67 | 60.681 | 10.227 | 29.092 | 65.794 |
How often this matchup comes up
How often does it happen? 36 of the 1,624,350 ordered deals (0.0022%) are ATo against A4s, and 72 (0.0044%) if either hand may sit in either seat.
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. ATo averages $132.38 from the $200, up $32.38; A4s averages $67.62, down $32.38.
In 1,000 deals of exactly this matchup, expect about 610 won outright by ATo, about 287 won outright by A4s and about 103 split.
The same matchup from the other side
One page covers both views. From A4s' side the equity is 33.81%, and from ATo's side it is 66.19%.
Keep exploring
Open the calculator with AsTh against Ad4d 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
The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 36 specific deals, both seven-card hands evaluated. A tie is worth half a win to each hand, and a board is tallied under each of its ten possible flops for the texture rows.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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