The deck is a probability space
Fifty-two equally likely cards, and why counting is all you need.
5 minute read
Every poker probability is a fraction: the number of outcomes you want, over the number of outcomes possible. A shuffled deck makes every card equally likely, so the whole subject reduces to counting carefully.
Probability
P = favourable outcomes ÷ possible outcomes
Ask: what is the chance the next card is an ace? Four aces, fifty-two cards, 4 ÷ 52 = 7.69%. Now suppose you already hold two cards, neither an ace. There are fifty unseen cards and still four aces: 4 ÷ 50 = 8%. The probability moved because the denominator did.
Unseen, not undealt
The cards in your opponents' hands are unseen to you, so they stay in the denominator. From your seat there are 50 unseen cards preflop, 47 on the flop, 46 on the turn — regardless of how many players are at the table.
Try it below. Change a card in the live table and watch the outs and the probability follow. Each number is a count over a count.
The 15 highlighted cards improve your hand. Click any card to change the scenario.
Flush draw (9) · Two overcards (6)
Quick check
You hold A♠ K♠ on a flop of Q♥ 7♦ 2♣. How many unseen cards are there, and how many are aces?
Show answer
47 unseen (52 − 2 − 3). Three aces remain (you hold one).