ATo
46.54%
Wins 46.31%, ties 0.44%
55
53.46%
Wins 53.25%, ties 0.44%
ATo against 55: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| ATo | 46.314 | 0.444 | 53.242 | 46.536 |
| 55 | 53.242 | 0.444 | 46.314 | 53.464 |
ATo and 55 are an offsuit hand and a pocket pair, in that order. One hand holds a pair and the other holds two cards that both outrank it, which keeps the equity closer than most people expect.
That is a slim edge: neither hand is far ahead. Ties are 0.44% of the outcomes here; each tied board gives both hands half the pot.
The hand ranking puts ATo at 19 and 55 at 27 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| ATo | 57,099,000 | 547,000 | 65,640,000 |
| 55 | 65,640,000 | 547,000 | 57,099,000 |
72 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) |
|---|---|---|---|---|
| ATo | 0.870 | 2.159 | 1.878 | 1.149 |
| 55 | 1.149 | 1.878 | 2.159 | 0.870 |
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
Split by what the flop looks like, 55 peaks at 78.22% on low rainbow flops (nine high or lower) and bottoms out at 46.83% on rainbow flops topped by a ten or better. The overall edge for 55 hides rainbow flops topped by a ten or better, where ATo comes out in front.
| Flop | Share of flops | ATo wins | Ties | 55 wins | ATo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 53.054 | 0.242 | 46.704 | 53.175 |
| Rainbow, nine or lower | 6.314 | 21.419 | 0.719 | 77.862 | 21.778 |
| Two-tone | 46.485 | 46.926 | 0.326 | 52.748 | 47.089 |
| Monotone | 5.151 | 48.566 | 1.844 | 49.590 | 49.488 |
| Paired | 17.333 | 43.464 | 0.532 | 56.004 | 43.730 |
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
A random hand would give ATo 62.72% and 55 60.33%. Against each other the change is -16.18 points for ATo and -6.87 for 55.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| ATo, all flops | 46.536 | 62.722 | -16.186 | 0.74194 |
| ATo, rainbow, ten or higher | 53.175 | 62.722 | -9.547 | 0.84779 |
| ATo, rainbow, nine or lower | 21.778 | 62.722 | -40.944 | 0.34721 |
| ATo, two-tone | 47.089 | 62.722 | -15.633 | 0.75076 |
| ATo, monotone | 49.488 | 62.722 | -13.234 | 0.78901 |
| ATo, paired | 43.730 | 62.722 | -18.992 | 0.69720 |
| 55, all flops | 53.464 | 60.325 | -6.861 | 0.88627 |
| 55, rainbow, ten or higher | 46.825 | 60.325 | -13.500 | 0.77621 |
| 55, rainbow, nine or lower | 78.222 | 60.325 | +17.897 | 1.29668 |
| 55, two-tone | 52.911 | 60.325 | -7.414 | 0.87710 |
| 55, monotone | 50.512 | 60.325 | -9.813 | 0.83733 |
| 55, paired | 56.270 | 60.325 | -4.055 | 0.93278 |
Does a shared suit matter?
When the hands share a suit, 55 holds 53.38%; when they do not, it holds 53.88%. 55 does better with no shared suit, by 0.50 points.
| Deals | Specific deals | Share of deals | ATo wins | Ties | 55 wins | ATo equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 46.390 | 0.459 | 53.151 | 46.620 |
| No shared suit | 12 | 16.67 | 45.936 | 0.370 | 53.694 | 46.121 |
How often this matchup comes up
ATo against 55 is made up of 72 specific-card matchups in one seat order, 0.0044% of the 1,624,350 ordered deals, and 144 counting both seat orders, 0.0089%.
A worked example
Take a $200 pot built from $100 each. 55's equity of 53.46% is worth $106.92, a $6.92 edge, and ATo's 46.54% is worth $93.08, which is $6.92 under its stake.
Think in thousands: about 532 of 1,000 go to 55, about 463 go to ATo, and about 5 are chopped.
The same matchup from the other side
Read it from the other side: 55 against ATo is the same matchup with the numbers swapped, so 55 holds 53.46% and ATo holds 46.54%. That address sends you back to this page.
Keep exploring
Open the calculator with AsTh against 5d5c 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 72 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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