# Probability of forming a flush question (dependent vs independent event)

I'm slightly confused at the probability calculations for hands. Here's the problem:

Suppose you have two hearts. The flop comes and has two hearts. What is the probability of forming a flush on the turn or the river?

``````Probability of a flush on the turn = 9/47 = 0.19
Probability of a flush on the river = 38/47 * 9/46 = 0.16
``````

Now where I am confused is why these are added together. Are these independent events because the probability of getting a flush on the turn does not influence the probability of a flush on the river?

Final question - how do you get quick at calculating these at the table? Do you memorize a table of hand probabilities?

You already account for the dependency of the events since in your second calculation you take into account the probability that the flush did not fall on the turn. You can just add the probabilities to get 0.35.

For a quick estimation of the probabilities of hitting the flush:

• Multiply by two on the flop
• Multiply by four and add 2 on the turn

For example: 9 outs for your flush gives you 4*9 = 36% on the flop and 2*9+2 = 20% on the turn.