A7s vs 44: preflop equity

The exact count puts 44 at 52.02% and A7s at 47.98% when the two hands see all five board cards.

A7s

47.98%

Wins 47.72%, ties 0.52%

44

52.02%

Wins 51.76%, ties 0.52%

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

A7s against 44: the numbers

Exact preflop results for A7s against 44, in percent
HandWinsTiesLosesEquity
A7s47.7150.52151.76447.975
4451.7640.52147.71552.025

The first hand is a suited 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.

44 leads by less than 5 points of equity, so the result of any one deal is close to a toss-up. Of every 100 boards, about 0.52 are split pots, and the equity figures already include them.

A7s ranks number 24 of 169 starting hands, and 44 ranks number 48, by equity against a random hand.

Boards behind the percentages: 41,095,296 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
A7s19,609,000214,00021,273,000
4421,273,000214,00019,609,000

Exact total: 24 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.

A7s against 44 read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
A7s0.9222.0961.9321.084
441.0841.9322.0960.922

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

The flop changes the picture. 44 does best on low rainbow flops (nine high or lower), at 59.16%, and worst on two-tone flops, at 50.84%. 44 stays ahead on all five textures.

A7s against 44 by flop texture, in percent
FlopShare of flopsA7s winsTies44 winsA7s equity
Rainbow, ten or higher25.22048.0640.26751.66948.198
Rainbow, nine or lower5.68940.4520.77958.76940.842
Two-tone46.54548.9970.33450.66949.164
Monotone5.21247.0922.82650.08248.505
Paired17.33446.3340.61753.04946.643

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 A7s from 60.98% by -13.00 points and 44 from 57.02% by -5.00 points.

A7s and 44 here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
A7s, all flops47.97560.984-13.0090.78668
A7s, rainbow, ten or higher48.19860.984-12.7860.79034
A7s, rainbow, nine or lower40.84260.984-20.1420.66972
A7s, two-tone49.16460.984-11.8200.80618
A7s, monotone48.50560.984-12.4790.79537
A7s, paired46.64360.984-14.3410.76484
44, all flops52.02557.023-4.9980.91235
44, rainbow, ten or higher51.80257.023-5.2210.90844
44, rainbow, nine or lower59.15857.023+2.1351.03744
44, two-tone50.83657.023-6.1870.89150
44, monotone51.49557.023-5.5280.90306
44, paired53.35757.023-3.6660.93571

Does a shared suit matter?

When the hands share a suit, 44 holds 52.20%; when they do not, it holds 51.85%. 44 does better with a shared suit, by 0.35 points.

A7s against 44 by suit overlap, in percent
DealsSpecific dealsShare of dealsA7s winsTies44 winsA7s equity
Share a suit1250.0047.5190.55651.92547.797
No shared suit1250.0047.9100.48651.60448.153

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 24 are A7s in one seat and 44 in the other (0.0015%); with the seats swapped too, 48 (0.0030%).

A worked example

With $100 from each side, the $200 pot is split on average as $104.04 for 44 and $95.96 for A7s; the first side gains $4.04 per all-in and the second gives up $4.04.

Run 1,000 deals and the tally comes out near 518 for 44, 477 for A7s and 5 ties.

The same matchup from the other side

The mirror image, 44 against A7s, is 52.02% to 47.98%, and its address redirects to this page.

Try As7s against 4h4d 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 24 specific A7s 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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