A4s
56.10%
Wins 55.85%, ties 0.51%
86s
43.90%
Wins 43.64%, ties 0.51%
A4s against 86s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A4s | 55.847 | 0.512 | 43.641 | 56.103 |
| 86s | 43.641 | 0.512 | 55.847 | 43.897 |
Both hands are suited hands: A4s and 86s. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
A4s is ahead, but 86s is far from dead: it takes 436 of every 1,000 deals outright. About 0.51% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
A4s ranks number 35 of 169 starting hands, and 86s ranks number 110, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A4s | 15,300,000 | 140,000 | 11,956,000 |
| 86s | 11,956,000 | 140,000 | 15,300,000 |
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) |
|---|---|---|---|---|
| A4s | 1.278 | 1.791 | 2.291 | 0.782 |
| 86s | 0.782 | 2.291 | 1.791 | 1.278 |
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
Paired flops are the best for A4s (61.97%); low rainbow flops (nine high or lower) are the worst (36.08%). The lead reverses on low rainbow flops (nine high or lower): there 86s is the favorite even though A4s is ahead overall.
| Flop | Share of flops | A4s wins | Ties | 86s wins | A4s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 59.363 | 0.209 | 40.428 | 59.467 |
| Rainbow, nine or lower | 5.689 | 35.740 | 0.674 | 63.586 | 36.077 |
| Two-tone | 46.727 | 54.706 | 0.268 | 45.026 | 54.840 |
| Monotone | 5.273 | 52.070 | 3.430 | 44.500 | 53.785 |
| Paired | 17.091 | 61.636 | 0.673 | 37.691 | 61.973 |
Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.
Compared with a random hand
Relative to a random opponent, A4s changes by -2.93 points (baseline 59.03%) and 86s by -2.34 points (baseline 46.24%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A4s, all flops | 56.103 | 59.034 | -2.931 | 0.95035 |
| A4s, rainbow, ten or higher | 59.467 | 59.034 | +0.433 | 1.00733 |
| A4s, rainbow, nine or lower | 36.077 | 59.034 | -22.957 | 0.61112 |
| A4s, two-tone | 54.840 | 59.034 | -4.194 | 0.92896 |
| A4s, monotone | 53.785 | 59.034 | -5.249 | 0.91109 |
| A4s, paired | 61.973 | 59.034 | +2.939 | 1.04978 |
| 86s, all flops | 43.897 | 46.243 | -2.346 | 0.94927 |
| 86s, rainbow, ten or higher | 40.533 | 46.243 | -5.710 | 0.87652 |
| 86s, rainbow, nine or lower | 63.923 | 46.243 | +17.680 | 1.38233 |
| 86s, two-tone | 45.160 | 46.243 | -1.083 | 0.97658 |
| 86s, monotone | 46.215 | 46.243 | -0.028 | 0.99939 |
| 86s, paired | 38.027 | 46.243 | -8.216 | 0.82233 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, A4s has 57.87%; looking only at deals where they do not, 55.51%. A4s does better with a shared suit, by 2.36 points.
| Deals | Specific deals | Share of deals | A4s wins | Ties | 86s wins | A4s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 57.574 | 0.592 | 41.834 | 57.870 |
| No shared suit | 12 | 75.00 | 55.271 | 0.486 | 44.243 | 55.514 |
How often this matchup comes up
A4s 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 A4s takes back $112.20 of it, which is $12.20 more than it put in, and 86s takes back $87.80, $12.20 less than it put in.
Per 1,000 deals: A4s wins about 559, 86s wins about 436, and about 5 end in a split pot.
The same matchup from the other side
One page covers both views. From 86s' side the equity is 43.90%, and from A4s' side it is 56.10%.
Keep exploring
The calculator link fills in As4s against 8h6h, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.
How this was computed
The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 16 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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