55
66.43%
Wins 65.40%, ties 2.07%
64s
33.57%
Wins 32.53%, ties 2.07%
55 against 64s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 55 | 65.397 | 2.072 | 32.531 | 66.433 |
| 64s | 32.531 | 2.072 | 65.397 | 33.567 |
The first hand is a pocket pair; the second is a suited hand. The pair is ahead of one card and behind the other, so the board decides how that plays out.
55 is well ahead, and 64s needs a specific kind of board to catch up. About 2.07% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
Among the 169 starting hands, 55 is number 27 and 64s is number 138 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 55 | 26,875,000 | 851,000 | 13,369,000 |
| 64s | 13,369,000 | 851,000 | 26,875,000 |
The board total is exact, 24 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| 55 | 1.979 | 1.529 | 3.074 | 0.505 |
| 64s | 0.505 | 3.074 | 1.529 | 1.979 |
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. 55 does best on rainbow flops topped by a ten or better, at 69.88%, and worst on low rainbow flops (nine high or lower), at 60.28%. 55 stays ahead on all five textures.
| Flop | Share of flops | 55 wins | Ties | 64s wins | 55 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.844 | 69.260 | 1.235 | 29.505 | 69.878 |
| Rainbow, nine or lower | 5.065 | 59.873 | 0.820 | 39.307 | 60.283 |
| Two-tone | 46.545 | 64.549 | 1.104 | 34.347 | 65.101 |
| Monotone | 5.212 | 60.621 | 3.295 | 36.084 | 62.268 |
| Paired | 17.334 | 64.963 | 5.918 | 29.119 | 67.922 |
A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.
Compared with a random hand
Start from the random-hand figures, 60.33% for 55 and 41.33% for 64s. This opponent changes them by +6.10 and -7.76 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 55, all flops | 66.433 | 60.325 | +6.108 | 1.10125 |
| 55, rainbow, ten or higher | 69.878 | 60.325 | +9.553 | 1.15836 |
| 55, rainbow, nine or lower | 60.283 | 60.325 | -0.042 | 0.99930 |
| 55, two-tone | 65.101 | 60.325 | +4.776 | 1.07917 |
| 55, monotone | 62.268 | 60.325 | +1.943 | 1.03221 |
| 55, paired | 67.922 | 60.325 | +7.597 | 1.12593 |
| 64s, all flops | 33.567 | 41.333 | -7.766 | 0.81211 |
| 64s, rainbow, ten or higher | 30.122 | 41.333 | -11.211 | 0.72876 |
| 64s, rainbow, nine or lower | 39.717 | 41.333 | -1.616 | 0.96090 |
| 64s, two-tone | 34.899 | 41.333 | -6.434 | 0.84434 |
| 64s, monotone | 37.732 | 41.333 | -3.601 | 0.91288 |
| 64s, paired | 32.078 | 41.333 | -9.255 | 0.77609 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common 55 has 66.65% equity, and with none in common it has 66.21%. 55 does better with a shared suit, by 0.44 points.
| Deals | Specific deals | Share of deals | 55 wins | Ties | 64s wins | 55 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 65.597 | 2.110 | 32.293 | 66.652 |
| No shared suit | 12 | 50.00 | 65.197 | 2.034 | 32.769 | 66.214 |
How often this matchup comes up
How often does it happen? 24 of the 1,624,350 ordered deals (0.0015%) are 55 against 64s, and 48 (0.0030%) if either hand may sit in either seat.
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average 55 takes back $132.86 of it, which is $32.86 more than it put in, and 64s takes back $67.14, $32.86 less than it put in.
Over a long run, 1,000 deals split into about 654 for 55, 325 for 64s and 21 tied.
The same matchup from the other side
One page covers both views. From 64s' side the equity is 33.57%, and from 55's side it is 66.43%.
Keep exploring
The calculator link fills in 5s5h against 6d4d, 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 24 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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