Poker math: understanding "outs" 🧮

The first step in learning poker math is to master the concept of "outs". Outs are cards that can improve your hand to a winning combination.

🔢 Defining and calculating outs

Outs help you estimate your chances of winning in percentage terms. For example, if you're expecting a flush in spades after the flop, there are 13 spades in the deck initially. If there are already four on the board, you have nine outs for a flush.

🎯 Calculating probabilities

To calculate the probability of drawing the desired card, you can use this probability table:

If you are waiting for one card (the turn), the probability of making a flush is 19.15%.

After the turn, on the river, the odds increase to 19.57%.

The overall chance of making a flush on the turn or river is 34.97%.

📈 Why the odds differ

The probabilities differ depending on the number of unknown cards remaining. After the turn, the number of these cards decreases, which increases the odds on the river.