A3s
55.27%
Wins 55.01%, ties 0.52%
86s
44.73%
Wins 44.47%, ties 0.52%
A3s against 86s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A3s | 55.013 | 0.519 | 44.468 | 55.273 |
| 86s | 44.468 | 0.519 | 55.013 | 44.727 |
Each side holds one of the suited hands: A3s and 86s. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
A3s is ahead, but 86s is far from dead: it takes 445 of every 1,000 deals outright. The tie share is 0.52%: on those boards the pot is chopped and neither hand wins outright.
Among the 169 starting hands, A3s is number 38 and 86s is number 110 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A3s | 15,072,000 | 142,000 | 12,183,000 |
| 86s | 12,183,000 | 142,000 | 15,072,000 |
The total is exact: 16 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and 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 | 1.236 | 1.818 | 2.249 | 0.809 |
| 86s | 0.809 | 2.249 | 1.818 | 1.236 |
The final column gives the least the pot must offer for each unit called for a call to break even at this equity.
Who is ahead on which flops
Break the boards down by their first three cards and A3s is strongest on paired flops (61.51%) and weakest on low rainbow flops (nine high or lower) (33.38%). The overall edge for A3s hides low rainbow flops (nine high or lower), where 86s comes out in front.
| Flop | Share of flops | A3s wins | Ties | 86s wins | A3s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 58.734 | 0.209 | 41.057 | 58.838 |
| Rainbow, nine or lower | 5.689 | 33.016 | 0.722 | 66.262 | 33.377 |
| Two-tone | 46.727 | 53.831 | 0.275 | 45.894 | 53.969 |
| Monotone | 5.273 | 51.460 | 3.434 | 45.106 | 53.177 |
| Paired | 17.091 | 61.173 | 0.678 | 38.149 | 61.512 |
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, A3s changes by -2.95 points (baseline 58.22%) and 86s by -1.51 points (baseline 46.24%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A3s, all flops | 55.273 | 58.220 | -2.947 | 0.94938 |
| A3s, rainbow, ten or higher | 58.838 | 58.220 | +0.618 | 1.01061 |
| A3s, rainbow, nine or lower | 33.377 | 58.220 | -24.843 | 0.57329 |
| A3s, two-tone | 53.969 | 58.220 | -4.251 | 0.92698 |
| A3s, monotone | 53.177 | 58.220 | -5.043 | 0.91338 |
| A3s, paired | 61.512 | 58.220 | +3.292 | 1.05654 |
| 86s, all flops | 44.727 | 46.243 | -1.516 | 0.96722 |
| 86s, rainbow, ten or higher | 41.162 | 46.243 | -5.081 | 0.89012 |
| 86s, rainbow, nine or lower | 66.623 | 46.243 | +20.380 | 1.44072 |
| 86s, two-tone | 46.031 | 46.243 | -0.212 | 0.99542 |
| 86s, monotone | 46.823 | 46.243 | +0.580 | 1.01254 |
| 86s, paired | 38.488 | 46.243 | -7.755 | 0.83230 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, A3s has 56.93%; looking only at deals where they do not, 54.72%. A3s does better with a shared suit, by 2.21 points.
| Deals | Specific deals | Share of deals | A3s wins | Ties | 86s wins | A3s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 56.626 | 0.600 | 42.774 | 56.926 |
| No shared suit | 12 | 75.00 | 54.476 | 0.492 | 45.032 | 54.722 |
How often this matchup comes up
The class pair covers 16 combinations of specific cards in a fixed seat order, 0.0010% of 1,624,350, and 32 (0.0020%) in either order.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. A3s is worth $110.54 on average (+$10.54); 86s is worth $89.46 (-$10.54).
Over a long run, 1,000 deals split into about 550 for A3s, 445 for 86s and 5 tied.
The same matchup from the other side
86s against A3s adds nothing new: it is 44.73% for 86s and 55.27% for A3s, the same figures reversed.
Keep exploring
Try As3s against 8h6h in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups 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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