99 vs 53s: preflop equity

Averaged over every possible board, 99 is ahead of 53s by 58.62 points of equity, 79.31% to 20.69%.

99

79.31%

Wins 78.96%, ties 0.70%

53s

20.69%

Wins 20.34%, ties 0.70%

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

99 against 53s: the numbers

Exact preflop results for 99 against 53s, in percent
HandWinsTiesLosesEquity
9978.9580.70320.33979.310
53s20.3390.70378.95820.690

One side is a pocket pair, the other is a suited hand. Here a pair faces two cards that are both smaller, so the other hand needs to pair up and still be behind.

99 is well ahead, and 53s needs a specific kind of board to catch up. 0.70% 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, 99 is number 6 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
9932,448,000289,0008,358,000
53s8,358,000289,00032,448,000

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.

99 against 53s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
993.8331.2664.9170.261
53s0.2614.9171.2663.833

The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.

Who is ahead on which flops

Split by what the flop looks like, 99 peaks at 83.45% on rainbow flops topped by a ten or better and bottoms out at 68.56% on low rainbow flops (nine high or lower). 99 stays ahead on all five textures.

99 against 53s by flop texture, in percent
FlopShare of flops99 winsTies53s wins99 equity
Rainbow, ten or higher25.84483.2550.39816.34783.454
Rainbow, nine or lower5.06568.1380.83731.02568.557
Two-tone46.54577.2920.44322.26577.514
Monotone5.21272.7502.58024.67074.040
Paired17.33482.0561.25016.69482.681

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

Relative to a random opponent, 99 changes by +7.25 points (baseline 72.06%) and 53s by -19.00 points (baseline 39.69%).

99 and 53s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
99, all flops79.31072.057+7.2531.10066
99, rainbow, ten or higher83.45472.057+11.3971.15817
99, rainbow, nine or lower68.55772.057-3.5000.95143
99, two-tone77.51472.057+5.4571.07573
99, monotone74.04072.057+1.9831.02752
99, paired82.68172.057+10.6241.14744
53s, all flops20.69039.693-19.0030.52125
53s, rainbow, ten or higher16.54639.693-23.1470.41685
53s, rainbow, nine or lower31.44339.693-8.2500.79215
53s, two-tone22.48639.693-17.2070.56650
53s, monotone25.96039.693-13.7330.65402
53s, paired17.31939.693-22.3740.43632

Does a shared suit matter?

The suit split reads 79.89% for 99 with a shared suit and 78.73% without one. 99 does better with a shared suit, by 1.16 points.

99 against 53s by suit overlap, in percent
DealsSpecific dealsShare of deals99 winsTies53s wins99 equity
Share a suit1250.0079.5150.74519.74079.888
No shared suit1250.0078.4020.66020.93878.732

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 24 are 99 in one seat and 53s in the other (0.0015%); with the seats swapped too, 48 (0.0030%).

A worked example

Worked example: both players commit $100, so $200 sits in the middle. Over every board, 99's average share is $158.62 (a gain of $58.62) and 53s' is $41.38 (a loss of $58.62).

Run 1,000 deals and the tally comes out near 790 for 99, 203 for 53s and 7 ties.

The same matchup from the other side

53s versus 99 is this same page seen from the other hand: 20.69% for 53s, 79.31% for 99.

9s9h 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

Method: exact enumeration. The 24 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.

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

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