AJo
58.94%
Wins 58.69%, ties 0.50%
54s
41.06%
Wins 40.81%, ties 0.50%
AJo against 54s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AJo | 58.685 | 0.500 | 40.815 | 58.935 |
| 54s | 40.815 | 0.500 | 58.685 | 41.065 |
One side is an offsuit hand, the other is a suited hand. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
The lead is steady rather than large, and the flop still has plenty of say in who wins. A split pot comes up on 0.50% of boards, so the wins and the equity differ by half of that.
Among the 169 starting hands, AJo is number 15 and 54s is number 136 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AJo | 48,234,000 | 411,000 | 33,546,000 |
| 54s | 33,546,000 | 411,000 | 48,234,000 |
48 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) |
|---|---|---|---|---|
| AJo | 1.435 | 1.704 | 2.450 | 0.697 |
| 54s | 0.697 | 2.450 | 1.704 | 1.435 |
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
The flop changes the picture. AJo does best on rainbow flops topped by a ten or better, at 66.74%, and worst on low rainbow flops (nine high or lower), at 32.74%. Low rainbow flops (nine high or lower) favor 54s, the hand that is behind overall.
| Flop | Share of flops | AJo wins | Ties | 54s wins | AJo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 66.647 | 0.195 | 33.158 | 66.744 |
| Rainbow, nine or lower | 6.313 | 32.280 | 0.915 | 66.805 | 32.737 |
| Two-tone | 46.667 | 56.990 | 0.322 | 42.688 | 57.151 |
| Monotone | 5.212 | 56.166 | 2.481 | 41.353 | 57.406 |
| Paired | 17.091 | 62.324 | 0.665 | 37.011 | 62.656 |
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
How much does the opponent matter? Compared with its random-hand 63.56%, AJo changes by -4.62 points, and 54s, from 41.45%, by -0.39.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AJo, all flops | 58.935 | 63.563 | -4.628 | 0.92719 |
| AJo, rainbow, ten or higher | 66.744 | 63.563 | +3.181 | 1.05004 |
| AJo, rainbow, nine or lower | 32.737 | 63.563 | -30.826 | 0.51503 |
| AJo, two-tone | 57.151 | 63.563 | -6.412 | 0.89912 |
| AJo, monotone | 57.406 | 63.563 | -6.157 | 0.90314 |
| AJo, paired | 62.656 | 63.563 | -0.907 | 0.98573 |
| 54s, all flops | 41.065 | 41.453 | -0.388 | 0.99064 |
| 54s, rainbow, ten or higher | 33.256 | 41.453 | -8.197 | 0.80226 |
| 54s, rainbow, nine or lower | 67.263 | 41.453 | +25.810 | 1.62263 |
| 54s, two-tone | 42.849 | 41.453 | +1.396 | 1.03368 |
| 54s, monotone | 42.594 | 41.453 | +1.141 | 1.02753 |
| 54s, paired | 37.344 | 41.453 | -4.109 | 0.90088 |
Does a shared suit matter?
When the hands share a suit, AJo holds 59.61%; when they do not, it holds 58.27%. AJo does better with a shared suit, by 1.34 points.
| Deals | Specific deals | Share of deals | AJo wins | Ties | 54s wins | AJo equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 59.335 | 0.539 | 40.126 | 59.605 |
| No shared suit | 24 | 50.00 | 58.035 | 0.460 | 41.505 | 58.265 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 48 are AJo in one seat and 54s in the other (0.0030%); with the seats swapped too, 96 (0.0059%).
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. AJo is worth $117.88 on average (+$17.88); 54s is worth $82.12 (-$17.88).
Over a long run, 1,000 deals split into about 587 for AJo, 408 for 54s and 5 tied.
The same matchup from the other side
The mirror image, 54s against AJo, is 41.06% to 58.94%, and its address redirects to this page.
Keep exploring
AsJh against 5d4d 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
Method: exact enumeration. The 48 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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