A7s
48.99%
Wins 48.71%, ties 0.57%
33
51.01%
Wins 50.72%, ties 0.57%
A7s against 33: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A7s | 48.706 | 0.572 | 50.722 | 48.992 |
| 33 | 50.722 | 0.572 | 48.706 | 51.008 |
We compare a suited hand with a pocket pair. One hand holds a pair and the other holds two cards that both outrank it, which keeps the equity closer than most people expect.
With only 2.02 points between them, the board decides this matchup far more than the cards in hand. 0.57% of boards are ties, so the equity of each hand is its win rate plus half of that.
Among the 169 starting hands, A7s is number 24 and 33 is number 66 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A7s | 20,016,000 | 235,000 | 20,844,000 |
| 33 | 20,844,000 | 235,000 | 20,016,000 |
The total is exact: 24 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) |
|---|---|---|---|---|
| A7s | 0.960 | 2.053 | 1.972 | 1.041 |
| 33 | 1.041 | 1.972 | 2.053 | 0.960 |
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
By flop texture, 33's equity runs from 50.05% on two-tone flops up to 56.79% on low rainbow flops (nine high or lower). 33 stays ahead on all five textures.
| Flop | Share of flops | A7s wins | Ties | 33 wins | A7s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 48.566 | 0.267 | 51.167 | 48.699 |
| Rainbow, nine or lower | 5.689 | 42.744 | 0.923 | 56.333 | 43.206 |
| Two-tone | 46.545 | 49.769 | 0.358 | 49.873 | 49.948 |
| Monotone | 5.212 | 47.645 | 3.191 | 49.164 | 49.240 |
| Paired | 17.334 | 48.334 | 0.689 | 50.977 | 48.679 |
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
Relative to a random opponent, A7s changes by -11.99 points (baseline 60.98%) and 33 by -2.68 points (baseline 53.69%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A7s, all flops | 48.992 | 60.984 | -11.992 | 0.80336 |
| A7s, rainbow, ten or higher | 48.699 | 60.984 | -12.285 | 0.79855 |
| A7s, rainbow, nine or lower | 43.206 | 60.984 | -17.778 | 0.70848 |
| A7s, two-tone | 49.948 | 60.984 | -11.036 | 0.81903 |
| A7s, monotone | 49.240 | 60.984 | -11.744 | 0.80742 |
| A7s, paired | 48.679 | 60.984 | -12.305 | 0.79823 |
| 33, all flops | 51.008 | 53.693 | -2.685 | 0.94999 |
| 33, rainbow, ten or higher | 51.301 | 53.693 | -2.392 | 0.95545 |
| 33, rainbow, nine or lower | 56.794 | 53.693 | +3.101 | 1.05775 |
| 33, two-tone | 50.052 | 53.693 | -3.641 | 0.93219 |
| 33, monotone | 50.760 | 53.693 | -2.933 | 0.94537 |
| 33, paired | 51.321 | 53.693 | -2.372 | 0.95582 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and 33 holds 51.19%. In 12 they do not, and it holds 50.82%. 33 does better with a shared suit, by 0.37 points.
| Deals | Specific deals | Share of deals | A7s wins | Ties | 33 wins | A7s equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 48.508 | 0.601 | 50.891 | 48.808 |
| No shared suit | 12 | 50.00 | 48.905 | 0.544 | 50.551 | 49.177 |
How often this matchup comes up
How often does it happen? 24 of the 1,624,350 ordered deals (0.0015%) are A7s against 33, 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 33 takes back $102.02 of it, which is $2.02 more than it put in, and A7s takes back $97.98, $2.02 less than it put in.
A thousand deals look like this: 33 takes 507, A7s takes 487, 6 are ties.
The same matchup from the other side
33 against A7s adds nothing new: it is 51.01% for 33 and 48.99% for A7s, the same figures reversed.
Keep exploring
Open the calculator with As7s against 3h3d already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.
How this was computed
This is an exact count with no sampling. For the 24 ways to deal one A7s and one 33 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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