AA
81.77%
Wins 81.53%, ties 0.49%
33
18.23%
Wins 17.98%, ties 0.49%
AA against 33: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 81.526 | 0.490 | 17.984 | 81.771 |
| 33 | 17.984 | 0.490 | 81.526 | 18.229 |
This is a contest between two pocket pairs, AA and 33. Both hands are pairs, so the bigger pair is ahead on every board that does not pair a card below it.
That is a heavy lead: 33 needs the board to help it on most runouts and still falls behind far more often than not. About 0.49% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
The hand ranking puts AA at 1 and 33 at 66 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 50,255,000 | 302,000 | 11,086,000 |
| 33 | 11,086,000 | 302,000 | 50,255,000 |
36 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, 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) |
|---|---|---|---|---|
| AA | 4.486 | 1.227 | 5.560 | 0.223 |
| 33 | 0.223 | 5.560 | 1.227 | 4.486 |
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
If you know the kind of flop that came, the numbers shift: AA holds 87.17% on paired flops and 69.38% on low rainbow flops (nine high or lower). AA stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | AA wins | Ties | 33 wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 84.185 | 0.287 | 15.528 | 84.328 |
| Rainbow, nine or lower | 6.314 | 68.739 | 1.279 | 29.982 | 69.378 |
| Two-tone | 46.363 | 80.440 | 0.468 | 19.092 | 80.674 |
| Monotone | 5.152 | 75.051 | 2.322 | 22.627 | 76.212 |
| Paired | 17.576 | 87.164 | 0.007 | 12.829 | 87.167 |
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, 85.20% for AA and 53.69% for 33. This opponent changes them by -3.43 and -35.46 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 81.771 | 85.204 | -3.433 | 0.95971 |
| AA, rainbow, ten or higher | 84.328 | 85.204 | -0.876 | 0.98972 |
| AA, rainbow, nine or lower | 69.378 | 85.204 | -15.826 | 0.81426 |
| AA, two-tone | 80.674 | 85.204 | -4.530 | 0.94683 |
| AA, monotone | 76.212 | 85.204 | -8.992 | 0.89447 |
| AA, paired | 87.167 | 85.204 | +1.963 | 1.02304 |
| 33, all flops | 18.229 | 53.693 | -35.464 | 0.33950 |
| 33, rainbow, ten or higher | 15.672 | 53.693 | -38.021 | 0.29188 |
| 33, rainbow, nine or lower | 30.622 | 53.693 | -23.071 | 0.57032 |
| 33, two-tone | 19.326 | 53.693 | -34.367 | 0.35994 |
| 33, monotone | 23.788 | 53.693 | -29.905 | 0.44304 |
| 33, paired | 12.833 | 53.693 | -40.860 | 0.23901 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common AA has 81.91% equity, and with none in common it has 81.10%. AA does better with a shared suit, by 0.81 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | 33 wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 30 | 83.33 | 81.655 | 0.500 | 17.845 | 81.905 |
| No shared suit | 6 | 16.67 | 80.884 | 0.434 | 18.682 | 81.101 |
How often this matchup comes up
AA against 33 is made up of 36 specific-card matchups in one seat order, 0.0022% of the 1,624,350 ordered deals, and 72 counting both seat orders, 0.0044%.
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says AA gets $163.54 of it on average and 33 gets $36.46.
Run 1,000 deals and the tally comes out near 815 for AA, 180 for 33 and 5 ties.
The same matchup from the other side
One page covers both views. From 33's side the equity is 18.23%, and from AA's side it is 81.77%.
Keep exploring
AsAh against 3d3c 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
Nothing here is simulated. The 36 deals of AA against 33 fall into a few suit patterns, each dealt against all 1,712,304 boards, with both best five-card hands compared on every board. Ties give each hand half a win, and the flop rows count a board under each of its ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
Bring your own hands to a session
Review the spots you actually play against these numbers in a Game Assessment, and leave with a one-page written plan.
Book a session