QQ vs 44: preflop equity

Counting every board, the equity split is 80.96% for QQ and 19.04% for 44, so QQ leads by 61.92 points.

QQ

80.96%

Wins 80.74%, ties 0.44%

44

19.04%

Wins 18.82%, ties 0.44%

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

QQ against 44: the numbers

Exact preflop results for QQ against 44, in percent
HandWinsTiesLosesEquity
QQ80.7390.44018.82180.959
4418.8210.44080.73919.041

Here pocket pairs face each other, QQ on one side and 44 on the other. Two pairs against each other is a one-way street: the lower pair needs one of its two remaining cards.

QQ is a big favorite here before anyone sees a flop. A split pot comes up on 0.44% of boards, so the wins and the equity differ by half of that.

Among the 169 starting hands, QQ is number 3 and 44 is number 48 by strength against a random hand.

Boards behind the percentages: 61,642,944 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
QQ49,770,000271,00011,602,000
4411,602,000271,00049,770,000

Exact total: 36 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.

QQ against 44 read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
QQ4.2521.2395.3130.235
440.2355.3131.2394.252

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

Break the boards down by their first three cards and QQ is strongest on paired flops (86.70%) and weakest on low rainbow flops (nine high or lower) (66.81%). QQ stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

QQ against 44 by flop texture, in percent
FlopShare of flopsQQ winsTies44 winsQQ equity
Rainbow, ten or higher24.59583.7310.21916.05083.840
Rainbow, nine or lower6.31466.2641.10132.63566.814
Two-tone46.36379.6040.38320.01379.796
Monotone5.15274.4162.02723.55775.430
Paired17.57686.6020.19313.20586.698

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

A random hand would give QQ 79.93% and 44 57.02%. Against each other the change is +1.03 points for QQ and -37.98 for 44.

QQ and 44 here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
QQ, all flops80.95979.925+1.0341.01294
QQ, rainbow, ten or higher83.84079.925+3.9151.04898
QQ, rainbow, nine or lower66.81479.925-13.1110.83596
QQ, two-tone79.79679.925-0.1290.99839
QQ, monotone75.43079.925-4.4950.94376
QQ, paired86.69879.925+6.7731.08474
44, all flops19.04157.023-37.9820.33392
44, rainbow, ten or higher16.16057.023-40.8630.28339
44, rainbow, nine or lower33.18657.023-23.8370.58198
44, two-tone20.20457.023-36.8190.35431
44, monotone24.57057.023-32.4530.43088
44, paired13.30257.023-43.7210.23327

Does a shared suit matter?

Looking only at deals where the hands share a suit, QQ has 81.09%; looking only at deals where they do not, 80.30%. QQ does better with a shared suit, by 0.79 points.

QQ against 44 by suit overlap, in percent
DealsSpecific dealsShare of dealsQQ winsTies44 winsQQ equity
Share a suit3083.3380.8650.45318.68281.091
No shared suit616.6780.1130.37219.51580.299

How often this matchup comes up

This page stands for 36 specific-card matchups (0.0022% of 1,624,350 ordered deals), or 72 once you count the seats both ways (0.0044%).

A worked example

Worked example: both players commit $100, so $200 sits in the middle. Over every board, QQ's average share is $161.92 (a gain of $61.92) and 44's is $38.08 (a loss of $61.92).

Per 1,000 deals: QQ wins about 807, 44 wins about 188, and about 5 end in a split pot.

The same matchup from the other side

One page covers both views. From 44's side the equity is 19.04%, and from QQ's side it is 80.96%.

Open the calculator with QsQh 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 QQ 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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