ATo vs 44: preflop equity

Before any board card is dealt, 44 holds 52.98% equity against ATo, which leaves ATo with 47.02%.

ATo

47.02%

Wins 46.79%, ties 0.46%

44

52.98%

Wins 52.75%, ties 0.46%

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

ATo against 44: the numbers

Exact preflop results for ATo against 44, in percent
HandWinsTiesLosesEquity
ATo46.7890.46452.74747.021
4452.7470.46446.78952.979

The first hand is an offsuit hand; the second is a pocket pair. This is a pair against two overcards, a matchup that stays close because the other hand only needs one of its ranks to appear.

That is a slim edge: neither hand is far ahead. About 0.46% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.

Ranked by equity against a random hand, ATo is number 19 of the 169 starting hands and 44 is number 48.

Boards behind the percentages: 123,285,888 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
ATo57,684,000572,00065,030,000
4465,030,000572,00057,684,000

The total is exact: 72 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.

ATo against 44 read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
ATo0.8882.1371.8961.127
441.1271.8962.1370.888

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

Break the boards down by their first three cards and 44 is strongest on low rainbow flops (nine high or lower) (77.82%) and weakest on rainbow flops topped by a ten or better (46.64%). Watch for rainbow flops topped by a ten or better: on those flops ATo holds the better equity.

ATo against 44 by flop texture, in percent
FlopShare of flopsATo winsTies44 winsATo equity
Rainbow, ten or higher24.71753.2390.24246.51953.360
Rainbow, nine or lower6.31421.8180.71977.46322.178
Two-tone46.48547.1560.32652.51847.319
Monotone5.15148.8071.98749.20649.800
Paired17.33345.1070.60454.28945.409

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 62.72%, ATo changes by -15.70 points, and 44, from 57.02%, by -4.04.

ATo and 44 here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
ATo, all flops47.02162.722-15.7010.74967
ATo, rainbow, ten or higher53.36062.722-9.3620.85074
ATo, rainbow, nine or lower22.17862.722-40.5440.35359
ATo, two-tone47.31962.722-15.4030.75442
ATo, monotone49.80062.722-12.9220.79398
ATo, paired45.40962.722-17.3130.72397
44, all flops52.97957.023-4.0440.92908
44, rainbow, ten or higher46.64057.023-10.3830.81792
44, rainbow, nine or lower77.82257.023+20.7991.36475
44, two-tone52.68157.023-4.3420.92386
44, monotone50.20057.023-6.8230.88035
44, paired54.59157.023-2.4320.95735

Does a shared suit matter?

Of the deals of this matchup, 60 share a suit (44 at 52.90%) and 12 do not (53.39%). 44 does better with no shared suit, by 0.49 points.

ATo against 44 by suit overlap, in percent
DealsSpecific dealsShare of dealsATo winsTies44 winsATo equity
Share a suit6083.3346.8660.47752.65747.104
No shared suit1216.6746.4090.39853.19346.608

How often this matchup comes up

You will meet this exact matchup 0.0089% of the time in a random heads-up deal: 144 of 1,624,350, counting either seat order.

A worked example

Put $100 each into a $200 pot and deal every board once: 44 averages $105.96 back, ahead of its $100 by $5.96, while ATo averages $94.04, short of its $100 by $5.96.

Run 1,000 deals and the tally comes out near 527 for 44, 468 for ATo and 5 ties.

The same matchup from the other side

Read it from the other side: 44 against ATo is the same matchup with the numbers swapped, so 44 holds 52.98% and ATo holds 47.02%. That address sends you back to this page.

Try AsTh against 4d4c 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

We counted every case. Each suit pattern of the 72 specific ATo against 44 deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.

Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.

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