AA
80.96%
Wins 80.72%, ties 0.48%
43s
19.04%
Wins 18.80%, ties 0.48%
AA against 43s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 80.720 | 0.478 | 18.802 | 80.959 |
| 43s | 18.802 | 0.478 | 80.720 | 19.041 |
AA and 43s are a pocket pair and a suited hand, in that order. A pair against two lower cards is a lopsided matchup: the pair is ahead and the other hand has no overcard to catch.
That is a heavy lead: 43s needs the board to help it on most runouts and still falls behind far more often than not. About 0.48% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
Among the 169 starting hands, AA is number 1 and 43s is number 150 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 33,172,000 | 196,000 | 7,727,000 |
| 43s | 7,727,000 | 196,000 | 33,172,000 |
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) |
|---|---|---|---|---|
| AA | 4.252 | 1.239 | 5.319 | 0.235 |
| 43s | 0.235 | 5.319 | 1.239 | 4.252 |
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
Split by what the flop looks like, AA peaks at 85.99% on rainbow flops topped by a ten or better and bottoms out at 70.25% 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 | 43s wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 85.852 | 0.276 | 13.872 | 85.990 |
| Rainbow, nine or lower | 6.314 | 69.651 | 1.188 | 29.161 | 70.245 |
| Two-tone | 46.545 | 78.917 | 0.424 | 20.659 | 79.129 |
| Monotone | 5.212 | 73.897 | 2.609 | 23.494 | 75.202 |
| Paired | 17.334 | 84.364 | 0.007 | 15.629 | 84.368 |
Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.
Compared with a random hand
Compared with a random opponent, this matchup shifts AA from 85.20% by -4.24 points and 43s from 38.64% by -19.60 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 80.959 | 85.204 | -4.245 | 0.95018 |
| AA, rainbow, ten or higher | 85.990 | 85.204 | +0.786 | 1.00922 |
| AA, rainbow, nine or lower | 70.245 | 85.204 | -14.959 | 0.82443 |
| AA, two-tone | 79.129 | 85.204 | -6.075 | 0.92870 |
| AA, monotone | 75.202 | 85.204 | -10.002 | 0.88261 |
| AA, paired | 84.368 | 85.204 | -0.836 | 0.99019 |
| 43s, all flops | 19.041 | 38.642 | -19.601 | 0.49275 |
| 43s, rainbow, ten or higher | 14.010 | 38.642 | -24.632 | 0.36256 |
| 43s, rainbow, nine or lower | 29.755 | 38.642 | -8.887 | 0.77002 |
| 43s, two-tone | 20.871 | 38.642 | -17.771 | 0.54011 |
| 43s, monotone | 24.798 | 38.642 | -13.844 | 0.64174 |
| 43s, paired | 15.632 | 38.642 | -23.010 | 0.40453 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common AA has 81.54% equity, and with none in common it has 80.37%. AA does better with a shared suit, by 1.17 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | 43s wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 81.288 | 0.513 | 18.199 | 81.544 |
| No shared suit | 12 | 50.00 | 80.153 | 0.442 | 19.405 | 80.374 |
How often this matchup comes up
You will meet this exact matchup 0.0030% of the time in a random heads-up deal: 48 of 1,624,350, counting either seat order.
A worked example
Take a $200 pot built from $100 each. AA's equity of 80.96% is worth $161.92, a $61.92 edge, and 43s' 19.04% is worth $38.08, which is $61.92 under its stake.
A thousand deals look like this: AA takes 807, 43s takes 188, 5 are ties.
The same matchup from the other side
43s versus AA is this same page seen from the other hand: 19.04% for 43s, 80.96% for AA.
Keep exploring
Try AsAh against 4d3d 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
The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 24 specific deals, both seven-card hands evaluated. A tie is worth half a win to each hand, and a board is tallied under each of its ten possible flops for the texture rows.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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