A5s vs QJo: preflop equity

The exact count puts A5s at 58.73% and QJo at 41.27% when the two hands see all five board cards.

A5s

58.73%

Wins 58.50%, ties 0.47%

QJo

41.27%

Wins 41.03%, ties 0.47%

Equity counts a tie as half a win. Exact over every board.

A5s against QJo: the numbers

Exact preflop results for A5s against QJo, in percent
HandWinsTiesLosesEquity
A5s58.4980.47141.03158.734
QJo41.0310.47158.49841.266

A5s is a suited hand and QJo is an offsuit hand. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.

That is a modest edge, the kind that shows up over many hands and is easy to miss in one. About 0.47% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.

The hand ranking puts A5s at 30 and QJo at 39 out of 169 starting hands.

Boards behind the percentages: 82,190,592 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
A5s48,080,000387,00033,724,000
QJo33,724,000387,00048,080,000

The total is exact: 48 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.

A5s against QJo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
A5s1.4231.7092.4370.703
QJo0.7032.4371.7091.423

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

By flop texture, A5s' equity runs from 50.95% on rainbow flops topped by a ten or better up to 76.23% on low rainbow flops (nine high or lower). A5s stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

A5s against QJo by flop texture, in percent
FlopShare of flopsA5s winsTiesQJo winsA5s equity
Rainbow, ten or higher23.98850.8930.11948.98850.952
Rainbow, nine or lower7.04275.7251.00323.27276.227
Two-tone46.66758.2350.29841.46758.384
Monotone5.21254.4772.39643.12755.675
Paired17.09164.0180.63335.34964.335

A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.

Compared with a random hand

A random hand would give A5s 59.92% and QJo 58.14%. Against each other the change is -1.19 points for A5s and -16.87 for QJo.

A5s and QJo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
A5s, all flops58.73459.923-1.1890.98016
A5s, rainbow, ten or higher50.95259.923-8.9710.85029
A5s, rainbow, nine or lower76.22759.923+16.3041.27208
A5s, two-tone58.38459.923-1.5390.97432
A5s, monotone55.67559.923-4.2480.92911
A5s, paired64.33559.923+4.4121.07363
QJo, all flops41.26658.135-16.8690.70983
QJo, rainbow, ten or higher49.04858.135-9.0870.84369
QJo, rainbow, nine or lower23.77358.135-34.3620.40893
QJo, two-tone41.61658.135-16.5190.71585
QJo, monotone44.32558.135-13.8100.76245
QJo, paired35.66558.135-22.4700.61349

Does a shared suit matter?

The suit split reads 58.39% for A5s with a shared suit and 59.08% without one. A5s does better with no shared suit, by 0.69 points.

A5s against QJo by suit overlap, in percent
DealsSpecific dealsShare of dealsA5s winsTiesQJo winsA5s equity
Share a suit2450.0058.1320.51341.35558.389
No shared suit2450.0058.8630.43040.70759.078

How often this matchup comes up

This page stands for 48 specific-card matchups (0.0030% of 1,624,350 ordered deals), or 96 once you count the seats both ways (0.0059%).

A worked example

With $100 from each side, the $200 pot is split on average as $117.46 for A5s and $82.54 for QJo; the first side gains $17.46 per all-in and the second gives up $17.46.

Run 1,000 deals and the tally comes out near 585 for A5s, 410 for QJo and 5 ties.

The same matchup from the other side

Read it from the other side: QJo against A5s is the same matchup with the numbers swapped, so QJo holds 41.27% and A5s holds 58.73%. That address sends you back to this page.

As5s against QhJd 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 48 deals of A5s against QJo 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.

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