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?