A4s
55.23%
Wins 54.97%, ties 0.50%
87s
44.77%
Wins 44.53%, ties 0.50%
A4s against 87s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A4s | 54.974 | 0.502 | 44.524 | 55.225 |
| 87s | 44.524 | 0.502 | 54.974 | 44.775 |
Two suited hands meet here: A4s against 87s. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
A 10.46 point lead is real, and 87s still takes about 445 of every 1,000 deals outright. A split pot comes up on 0.50% of boards, so the wins and the equity differ by half of that.
The hand ranking puts A4s at 35 and 87s at 100 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A4s | 15,061,000 | 138,000 | 12,198,000 |
| 87s | 12,198,000 | 138,000 | 15,061,000 |
Exact total: 16 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| A4s | 1.233 | 1.819 | 2.246 | 0.811 |
| 87s | 0.811 | 2.246 | 1.819 | 1.233 |
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
A4s prefers paired flops, where it holds 61.10%, and likes low rainbow flops (nine high or lower) least, where it holds 37.21%. Watch for low rainbow flops (nine high or lower): on those flops 87s holds the better equity.
| Flop | Share of flops | A4s wins | Ties | 87s wins | A4s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 57.914 | 0.221 | 41.865 | 58.024 |
| Rainbow, nine or lower | 5.689 | 36.941 | 0.538 | 62.521 | 37.210 |
| Two-tone | 46.727 | 53.861 | 0.257 | 45.882 | 53.989 |
| Monotone | 5.273 | 51.453 | 3.426 | 45.121 | 53.166 |
| Paired | 17.091 | 60.768 | 0.670 | 38.562 | 61.103 |
Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.
Compared with a random hand
A random hand would give A4s 59.03% and 87s 47.94%. Against each other the change is -3.80 points for A4s and -3.17 for 87s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A4s, all flops | 55.225 | 59.034 | -3.809 | 0.93548 |
| A4s, rainbow, ten or higher | 58.024 | 59.034 | -1.010 | 0.98289 |
| A4s, rainbow, nine or lower | 37.210 | 59.034 | -21.824 | 0.63031 |
| A4s, two-tone | 53.989 | 59.034 | -5.045 | 0.91454 |
| A4s, monotone | 53.166 | 59.034 | -5.868 | 0.90060 |
| A4s, paired | 61.103 | 59.034 | +2.069 | 1.03505 |
| 87s, all flops | 44.775 | 47.936 | -3.161 | 0.93406 |
| 87s, rainbow, ten or higher | 41.976 | 47.936 | -5.960 | 0.87567 |
| 87s, rainbow, nine or lower | 62.790 | 47.936 | +14.854 | 1.30987 |
| 87s, two-tone | 46.011 | 47.936 | -1.925 | 0.95984 |
| 87s, monotone | 46.834 | 47.936 | -1.102 | 0.97701 |
| 87s, paired | 38.897 | 47.936 | -9.039 | 0.81144 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common A4s has 56.88% equity, and with none in common it has 54.67%. A4s does better with a shared suit, by 2.21 points.
| Deals | Specific deals | Share of deals | A4s wins | Ties | 87s wins | A4s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 56.587 | 0.581 | 42.832 | 56.877 |
| No shared suit | 12 | 75.00 | 54.436 | 0.475 | 45.089 | 54.674 |
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
Try it with money: two players each put in $100 and the whole board runs out every possible way. A4s averages $110.46 from the $200, up $10.46; 87s averages $89.54, down $10.46.
Out of 1,000 deals you should see around 550 outright wins for A4s, 445 for 87s, and 5 split pots.
The same matchup from the other side
87s against A4s adds nothing new: it is 44.77% for 87s and 55.23% for A4s, the same figures reversed.
Keep exploring
Try As4s against 8h7h 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 16 specific deals of A4s against 87s, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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