87s
62.50%
Wins 60.37%, ties 4.26%
54s
37.50%
Wins 35.37%, ties 4.26%
87s against 54s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 87s | 60.371 | 4.261 | 35.368 | 62.502 |
| 54s | 35.368 | 4.261 | 60.371 | 37.498 |
Each side holds one of the suited hands: 87s and 54s. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
A 25.00 point lead is real, and 54s still takes about 354 of every 1,000 deals outright. A split pot comes up on 4.26% of boards, so the wins and the equity differ by half of that.
In the ranking of all 169 starting hands, 87s is number 100 and 54s is number 136.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 87s | 16,540,000 | 1,167,000 | 9,690,000 |
| 54s | 9,690,000 | 1,167,000 | 16,540,000 |
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) |
|---|---|---|---|---|
| 87s | 1.667 | 1.656 | 2.827 | 0.600 |
| 54s | 0.600 | 2.827 | 1.656 | 1.667 |
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 87s is strongest on rainbow flops topped by a ten or better (64.16%) and weakest on low rainbow flops (nine high or lower) (59.36%). 87s stays ahead on all five textures.
| Flop | Share of flops | 87s wins | Ties | 54s wins | 87s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.844 | 62.360 | 3.609 | 34.031 | 64.164 |
| Rainbow, nine or lower | 5.065 | 59.070 | 0.570 | 40.360 | 59.355 |
| Two-tone | 46.727 | 61.027 | 2.758 | 36.215 | 62.406 |
| Monotone | 5.273 | 57.735 | 5.167 | 37.098 | 60.319 |
| Paired | 17.091 | 56.767 | 10.174 | 33.059 | 61.854 |
Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.
Compared with a random hand
Start from the random-hand figures, 47.94% for 87s and 41.45% for 54s. This opponent changes them by +14.56 and -3.95 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 87s, all flops | 62.502 | 47.936 | +14.566 | 1.30386 |
| 87s, rainbow, ten or higher | 64.164 | 47.936 | +16.228 | 1.33853 |
| 87s, rainbow, nine or lower | 59.355 | 47.936 | +11.419 | 1.23821 |
| 87s, two-tone | 62.406 | 47.936 | +14.470 | 1.30186 |
| 87s, monotone | 60.319 | 47.936 | +12.383 | 1.25832 |
| 87s, paired | 61.854 | 47.936 | +13.918 | 1.29035 |
| 54s, all flops | 37.498 | 41.453 | -3.955 | 0.90459 |
| 54s, rainbow, ten or higher | 35.836 | 41.453 | -5.617 | 0.86450 |
| 54s, rainbow, nine or lower | 40.645 | 41.453 | -0.808 | 0.98051 |
| 54s, two-tone | 37.594 | 41.453 | -3.859 | 0.90691 |
| 54s, monotone | 39.681 | 41.453 | -1.772 | 0.95725 |
| 54s, paired | 38.146 | 41.453 | -3.307 | 0.92022 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common 87s has 64.85% equity, and with none in common it has 61.72%. 87s does better with a shared suit, by 3.13 points.
| Deals | Specific deals | Share of deals | 87s wins | Ties | 54s wins | 87s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 62.562 | 4.579 | 32.859 | 64.852 |
| No shared suit | 12 | 75.00 | 59.640 | 4.156 | 36.204 | 61.718 |
How often this matchup comes up
87s against 54s 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
Try it with money: two players each put in $100 and the whole board runs out every possible way. 87s averages $125.00 from the $200, up $25.00; 54s averages $75.00, down $25.00.
Run 1,000 deals and the tally comes out near 604 for 87s, 354 for 54s and 42 ties.
The same matchup from the other side
54s against 87s adds nothing new: it is 37.50% for 54s and 62.50% for 87s, the same figures reversed.
Keep exploring
8s7s against 5h4h 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 16 specific deals of 87s against 54s, 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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