Combinatorics

8 steps · read as text

deck

count

52 cards

combos

K♠K♥K♦K♣

A♠

♠♠

♠♥

♠♦

♠♣

A♥

♥♠

♥♥

♥♦

♥♣

A♦

♦♠

♦♥

♦♦

♦♣

A♣

♣♠

♣♥

♣♦

♣♣

AK · 16 combos

A♠A♥A♦A♣

A♠

♠♥

♠♦

♠♣

A♥

♥♦

♥♣

A♦

♦♣

A♣

AA · 6 combos

1 / 8

How many different two-card hands can you be dealt? Start with the deck: 52 cards.

the numbers

any pair6suited, like AKs4offsuit, like AKo12unpaired, like AK16all two-card hands1,326

why it matters

When you guess what someone holds, count combos, not hands. "Aces or ace–king" sounds like a coin flip, but it’s 6 combos against 16.

An ace you can see cuts AA from 6 to 3 and AK from 16 to 12.

02Expected value 04Range vs range →Practice: count the outs

sources & further reading

Applications of No-Limit Hold’emMatthew Janda · 2013 · book

Modern Poker TheoryMichael Acevedo · 2019 · book

The Mathematics of PokerBill Chen, Jerrod Ankenman · 2006 · book