A3s
56.17%
Wins 55.88%, ties 0.57%
65s
43.83%
Wins 43.55%, ties 0.57%
A3s against 65s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A3s | 55.881 | 0.569 | 43.550 | 56.166 |
| 65s | 43.550 | 0.569 | 55.881 | 43.834 |
A3s and 65s are both suited hands. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
That is a modest edge, the kind that shows up over many hands and is easy to miss in one. A split pot comes up on 0.57% of boards, so the wins and the equity differ by half of that.
By strength against a random hand, A3s holds place 38 of 169 and 65s holds place 128.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A3s | 15,310,000 | 156,000 | 11,931,000 |
| 65s | 11,931,000 | 156,000 | 15,310,000 |
16 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) |
|---|---|---|---|---|
| A3s | 1.281 | 1.790 | 2.296 | 0.780 |
| 65s | 0.780 | 2.296 | 1.790 | 1.281 |
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
Across the five flop textures A3s' equity moves by 29.23 points, from 33.12% on low rainbow flops (nine high or lower) to 62.35% on paired flops. The lead reverses on low rainbow flops (nine high or lower): there 65s is the favorite even though A3s is ahead overall.
| Flop | Share of flops | A3s wins | Ties | 65s wins | A3s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 60.009 | 0.255 | 39.736 | 60.136 |
| Rainbow, nine or lower | 5.689 | 32.694 | 0.860 | 66.446 | 33.124 |
| Two-tone | 46.727 | 54.671 | 0.328 | 45.001 | 54.835 |
| Monotone | 5.273 | 52.027 | 3.504 | 44.469 | 53.779 |
| Paired | 17.091 | 62.008 | 0.690 | 37.302 | 62.353 |
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
The table below sets each hand against its own random-hand baseline: a change of -2.05 points for A3s, from 58.22%, and +0.70 for 65s, from 43.13%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A3s, all flops | 56.166 | 58.220 | -2.054 | 0.96472 |
| A3s, rainbow, ten or higher | 60.136 | 58.220 | +1.916 | 1.03291 |
| A3s, rainbow, nine or lower | 33.124 | 58.220 | -25.096 | 0.56895 |
| A3s, two-tone | 54.835 | 58.220 | -3.385 | 0.94186 |
| A3s, monotone | 53.779 | 58.220 | -4.441 | 0.92372 |
| A3s, paired | 62.353 | 58.220 | +4.133 | 1.07099 |
| 65s, all flops | 43.834 | 43.133 | +0.701 | 1.01625 |
| 65s, rainbow, ten or higher | 39.864 | 43.133 | -3.269 | 0.92421 |
| 65s, rainbow, nine or lower | 66.876 | 43.133 | +23.743 | 1.55046 |
| 65s, two-tone | 45.165 | 43.133 | +2.032 | 1.04711 |
| 65s, monotone | 46.221 | 43.133 | +3.088 | 1.07159 |
| 65s, paired | 37.647 | 43.133 | -5.486 | 0.87281 |
Does a shared suit matter?
Two kinds of deal exist here. In 4 of them the hands share a suit and A3s holds 57.93%. In 12 they do not, and it holds 55.58%. A3s does better with a shared suit, by 2.35 points.
| Deals | Specific deals | Share of deals | A3s wins | Ties | 65s wins | A3s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 57.609 | 0.651 | 41.740 | 57.934 |
| No shared suit | 12 | 75.00 | 55.305 | 0.542 | 44.153 | 55.576 |
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
Worked example: both players commit $100, so $200 sits in the middle. Over every board, A3s' average share is $112.34 (a gain of $12.34) and 65s' is $87.66 (a loss of $12.34).
A thousand deals look like this: A3s takes 559, 65s takes 435, 6 are ties.
The same matchup from the other side
If you came looking for 65s against A3s, the numbers are the same with the hands swapped: 43.83% and 56.17%.
Keep exploring
Open the calculator with As3s against 6h5h 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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