55
61.22%
Wins 59.56%, ties 3.32%
75s
38.78%
Wins 37.12%, ties 3.32%
55 against 75s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 55 | 59.556 | 3.323 | 37.121 | 61.217 |
| 75s | 37.121 | 3.323 | 59.556 | 38.783 |
We compare a pocket pair with a suited hand. The non-pair hand shares a rank with the pair, so two of its outs for pairing are blocked by the pair itself.
That is a modest edge, the kind that shows up over many hands and is easy to miss in one. About 3.32% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
For context, 55 sits at number 27 of 169 starting hands and 75s at number 124 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 55 | 12,237,000 | 683,000 | 7,627,000 |
| 75s | 7,627,000 | 683,000 | 12,237,000 |
The total is exact: 12 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) |
|---|---|---|---|---|
| 55 | 1.578 | 1.679 | 2.694 | 0.634 |
| 75s | 0.634 | 2.694 | 1.679 | 1.578 |
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
55 prefers rainbow flops topped by a ten or better, where it holds 65.30%, and likes low rainbow flops (nine high or lower) least, where it holds 46.46%. Low rainbow flops (nine high or lower) favor 75s, the hand that is behind overall.
| Flop | Share of flops | 55 wins | Ties | 75s wins | 55 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.786 | 64.202 | 2.185 | 33.613 | 65.295 |
| Rainbow, nine or lower | 4.995 | 43.292 | 6.341 | 50.367 | 46.463 |
| Two-tone | 46.236 | 57.953 | 2.650 | 39.397 | 59.278 |
| Monotone | 5.152 | 56.654 | 3.634 | 39.712 | 58.471 |
| Paired | 17.831 | 62.387 | 5.776 | 31.837 | 65.275 |
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
Each hand has a baseline against a random hand: 60.33% for 55, 43.68% for 75s. Here the change is +0.89 and -4.90 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 55, all flops | 61.217 | 60.325 | +0.892 | 1.01479 |
| 55, rainbow, ten or higher | 65.295 | 60.325 | +4.970 | 1.08239 |
| 55, rainbow, nine or lower | 46.463 | 60.325 | -13.862 | 0.77021 |
| 55, two-tone | 59.278 | 60.325 | -1.047 | 0.98264 |
| 55, monotone | 58.471 | 60.325 | -1.854 | 0.96927 |
| 55, paired | 65.275 | 60.325 | +4.950 | 1.08206 |
| 75s, all flops | 38.783 | 43.676 | -4.893 | 0.88797 |
| 75s, rainbow, ten or higher | 34.705 | 43.676 | -8.971 | 0.79460 |
| 75s, rainbow, nine or lower | 53.537 | 43.676 | +9.861 | 1.22578 |
| 75s, two-tone | 40.722 | 43.676 | -2.954 | 0.93237 |
| 75s, monotone | 41.529 | 43.676 | -2.147 | 0.95084 |
| 75s, paired | 34.725 | 43.676 | -8.951 | 0.79506 |
Does a shared suit matter?
Suits do not split this matchup, because no legal deal has the hands holding the same suit.
| Deals | Specific deals | Share of deals | 55 wins | Ties | 75s wins | 55 equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 59.556 | 3.323 | 37.121 | 61.217 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 12 are 55 in one seat and 75s in the other (0.0007%); with the seats swapped too, 24 (0.0015%).
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says 55 gets $122.44 of it on average and 75s gets $77.56.
Over a long run, 1,000 deals split into about 596 for 55, 371 for 75s and 33 tied.
The same matchup from the other side
75s against 55 adds nothing new: it is 38.78% for 75s and 61.22% for 55, the same figures reversed.
Keep exploring
Try 5s5h against 7d5d 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 12 specific deals of 55 against 75s, 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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