AKs
62.25%
Wins 62.01%, ties 0.47%
86s
37.75%
Wins 37.52%, ties 0.47%
AKs against 86s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AKs | 62.013 | 0.473 | 37.514 | 62.250 |
| 86s | 37.514 | 0.473 | 62.013 | 37.750 |
Each side holds one of the suited hands: AKs and 86s. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.
That is a modest edge, the kind that shows up over many hands and is easy to miss in one. Of every 100 boards, about 0.47 are split pots, and the equity figures already include them.
The hand ranking puts AKs at 8 and 86s at 110 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AKs | 16,990,000 | 130,000 | 10,278,000 |
| 86s | 10,278,000 | 130,000 | 16,990,000 |
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) |
|---|---|---|---|---|
| AKs | 1.649 | 1.613 | 2.666 | 0.606 |
| 86s | 0.606 | 2.666 | 1.613 | 1.649 |
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
By flop texture, AKs' equity runs from 36.09% on low rainbow flops (nine high or lower) up to 69.08% on rainbow flops topped by a ten or better. Watch for low rainbow flops (nine high or lower): on those flops 86s holds the better equity.
| Flop | Share of flops | AKs wins | Ties | 86s wins | AKs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 69.017 | 0.133 | 30.850 | 69.084 |
| Rainbow, nine or lower | 6.314 | 35.735 | 0.709 | 63.556 | 36.090 |
| Two-tone | 46.727 | 61.413 | 0.230 | 38.357 | 61.528 |
| Monotone | 5.273 | 57.881 | 3.402 | 38.717 | 59.582 |
| Paired | 17.091 | 64.558 | 0.637 | 34.805 | 64.876 |
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
A random hand would give AKs 67.05% and 86s 46.24%. Against each other the change is -4.80 points for AKs and -8.49 for 86s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AKs, all flops | 62.250 | 67.045 | -4.795 | 0.92848 |
| AKs, rainbow, ten or higher | 69.084 | 67.045 | +2.039 | 1.03041 |
| AKs, rainbow, nine or lower | 36.090 | 67.045 | -30.955 | 0.53830 |
| AKs, two-tone | 61.528 | 67.045 | -5.517 | 0.91771 |
| AKs, monotone | 59.582 | 67.045 | -7.463 | 0.88869 |
| AKs, paired | 64.876 | 67.045 | -2.169 | 0.96765 |
| 86s, all flops | 37.750 | 46.243 | -8.493 | 0.81634 |
| 86s, rainbow, ten or higher | 30.916 | 46.243 | -15.327 | 0.66856 |
| 86s, rainbow, nine or lower | 63.910 | 46.243 | +17.667 | 1.38205 |
| 86s, two-tone | 38.472 | 46.243 | -7.771 | 0.83195 |
| 86s, monotone | 40.418 | 46.243 | -5.825 | 0.87403 |
| 86s, paired | 35.124 | 46.243 | -11.119 | 0.75955 |
Does a shared suit matter?
Does suit overlap move the numbers? AKs has 64.48% when the hands share a suit and 61.51% when they do not. AKs does better with a shared suit, by 2.97 points.
| Deals | Specific deals | Share of deals | AKs wins | Ties | 86s wins | AKs equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 64.209 | 0.551 | 35.240 | 64.484 |
| No shared suit | 12 | 75.00 | 61.282 | 0.447 | 38.271 | 61.505 |
How often this matchup comes up
AKs against 86s is made up of 16 specific-card matchups in one seat order, 0.0010% of the 1,624,350 ordered deals, and 32 counting both seat orders, 0.0020%.
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average AKs takes back $124.50 of it, which is $24.50 more than it put in, and 86s takes back $75.50, $24.50 less than it put in.
Think in thousands: about 620 of 1,000 go to AKs, about 375 go to 86s, and about 5 are chopped.
The same matchup from the other side
If you came looking for 86s against AKs, the numbers are the same with the hands swapped: 37.75% and 62.25%.
Keep exploring
Open the calculator with AsKs against 8h6h 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
This is an exact count with no sampling. For the 16 ways to deal one AKs and one 86s without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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