Q9s
63.35%
Wins 62.89%, ties 0.90%
86s
36.65%
Wins 36.21%, ties 0.90%
Q9s against 86s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| Q9s | 62.894 | 0.904 | 36.202 | 63.346 |
| 86s | 36.202 | 0.904 | 62.894 | 36.654 |
Here suited hands face each other, Q9s on one side and 86s on the other. 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. The tie share is 0.90%: on those boards the pot is chopped and neither hand wins outright.
By strength against a random hand, Q9s holds place 43 of 169 and 86s holds place 110.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| Q9s | 17,231,000 | 248,000 | 9,918,000 |
| 86s | 9,918,000 | 248,000 | 17,231,000 |
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) |
|---|---|---|---|---|
| Q9s | 1.728 | 1.590 | 2.762 | 0.579 |
| 86s | 0.579 | 2.762 | 1.590 | 1.728 |
The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.
Who is ahead on which flops
The flop changes the picture. Q9s does best on rainbow flops topped by a ten or better, at 67.74%, and worst on low rainbow flops (nine high or lower), at 46.15%. The lead reverses on low rainbow flops (nine high or lower): there 86s is the favorite even though Q9s is ahead overall.
| Flop | Share of flops | Q9s wins | Ties | 86s wins | Q9s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 67.516 | 0.441 | 32.043 | 67.736 |
| Rainbow, nine or lower | 5.689 | 45.908 | 0.491 | 53.601 | 46.153 |
| Two-tone | 46.727 | 62.506 | 0.417 | 37.077 | 62.715 |
| Monotone | 5.273 | 58.585 | 3.520 | 37.895 | 60.345 |
| Paired | 17.091 | 64.116 | 2.248 | 33.636 | 65.240 |
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
A random hand would give Q9s 57.66% and 86s 46.24%. Against each other the change is +5.69 points for Q9s and -9.59 for 86s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| Q9s, all flops | 63.346 | 57.664 | +5.682 | 1.09854 |
| Q9s, rainbow, ten or higher | 67.736 | 57.664 | +10.072 | 1.17467 |
| Q9s, rainbow, nine or lower | 46.153 | 57.664 | -11.511 | 0.80038 |
| Q9s, two-tone | 62.715 | 57.664 | +5.051 | 1.08759 |
| Q9s, monotone | 60.345 | 57.664 | +2.681 | 1.04649 |
| Q9s, paired | 65.240 | 57.664 | +7.576 | 1.13138 |
| 86s, all flops | 36.654 | 46.243 | -9.589 | 0.79264 |
| 86s, rainbow, ten or higher | 32.264 | 46.243 | -13.979 | 0.69771 |
| 86s, rainbow, nine or lower | 53.847 | 46.243 | +7.604 | 1.16444 |
| 86s, two-tone | 37.285 | 46.243 | -8.958 | 0.80628 |
| 86s, monotone | 39.655 | 46.243 | -6.588 | 0.85754 |
| 86s, paired | 34.760 | 46.243 | -11.483 | 0.75168 |
Does a shared suit matter?
Does suit overlap move the numbers? Q9s has 65.77% when the hands share a suit and 62.54% when they do not. Q9s does better with a shared suit, by 3.23 points.
| Deals | Specific deals | Share of deals | Q9s wins | Ties | 86s wins | Q9s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 65.267 | 1.000 | 33.733 | 65.767 |
| No shared suit | 12 | 75.00 | 62.103 | 0.872 | 37.025 | 62.539 |
How often this matchup comes up
How often does it happen? 16 of the 1,624,350 ordered deals (0.0010%) are Q9s against 86s, and 32 (0.0020%) if either hand may sit in either seat.
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says Q9s gets $126.70 of it on average and 86s gets $73.30.
In 1,000 deals of exactly this matchup, expect about 629 won outright by Q9s, about 362 won outright by 86s and about 9 split.
The same matchup from the other side
If you came looking for 86s against Q9s, the numbers are the same with the hands swapped: 36.65% and 63.35%.
Keep exploring
Qs9s against 8h6h is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.
How this was computed
This is an exact count with no sampling. For the 16 ways to deal one Q9s 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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