55 vs 44: preflop equity

Averaged over every possible board, 55 is ahead of 44 by 62.96 points of equity, 81.48% to 18.52%.

55

81.48%

Wins 80.11%, ties 2.74%

44

18.52%

Wins 17.15%, ties 2.74%

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

55 against 44: the numbers

Exact preflop results for 55 against 44, in percent
HandWinsTiesLosesEquity
5580.1052.74417.15181.477
4417.1512.74480.10518.523

Two pocket pairs meet here: 55 against 44. Both hands are pairs, so the bigger pair is ahead on every board that does not pair a card below it.

A gap this wide means 44 is in trouble before the flop and has few good runouts. 2.74% of boards are ties, so the equity of each hand is its win rate plus half of that.

In the ranking of all 169 starting hands, 55 is number 27 and 44 is number 48.

Boards behind the percentages: 61,642,944 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
5549,379,0001,691,00010,572,000
4410,572,0001,691,00049,379,000

The total is exact: 36 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.

55 against 44 read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
554.3991.2485.8310.227
440.2275.8311.2484.399

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

55 prefers paired flops, where it holds 83.36%, and likes low rainbow flops (nine high or lower) least, where it holds 76.17%. 55 stays ahead on all five textures.

55 against 44 by flop texture, in percent
FlopShare of flops55 winsTies44 wins55 equity
Rainbow, ten or higher25.84482.0991.57516.32682.886
Rainbow, nine or lower5.06575.6101.11823.27276.169
Two-tone46.36380.4051.48118.11481.145
Monotone5.15274.4983.36922.13376.183
Paired17.57679.3198.07912.60283.358

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 55 60.33% and 44 57.02%. Against each other the change is +21.15 points for 55 and -38.50 for 44.

55 and 44 here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
55, all flops81.47760.325+21.1521.35063
55, rainbow, ten or higher82.88660.325+22.5611.37399
55, rainbow, nine or lower76.16960.325+15.8441.26264
55, two-tone81.14560.325+20.8201.34513
55, monotone76.18360.325+15.8581.26288
55, paired83.35860.325+23.0331.38182
44, all flops18.52357.023-38.5000.32483
44, rainbow, ten or higher17.11457.023-39.9090.30012
44, rainbow, nine or lower23.83157.023-33.1920.41792
44, two-tone18.85557.023-38.1680.33066
44, monotone23.81757.023-33.2060.41767
44, paired16.64257.023-40.3810.29185

Does a shared suit matter?

The suit split reads 81.62% for 55 with a shared suit and 80.78% without one. 55 does better with a shared suit, by 0.84 points.

55 against 44 by suit overlap, in percent
DealsSpecific dealsShare of deals55 winsTies44 wins55 equity
Share a suit3083.3380.2372.75717.00681.615
No shared suit616.6779.4452.67717.87880.783

How often this matchup comes up

How often does it happen? 36 of the 1,624,350 ordered deals (0.0022%) are 55 against 44, and 72 (0.0044%) if either hand may sit in either seat.

A worked example

Try it with money: two players each put in $100 and the whole board runs out every possible way. 55 averages $162.96 from the $200, up $62.96; 44 averages $37.04, down $62.96.

In 1,000 deals of exactly this matchup, expect about 801 won outright by 55, about 172 won outright by 44 and about 27 split.

The same matchup from the other side

The mirror image, 44 against 55, is 18.52% to 81.48%, and its address redirects to this page.

Open the calculator with 5s5h against 4d4c already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.

How this was computed

We counted every case. Each suit pattern of the 36 specific 55 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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