Once you are in a hand in Texas hold'em, one of the keys to deciding how to play after the flop is know the odds that you, or others, have of hitting a hand. This is key since it will help you decide if you should call when you are on a drawing hand. Also, if you are trying to bet someone out of the pot and you think that they are on a draw, it will help you decide how much to bet such that they do not have pot odds.
There are two simple ways to estimate the odds of hitting a hand after the flop, and they are both based on computing the number of "outs", where "outs" are the number of cards remaining in the deck that will make a winning hand.
The first method is that you multiply the number of outs by four, and that is the probability that the hand will be made before the end of the hand. For example, the probability of hitting your hand when you have eight outs is: 8 * 4 = 32%.
The computed and actual odds are shown in the table below. As you can see, this method works well when the number of outs are below 10. But as the number of outs gets over 10, this method tends to overestimate the odds of making your hand.
The second method is a slight variation on the first method. You still multiply the number of outs by four. But you then subtract your distance from all previous outs that end with 9. For example, if you have 15 outs, the probability of hitting your hand is: 15 * 4 - (15 - 9) = 54%. If you have more outs than 19 (lucky you), you actually subtract the distance from 9 *and* the distance from 19. For example if you have 22 outs, the probability of hitting your hand is: 22 * 4 - (22 - 9) - (22 - 19) = 88 - 13 - 3 = 72%.
The computed and actual odds are shown in the table below. As you can see, this method works extremely well for all number of outs with the worst difference being 1%. You'll also notice that the 1% error always occurs when the number of outs ends in a 9 (which is also the trigger point to start subtracting odds); if you remember this it's a simple matter to just remember to subtract 1 from the result when the number of outs ends in 9. If you do this, the worst 0.6% which is pretty darn good for a method that requires only very simple math.
Using this method, you can easily compute the odds of hitting a hand after the flop in Texas hold'em to with 0.6%. All that is needed to know is the number of outs.
Actual versus estimated odds of hitting a hand after the flop in Texas hold'em
