Calculating the Odds of Making Your Hand (Poker)
You will always hear poker players talking about poker odds. Ok what is it all about? Well lets take a look at odds and more importantly, the odds of hitting the cards you need to give you a winning hand. Understand that there a 52 cards in a deck of cards. Now depending on how many people are at your table there will be a certain number of cards on the board (visible) as well as your and everyone elses hole cards (not visible - cards in hand). You can therefore use this information to your advantage as you know what cards are left in the deck. Now the calculation of odds is all based on percentages. Knowing the likely hood of a card that you need being dealt to give you your winning hand.
For instance, you may need to know the odds of
catching that Heart on the river to make your flush, or flopping the third 5 to make your set. In
order to calculate 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 left in the deck
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 total in your hand and on the board = 9 clubs
remaining). In Holdem approximate percentage probability that a player will hit an out is calculated by (number of outs) x 2 + 1 where 1 card is to come. So with 9 outs there is roughly a 19% (9 x 2 + 1) probability the next card will give him his flush. Where 2 cards are to come the approximate percentage probability is: (number of outs) x 4 - 1. So in this case if you had 9 outs to make you your flush - it would be (9) x 4-1 = 35%. This is to say if you played the same hand an infinite number of times you would hit your flush just under half of the time.
Odds may be converted into percentage probabilities using the formula: win-to-loss odds = win / (win + loss) % probability. For example 1-to-4 odds translate to 1 / (1 + 4) = 20% probability.
Some Quick Odds
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 card 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 on 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 are 11.8% (more cards are dealt at once). These stats should emphisise the fact that you shouldn't commit too many chips trying to catch trips as you will do so less than 1 in 10 times. See our guide to seeing a cheap flop.
So you see knowing how many cards are left in the deck is key. Now imagine you have a 4-5 Clubs in your hand and the board reads 3C-6H-4C. Now you have a good hand here. You know there are 13 clubs in the deck and you have a flush draw meaning you need one more flush to be dealt to give you a flush. So as you have 2 Clubs in your hand and 2 are on the board there are 9 left. You also have an open ended straight draw meaning that any 2 or 7 (any suit) would give you a straight. So potentially you can add another 4 cards to your number of outs (9 clubs + 4 = 13 outs).
Now you are not finished here as any 4 would give you trip 4's (3 of a kind) and with another 2 cards in the deck you now have 15 outs. That is 15 cards that could give you a winning hand (or at least a very good chance).
A quick way to calculate odds is on the flop, multiply your outs by four and by two on the turn. To calculate this the calculation is : (number of outs * 4) - (number of outs - 8) = Likelyhood. So with 15 outs: (15 * 4) - (15 - 8) = 53%.
Now read our guide on pot odds calculation. This is used in conjunction with the odds of making your hand. You will hit your hand just over every 2 times you play the hand. Now the value of the pot and the bet made is also important. As you know you will hit your hand every 2 times you need the value of the pot to be at least 2 - 1 on your money. So if the pot is $50 and your opponent bets $10 into that pot. You know that you would hit your hand every 2 (2-1 odds) times but you are getting 5-1 odds on calling the bet ($50 divided by $10 = 5). So you are getting value for money and should make the call. If the pot odds were less than the odds of making your hand you should fold.
Other Relevant Guides
Possible Starting Poker Hands
Poker Hand Rankings
Calculating Pot Odds
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