44 vs 53s: preflop equity

The exact count puts 44 at 66.19% and 53s at 33.81% when the two hands see all five board cards.

44

66.19%

Wins 64.75%, ties 2.87%

53s

33.81%

Wins 32.38%, ties 2.87%

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

44 against 53s: the numbers

Exact preflop results for 44 against 53s, in percent
HandWinsTiesLosesEquity
4464.7542.86832.37866.188
53s32.3782.86864.75433.812

Here a pocket pair (44) meets a suited hand (53s). One of the other hand's cards outranks the pair and one is below it, which makes this a closer race than a pair against two small cards.

That is a clear edge, 66.19% to 33.81%, but 53s still wins often enough that one hand proves nothing. 2.87% of boards are ties, so the equity of each hand is its win rate plus half of that.

Ranked by equity against a random hand, 44 is number 48 of the 169 starting hands and 53s is number 146.

Boards behind the percentages: 41,095,296 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
4426,611,0001,179,00013,306,000
53s13,306,0001,179,00026,611,000

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.

44 against 53s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
441.9581.5443.0890.511
53s0.5113.0891.5441.958

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

Break the boards down by their first three cards and 44 is strongest on rainbow flops topped by a ten or better (69.82%) and weakest on low rainbow flops (nine high or lower) (59.68%). 44 stays ahead on all five textures.

44 against 53s by flop texture, in percent
FlopShare of flops44 winsTies53s wins44 equity
Rainbow, ten or higher25.84469.0061.63529.35969.823
Rainbow, nine or lower5.06558.9911.38439.62559.683
Two-tone46.54564.2101.51034.28064.965
Monotone5.21260.1453.90035.95562.095
Paired17.33462.9488.47428.57867.185

Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.

Compared with a random hand

Compared with a random opponent, this matchup shifts 44 from 57.02% by +9.17 points and 53s from 39.69% by -5.88 points.

44 and 53s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
44, all flops66.18857.023+9.1651.16072
44, rainbow, ten or higher69.82357.023+12.8001.22447
44, rainbow, nine or lower59.68357.023+2.6601.04665
44, two-tone64.96557.023+7.9421.13928
44, monotone62.09557.023+5.0721.08895
44, paired67.18557.023+10.1621.17821
53s, all flops33.81239.693-5.8810.85184
53s, rainbow, ten or higher30.17739.693-9.5160.76026
53s, rainbow, nine or lower40.31739.693+0.6241.01572
53s, two-tone35.03539.693-4.6580.88265
53s, monotone37.90539.693-1.7880.95495
53s, paired32.81539.693-6.8780.82672

Does a shared suit matter?

Split by suits, the deals give 44 66.41% when the hands overlap in a suit and 65.97% when they do not. 44 does better with a shared suit, by 0.44 points.

44 against 53s by suit overlap, in percent
DealsSpecific dealsShare of deals44 winsTies53s wins44 equity
Share a suit1250.0064.9582.90232.14066.409
No shared suit1250.0064.5512.83332.61665.968

How often this matchup comes up

44 against 53s is made up of 24 specific-card matchups in one seat order, 0.0015% of the 1,624,350 ordered deals, and 48 counting both seat orders, 0.0030%.

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average 44 takes back $132.38 of it, which is $32.38 more than it put in, and 53s takes back $67.62, $32.38 less than it put in.

Over a long run, 1,000 deals split into about 647 for 44, 324 for 53s and 29 tied.

The same matchup from the other side

Swap the hands and you get 53s with 33.81% against 44 with 66.19%. We keep one page per matchup, with the better-ranked hand first.

4s4h against 5d3d 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

Each figure is a complete count over boards. Take the 24 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.

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

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