Poker Probabilities Every Player Should Memorize

Poker maths is not a large body of knowledge. About twenty numbers cover nearly every decision you will make, and once they are memorised you stop calculating at the table and start recognising. Aces beat a random hand about 85% of the time, a pocket pair flops a set roughly 12% of the time, and AK is a modest underdog against pocket queens. Here is the full list worth knowing cold, grouped by when you actually use it.

What you get dealt

There are 1,326 possible two-card starting hands. Every preflop frequency comes from that single number.

Starting hand	Probability	Roughly once every
A specific pair, such as AA	0.45%	221 hands
Any pocket pair	5.9%	17 hands
AK, suited or offsuit	1.2%	83 hands
AKs specifically	0.3%	332 hands
Any suited ace	3.6%	28 hands
Two broadway cards	14.3%	7 hands

The engine underneath is combination counting. Every pocket pair has 6 combinations, every unpaired hand has 16, and those 16 split into 4 suited and 12 offsuit. So offsuit hands are three times as common as suited ones, which is exactly why AKo shows up in ranges far more often than AKs does.

This is also why premium hands feel scarce. All the pairs from TT up plus AK and AQ together make up under 5% of starting hands, so a UTG range of 15-17% is mostly hands that are merely good rather than genuinely strong. A BTN opening 40-45% is playing a completely different distribution, and the gap between those two ranges drives most of the money in 6-max.

Those counts also do the heavy lifting after the flop, when you are working out how many ways an opponent can hold a set or a flush. The mechanics are covered in poker combinatorics basics, and they turn vague reads into countable ones.

Who is ahead before the flop

Almost every preflop all-in falls into one of five shapes. Learn the shapes and you never need the exact hand.

Matchup	Example	Favourite's equity
Pair over lower pair	AA vs KK	82%
Pair over random hand	AA vs 72o	85%
Pair over two overcards	QQ vs AKo	57%
Big pair over small pair with a suited overcard	worst case near even	50-55%
Dominated ace	AK vs AQ	74%

Two of these deserve a closer look.

The classic race is not a race. Pocket queens beat AKo about 57% of the time and AKs about 54%. The suited version picks up roughly three points from its flush equity alone. If you want the full breakdown of how the board changes that fight, look at AK against pocket queens — the flop turns a near-coin-flip into a rout in one direction or the other about two thirds of the time.

Small pairs hold up better than they feel. AKs against 22 is close to a genuine coin flip. The deuces are ahead on raw pair equity, and the suited big cards claw it all back with straights and flushes. Getting 22 all-in for 100bb against AKs is a break-even proposition, not a disaster.

The number that matters most from this table is 82%. Aces over kings is as close to a lock as preflop poker offers, and it still loses one time in five. That single fact explains most of the bad beat stories you have ever heard.

What the flop does

The flop is where hands are decided, and it misses far more often than players expect.

• A pocket pair flops a set 12% of the time, about once in every 8.5 flops. Set mining is profitable only when the payoff covers the seven misses, which is why it wants deep stacks.
• Two unpaired cards pair the flop about 32% of the time. So AK flops at least a pair roughly one time in three, and whiffs completely the other two.
• A suited hand flops a flush draw about 11% of the time and flops the made flush 0.8% of the time.
• The flop comes paired about 17% of the time. Every sixth board is one where full houses and trips are live.
• The flop is monotone about 5% of the time — rare enough that it changes everyone's strategy when it lands.

Two thirds of the time your big unpaired hand is just ace high on the flop. That is not a leak, it is the game, and the players who win are the ones comfortable betting and folding those hands rather than treating every miss as bad luck. If the ranking of what you have flopped is not yet automatic, the full hand rankings guide is ten minutes well spent.

Drawing odds after the flop

Once you have a draw, everything reduces to counting clean outs and converting them.

Multiply your outs by two for one card, by four for two cards. Nine outs is about 18% on the turn and about 35% by the river.

Draw	Outs	Next card	By the river
Gutshot	4	8.5%	16.5%
Two overcards	6	13%	24%
Open-ended straight draw	8	17%	31.5%
Flush draw	9	19%	35%
Flush draw plus gutshot	12	26%	45%
Flush draw plus open-ender	15	32%	54%

The rule of 4 comes with a condition that costs people money: it only applies when you are paying once to see both cards, which in practice means you are all-in. Facing a flop bet with more streets to come, your flush draw is an 18% shot, not a 35% one, because the turn brings another bet.

Clean outs matter as much as counted outs. Four straight outs on a two-tone board are not four full outs, because one of them completes a flush for someone else. The habit of discounting them is the difference between a number and a useful number, and counting outs at the table walks through how to do it in the two seconds you actually have.

Turning probabilities into decisions

A probability on its own decides nothing. It becomes a decision when you compare it against the price.

Say the pot is $100 and your opponent bets $50 on the flop. You are risking $50 to win $150, so you need 25% equity to break even. Your flush draw is worth about 18% on the next card alone — short of the price on raw odds, and profitable only when the implied money on later streets covers the gap.

Change one detail and the answer flips. If that $50 bet puts you all-in, you are buying both cards for one payment, your 35% comfortably beats the 25% price, and the call is clear. Same cards, same bet, opposite decision.

The other direction is just as useful. When you bet $50 into $100 as a bluff, you risk $50 to win $100, so it needs to work more than a third of the time. Small bluffs need to work far less often than large ones, which is why the reflex to shove is usually the expensive option.

The defensive version of the same arithmetic is minimum defence frequency: pot divided by pot plus bet. Against a half-pot bet that is about 67% of your range, and against a pot-sized bet about 50%. Folding well past those thresholds is the quietest leak in low-stakes poker, costing a couple of big blinds per hundred without ever feeling like a mistake.

The numbers that mislead

Some probabilities are memorised correctly and then applied badly.

82% is not safety. Aces over kings loses one hand in five. Over a year of play you will lose that spot dozens of times, and none of those losses are evidence of anything.

12% is not rare. A pocket pair flops a set often enough that in any big pot where a passive opponent suddenly raises, sets should be near the top of the list of things they hold.

Rare events are common in aggregate. Any one player flopping quads is a long shot, but across every hand dealt at your table for a year, something absurd happening is close to certain. Extremely unlikely and never are not the same thing.

Your sample is smaller than you think. Aces once per 221 hands means a four-hour live session of about 120 hands is a coin flip on whether you see them at all. Running bad for a week is entirely normal and carries no information about your game.

Making them automatic

Reading a table does not memorise it. Four things move these numbers into recall.

1. Learn the shapes, not the hands. Pair over pair, pair versus overcards, dominated ace. Three categories cover nearly every all-in.
2. Guess before you check. Estimate the equity in a spot, then verify it. The gap between your guess and the answer is the part you are actually learning.
3. Count outs on every hand you fold. Free repetitions, no money at risk, and the counting becomes reflexive within a few sessions.
4. Review the spots you got wrong, not the ones you got right. Wrong answers are where the learning is.

Run your real hands through a poker equity calculator after each session — guess the number first, then check it — and within a few weeks the table above stops being something you consult and becomes something you simply know.