Combinatorics
Why there are 1,326 starting hands, how many ways each can be dealt, and how the cards you can see remove combinations.
- 01, open this step in the interactive version
How many different two-card hands can you be dealt? Start with the deck: 52 cards.
- 02, open this step in the interactive version
Your first card can be any of 52. Your second, any of the 51 left.
- 03, open this step in the interactive version
But A♠ K♥ and K♥ A♠ are the same hand, so every hand was counted twice.
- 04, open this step in the interactive version
Now one hand: ace–king. Four aces, four kings. Pair any ace with any king.
- 05, open this step in the interactive version
Four of those share a suit: ace–king suited. The other twelve are offsuit.
- 06, open this step in the interactive version
Pocket aces work differently. Pick two of the four aces. A♠A♥ and A♥A♠ are the same, so halve it.
- 07, open this step in the interactive version
So you’re dealt ace–king almost three times as often as pocket aces.
- 08, open this step in the interactive version
Cards you can see remove combos. These are called blockers. Tap a card to show or hide it.