75s
63.00%
Wins 54.25%, ties 17.49%
54s
37.00%
Wins 28.26%, ties 17.49%
75s against 54s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 75s | 54.253 | 17.493 | 28.254 | 63.000 |
| 54s | 28.254 | 17.493 | 54.253 | 37.000 |
Both hands are suited hands: 75s and 54s. Because the hands share one rank, the one with the higher kicker is ahead when that rank pairs and the other hand is mostly drawing.
A 26.00 point lead is real, and 54s still takes about 283 of every 1,000 deals outright. Split pots make up 17.49% of the boards, and both equity figures count them as half a win each.
Among the 169 starting hands, 75s is number 124 and 54s is number 136 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 75s | 11,148,000 | 3,594,000 | 5,806,000 |
| 54s | 5,806,000 | 3,594,000 | 11,148,000 |
Exact total: 12 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) |
|---|---|---|---|---|
| 75s | 1.703 | 1.843 | 3.539 | 0.587 |
| 54s | 0.587 | 3.539 | 1.843 | 1.703 |
In the last column, a pot-to-call ratio at or above the figure makes a call break even or better at this equity.
Who is ahead on which flops
Across the five flop textures 75s' equity moves by 6.17 points, from 58.73% on monotone flops to 64.90% on rainbow flops topped by a ten or better. 75s stays ahead on all five textures.
| Flop | Share of flops | 75s wins | Ties | 54s wins | 75s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.844 | 56.053 | 17.702 | 26.245 | 64.904 |
| Rainbow, nine or lower | 5.065 | 56.244 | 11.500 | 32.256 | 61.994 |
| Two-tone | 46.543 | 54.966 | 15.037 | 29.997 | 62.485 |
| Monotone | 5.215 | 51.438 | 14.587 | 33.975 | 58.732 |
| Paired | 17.333 | 49.921 | 26.400 | 23.679 | 63.121 |
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
How much does the opponent matter? Compared with its random-hand 43.68%, 75s changes by +19.32 points, and 54s, from 41.45%, by -4.45.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 75s, all flops | 63.000 | 43.676 | +19.324 | 1.44244 |
| 75s, rainbow, ten or higher | 64.904 | 43.676 | +21.228 | 1.48603 |
| 75s, rainbow, nine or lower | 61.994 | 43.676 | +18.318 | 1.41941 |
| 75s, two-tone | 62.485 | 43.676 | +18.809 | 1.43065 |
| 75s, monotone | 58.732 | 43.676 | +15.056 | 1.34472 |
| 75s, paired | 63.121 | 43.676 | +19.445 | 1.44521 |
| 54s, all flops | 37.000 | 41.453 | -4.453 | 0.89258 |
| 54s, rainbow, ten or higher | 35.096 | 41.453 | -6.357 | 0.84665 |
| 54s, rainbow, nine or lower | 38.006 | 41.453 | -3.447 | 0.91685 |
| 54s, two-tone | 37.515 | 41.453 | -3.938 | 0.90500 |
| 54s, monotone | 41.268 | 41.453 | -0.185 | 0.99554 |
| 54s, paired | 36.879 | 41.453 | -4.574 | 0.88966 |
Does a shared suit matter?
For this pair the shared-suit row is empty: the two hands cannot both own a card of one suit without reusing a card.
| Deals | Specific deals | Share of deals | 75s wins | Ties | 54s wins | 75s equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 54.253 | 17.493 | 28.254 | 63.000 |
How often this matchup comes up
How often does it happen? 12 of the 1,624,350 ordered deals (0.0007%) are 75s against 54s, and 24 (0.0015%) if either hand may sit in either seat.
A worked example
Put $100 each into a $200 pot and deal every board once: 75s averages $126.00 back, ahead of its $100 by $26.00, while 54s averages $74.00, short of its $100 by $26.00.
Run 1,000 deals and the tally comes out near 542 for 75s, 283 for 54s and 175 ties.
The same matchup from the other side
54s versus 75s is this same page seen from the other hand: 37.00% for 54s, 63.00% for 75s.
Keep exploring
The calculator link fills in 7s5s against 5h4h, 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
Method: exact enumeration. The 12 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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