44 vs 65s: preflop equity

In equity, 44 against 65s stands at 50.34% to 49.66%, a gap of 0.68 points.

44

50.34%

Wins 49.30%, ties 2.08%

65s

49.66%

Wins 48.62%, ties 2.08%

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

44 against 65s: the numbers

Exact preflop results for 44 against 65s, in percent
HandWinsTiesLosesEquity
4449.3002.07648.62450.338
65s48.6242.07649.30049.662

44 and 65s are a pocket pair and a suited hand, in that order. This is a pair against two overcards, a matchup that stays close because the other hand only needs one of its ranks to appear.

With only 0.68 points between them, the board decides this matchup far more than the cards in hand. Ties are 2.08% of the outcomes here; each tied board gives both hands half the pot.

The hand ranking puts 44 at 48 and 65s at 128 out of 169 starting hands.

Boards behind the percentages: 41,095,296 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
4420,260,000853,00019,982,000
65s19,982,000853,00020,260,000

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 65s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
441.0142.0282.0570.987
65s0.9872.0572.0281.014

In the last column, a pot-to-call ratio at or above the figure makes a call break even or better at this equity.

Who is ahead on which flops

Across the five flop textures 44's equity moves by 16.81 points, from 38.62% on low rainbow flops (nine high or lower) to 55.43% on paired flops. Low rainbow flops (nine high or lower), two-tone flops and monotone flops favor 65s, the hand that is behind overall.

44 against 65s by flop texture, in percent
FlopShare of flops44 winsTies65s wins44 equity
Rainbow, ten or higher25.84452.2001.23546.56552.818
Rainbow, nine or lower5.06538.2080.82460.96838.620
Two-tone46.54547.8651.10751.02848.419
Monotone5.21247.8713.49948.63049.621
Paired17.33452.4985.86841.63455.432

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

Relative to a random opponent, 44 changes by -6.68 points (baseline 57.02%) and 65s by +6.53 points (baseline 43.13%).

44 and 65s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
44, all flops50.33857.023-6.6850.88277
44, rainbow, ten or higher52.81857.023-4.2050.92626
44, rainbow, nine or lower38.62057.023-18.4030.67727
44, two-tone48.41957.023-8.6040.84911
44, monotone49.62157.023-7.4020.87019
44, paired55.43257.023-1.5910.97210
65s, all flops49.66243.133+6.5291.15137
65s, rainbow, ten or higher47.18243.133+4.0491.09387
65s, rainbow, nine or lower61.38043.133+18.2471.42304
65s, two-tone51.58143.133+8.4481.19586
65s, monotone50.37943.133+7.2461.16799
65s, paired44.56843.133+1.4351.03327

Does a shared suit matter?

Looking only at deals where the hands share a suit, 44 has 50.43%; looking only at deals where they do not, 50.24%. The two rows differ by only 0.19 points, so suits barely change this matchup.

44 against 65s by suit overlap, in percent
DealsSpecific dealsShare of deals44 winsTies65s wins44 equity
Share a suit1250.0049.3772.11048.51350.432
No shared suit1250.0049.2222.04248.73650.243

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 24 are 44 in one seat and 65s in the other (0.0015%); with the seats swapped too, 48 (0.0030%).

A worked example

Try it with money: two players each put in $100 and the whole board runs out every possible way. 44 averages $100.68 from the $200, up $0.68; 65s averages $99.32, down $0.68.

Run 1,000 deals and the tally comes out near 493 for 44, 486 for 65s and 21 ties.

The same matchup from the other side

One page covers both views. From 65s' side the equity is 49.66%, and from 44's side it is 50.34%.

The calculator link fills in 4s4h against 6d5d, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.

How this was computed

We counted every case. Each suit pattern of the 24 specific 44 against 65s 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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