33
47.00%
Wins 46.16%, ties 1.68%
98s
53.00%
Wins 52.16%, ties 1.68%
33 against 98s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 33 | 46.163 | 1.679 | 52.158 | 47.003 |
| 98s | 52.158 | 1.679 | 46.163 | 52.997 |
33 and 98s are a pocket pair and a suited hand, in that order. One hand holds a pair and the other holds two cards that both outrank it, which keeps the equity closer than most people expect.
98s leads by less than 6 points of equity, so the result of any one deal is close to a toss-up. Ties are part of the picture: 1.68% of boards end in a split pot, and each side counts that as half a win.
For context, 33 sits at number 66 of 169 starting hands and 98s at number 83 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 33 | 18,971,000 | 690,000 | 21,434,000 |
| 98s | 21,434,000 | 690,000 | 18,971,000 |
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) |
|---|---|---|---|---|
| 33 | 0.887 | 2.166 | 1.917 | 1.128 |
| 98s | 1.128 | 1.917 | 2.166 | 0.887 |
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 98s is strongest on low rainbow flops (nine high or lower) (58.15%) and weakest on paired flops (49.72%). Watch for paired flops: on those flops 33 holds the better equity.
| Flop | Share of flops | 33 wins | Ties | 98s wins | 33 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.844 | 47.881 | 0.961 | 51.158 | 48.362 |
| Rainbow, nine or lower | 5.065 | 41.527 | 0.648 | 57.825 | 41.851 |
| Two-tone | 46.545 | 45.084 | 0.869 | 54.047 | 45.519 |
| Monotone | 5.212 | 45.831 | 3.616 | 50.553 | 47.639 |
| Paired | 17.334 | 47.956 | 4.642 | 47.402 | 50.277 |
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 33 53.69% and 98s 50.80%. Against each other the change is -6.69 points for 33 and +2.20 for 98s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 33, all flops | 47.003 | 53.693 | -6.690 | 0.87540 |
| 33, rainbow, ten or higher | 48.362 | 53.693 | -5.331 | 0.90071 |
| 33, rainbow, nine or lower | 41.851 | 53.693 | -11.842 | 0.77945 |
| 33, two-tone | 45.519 | 53.693 | -8.174 | 0.84776 |
| 33, monotone | 47.639 | 53.693 | -6.054 | 0.88725 |
| 33, paired | 50.277 | 53.693 | -3.416 | 0.93638 |
| 98s, all flops | 52.997 | 50.801 | +2.196 | 1.04323 |
| 98s, rainbow, ten or higher | 51.638 | 50.801 | +0.837 | 1.01648 |
| 98s, rainbow, nine or lower | 58.149 | 50.801 | +7.348 | 1.14464 |
| 98s, two-tone | 54.481 | 50.801 | +3.680 | 1.07244 |
| 98s, monotone | 52.361 | 50.801 | +1.560 | 1.03071 |
| 98s, paired | 49.723 | 50.801 | -1.078 | 0.97878 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and 98s holds 52.86%. In 12 they do not, and it holds 53.13%. 98s does better with no shared suit, by 0.27 points.
| Deals | Specific deals | Share of deals | 33 wins | Ties | 98s wins | 33 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 46.286 | 1.708 | 52.006 | 47.140 |
| No shared suit | 12 | 50.00 | 46.041 | 1.649 | 52.310 | 46.866 |
How often this matchup comes up
The class pair covers 24 combinations of specific cards in a fixed seat order, 0.0015% of 1,624,350, and 48 (0.0030%) in either order.
A worked example
Worked example: both players commit $100, so $200 sits in the middle. Over every board, 98s' average share is $106.00 (a gain of $6.00) and 33's is $94.00 (a loss of $6.00).
Out of 1,000 deals you should see around 521 outright wins for 98s, 462 for 33, and 17 split pots.
The same matchup from the other side
If you came looking for 98s against 33, the numbers are the same with the hands swapped: 53.00% and 47.00%.
Keep exploring
The calculator link fills in 3s3h against 9d8d, 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
This is an exact count with no sampling. For the 24 ways to deal one 33 and one 98s without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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