Q9s vs 33: preflop equity

Q9s against 33: the numbers

The first hand is a suited hand; the second is a pocket pair. One hand holds a pair and the other holds two cards that both outrank it, which keeps the equity closer than most people expect.

This is close to even money, with Q9s a little ahead. Ties are 0.98% of the outcomes here; each tied board gives both hands half the pot.

In the ranking of all 169 starting hands, Q9s is number 43 and 33 is number 66.

24 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, rounded to the nearest thousand.

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

The flop changes the picture. Q9s does best on two-tone flops, at 52.26%, and worst on low rainbow flops (nine high or lower), at 41.77%. 33 is ahead on low rainbow flops (nine high or lower) and paired flops, even though it trails Q9s when every flop is counted.

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

Each hand has a baseline against a random hand: 57.66% for Q9s, 53.69% for 33. Here the change is -6.58 and -4.77 points.

Does a shared suit matter?

Two kinds of deal exist here. In 12 of them the hands share a suit and Q9s holds 50.91%. In 12 they do not, and it holds 51.25%. Q9s does better with no shared suit, by 0.34 points.

How often this matchup comes up

You will meet this exact matchup 0.0030% of the time in a random heads-up deal: 48 of 1,624,350, counting either seat order.

A worked example

Put $100 each into a $200 pot and deal every board once: Q9s averages $102.16 back, ahead of its $100 by $2.16, while 33 averages $97.84, short of its $100 by $2.16.

In 1,000 deals of exactly this matchup, expect about 506 won outright by Q9s, about 484 won outright by 33 and about 10 split.

The same matchup from the other side

The reversed view, 33 against Q9s, shows 48.92% for 33 and 51.08% for Q9s. It is the same count, so it redirects here.

Keep exploring

Open the calculator with Qs9s against 3h3d 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.

• Open Qs9s against 3h3d in the equity calculator
• Q9s combos
• 33 combos
• Q9s vs T8s
• Q9s vs T9o
• JTs vs 33
• All hand matchups