Poker Hand Odds

In the game of Texas Hold'em there are plenty of times you will need a card to show itself on the flop, turn, or on the river. For example, 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 in the game, you will need to know two things. The first is how many 'Outs' you have.

'Outs' are the number of cards that can 'make' your card hands. If you are looking for that flush on the river, there are up to 9 cards that can help you (13 clubs in the deck - 4 clubs in your hand or on the board = 9 clubs still remaining).
The second thing to know is the total of unseen cards. Since two cards are in your hand, and four are on the board, there are 46 card still remaining. (52-2=50 followed by 50-4=46).
Now computing the odds is a very simple division problem. 9 cards that can help you, divided by 46 cards out there, equals 19.6%. (9÷46=19.56%). This is how you do it, 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 of flush, the odds of catching it on the turn is 19.1%, on the river is 19.6%.
  Catching it on the turn or on the river is 35.0%.
  
  
• Open Straight: Odds of catching your card on the turn is 17.0%. On the river is 17.4%.
  On the turn or the river is 31.5%.
  
  
• Gunshot Straight: Catching your card on the turn is 8.5%. Catching your card on a river is 8.7%.
  Catching it on the turn or the river it is 16.5%.
  
  
• Trips: Turn your pair into Three of a Kind on the turn is 4.3%. Catch at the river is 4.3%.
  Catch at the turn or the river is 8.4%.
  With pocket pairs it is more likely you'll want to catch on the flop. Odds of that is 11.8%.