Question 1

What are combinatorics in poker?

Accepted Answer

Combinatorics is the branch of probability that counts the exact number of possible hand combinations (combos) a player can hold from the 1,326 total starting combinations in Texas Hold'em.

Question 2

How many combos of each hand type exist?

Accepted Answer

Unpaired hands have 16 combos (4 suited, 12 offsuit). Pocket pairs have 6 combos: C(4,2) = 6.

Question 3

What is the blocker effect (card removal)?

Accepted Answer

When you hold a card (e.g. an Ace), your opponent is mathematically less likely to hold hands containing that card. For instance, holding an Ace cuts your opponent's pocket Aces from 6 combos to 3 (-50%) and their AK combos from 16 to 12 (-25%).

Question 4

Why are blockers critical for bluffing?

Accepted Answer

Holding key blockers (like the Ace of trump suit or straight blockers) drastically reduces the probability that your opponent holds nut hands, making your bluffs significantly higher EV.

Question 5

How does board runout affect combos on later streets?

Accepted Answer

Each exposed board card removes 1 out of 4 ranks or suits, progressively reducing opponents' value hands and drawing combos as the hand develops to the river.

Combinatorics & Blocker Matrix Calculator

Known Dead Cards (Blockers)

Range Presets

13×13 Blocker Density Grid