The Odds of Making Your Hand

In the game of Hold'em there are plenty of times you will need a card to show itself on the flop, turn, or the river. For instance, you may need to know the odds of catching that club on the river for the flush, or flopping the third 8 to go with the two in your hand.
In order to compute the odds of finding the card you need on the board, you will need to know two things. The first is how many 'Outs' you have. 'Outs' are simply the number of cards that can 'make' your hand. If you are looking for that flush on the river, there are 9 cards that can help you. (13 clubs in the deck - 4 clubs in your hand or on the board = 9 clubs remaining).
The second thing to know is the number of unseen cards. Since two cards are in your hand, and four are on the board, there are 46 card remaining. (52-2=50 followed by 50-4=46).
Now computing the odds is a simple division problem. 9 cards that can help, divided by 46 cards out there, equals 19.6%. (9÷46=19.56%). That's how you do it. Ok, 9÷46 isn't so simple, but still, that's how it's done.
Information you can use right away: Flush: If you hold a four flush, the odds of catching it on the turn are 19.1%, on the river is 19.6%. Catching it on the turn or the river is 35.0% Open-Ended Straight: Odds of catching your card on the turn, 17.0%. On the river, 17.4%. On the turn or the river, 31.5% Gutshot Straight: Catching your card on the turn, 8.5%. Catching your cad on the river, 8.7%. Catching it on the turn or the river, 16.5% Trips: Turn your pair into Three-of-a-Kind on the turn, 4.3%. Catch at the river, 4.3%. Catch at the turn or the river, 8.4%. With pocket pairs it is more likely you'll want to catch on the flop. Odds of that are 11.8%
Number of Outs Available to Improve Your Hand Outs You Hold Hope to Make 2 A Pair Three of a Kind 4 Two Pair Full House 4 Inside Straight Straight 8 Open-ended Straight Straight 9 Four Flush Flush 15 Open Straight Flush Draw Striaght, a Flush, or Straight Flush Probability of Catching an Out Outs Turn (%) River (%) Turn or River 20 42.6 43.5 67.5% 19 40.4 41.3 65.0% 18 38.3 39.1 62.4% 17 36.2 37.0 59.8% 16 34.0 34.8 57.0% 15 31.9 32.6 54.1% 14 29.8 30.4 51.2% 13 27.7 28.3 48.1% 12 25.5 26.1 45.0% 11 23.4 23.9 41.7% 10 21.3 21.7 38.4% 9 19.1 19.6 35.0% 8 17.0 17.4 31.5% 7 14.9 15.2 27.8% 6 12.8 13.0 24.1% 5 10.6 10.9 20.4% 4 8.5 8.7 16.5% 3 6.4 6.5 12.5% 2 4.3 4.3 8.4% 1 2.1 2.2 4.3%