ATo
59.35%
Wins 59.10%, ties 0.50%
54s
40.65%
Wins 40.40%, ties 0.50%
ATo against 54s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| ATo | 59.096 | 0.498 | 40.406 | 59.345 |
| 54s | 40.406 | 0.498 | 59.096 | 40.655 |
ATo is an offsuit hand and 54s is a suited hand. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
A 18.70 point lead is real, and 54s still takes about 404 of every 1,000 deals outright. Split pots make up 0.50% of the boards, and both equity figures count them as half a win each.
Place 19 of 169 belongs to ATo and place 136 belongs to 54s in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| ATo | 48,571,000 | 409,000 | 33,210,000 |
| 54s | 33,210,000 | 409,000 | 48,571,000 |
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) |
|---|---|---|---|---|
| ATo | 1.460 | 1.692 | 2.475 | 0.685 |
| 54s | 0.685 | 2.475 | 1.692 | 1.460 |
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
If you know the kind of flop that came, the numbers shift: ATo holds 66.91% on rainbow flops topped by a ten or better and 34.59% on low rainbow flops (nine high or lower). Low rainbow flops (nine high or lower) favor 54s, the hand that is behind overall.
| Flop | Share of flops | ATo wins | Ties | 54s wins | ATo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 66.790 | 0.234 | 32.976 | 66.907 |
| Rainbow, nine or lower | 6.313 | 34.208 | 0.757 | 65.035 | 34.587 |
| Two-tone | 46.667 | 57.448 | 0.320 | 42.232 | 57.608 |
| Monotone | 5.212 | 56.485 | 2.477 | 41.038 | 57.723 |
| Paired | 17.091 | 62.462 | 0.669 | 36.869 | 62.797 |
Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.
Compared with a random hand
Each hand has a baseline against a random hand: 62.72% for ATo, 41.45% for 54s. Here the change is -3.37 and -0.80 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| ATo, all flops | 59.345 | 62.722 | -3.377 | 0.94616 |
| ATo, rainbow, ten or higher | 66.907 | 62.722 | +4.185 | 1.06672 |
| ATo, rainbow, nine or lower | 34.587 | 62.722 | -28.135 | 0.55143 |
| ATo, two-tone | 57.608 | 62.722 | -5.114 | 0.91847 |
| ATo, monotone | 57.723 | 62.722 | -4.999 | 0.92030 |
| ATo, paired | 62.797 | 62.722 | +0.075 | 1.00120 |
| 54s, all flops | 40.655 | 41.453 | -0.798 | 0.98075 |
| 54s, rainbow, ten or higher | 33.093 | 41.453 | -8.360 | 0.79833 |
| 54s, rainbow, nine or lower | 65.413 | 41.453 | +23.960 | 1.57800 |
| 54s, two-tone | 42.392 | 41.453 | +0.939 | 1.02265 |
| 54s, monotone | 42.277 | 41.453 | +0.824 | 1.01988 |
| 54s, paired | 37.203 | 41.453 | -4.250 | 0.89747 |
Does a shared suit matter?
Of the deals of this matchup, 24 share a suit (ATo at 60.02%) and 24 do not (58.67%). ATo does better with a shared suit, by 1.35 points.
| Deals | Specific deals | Share of deals | ATo wins | Ties | 54s wins | ATo equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 59.751 | 0.538 | 39.711 | 60.020 |
| No shared suit | 24 | 50.00 | 58.442 | 0.458 | 41.100 | 58.671 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 48 are ATo in one seat and 54s in the other (0.0030%); with the seats swapped too, 96 (0.0059%).
A worked example
Take a $200 pot built from $100 each. ATo's equity of 59.35% is worth $118.70, a $18.70 edge, and 54s' 40.65% is worth $81.30, which is $18.70 under its stake.
Run 1,000 deals and the tally comes out near 591 for ATo, 404 for 54s and 5 ties.
The same matchup from the other side
Swap the hands and you get 54s with 40.65% against ATo with 59.35%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
Open the calculator with AsTh 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
Nothing here is simulated. The 48 deals of ATo against 54s fall into a few suit patterns, each dealt against all 1,712,304 boards, with both best five-card hands compared on every board. Ties give each hand half a win, and the flop rows count a board under each of its ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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