Probability and Statistics – Pot Odds

You must know some of the simple mathematical calculations before deciding whether to call a bet or fold. When you need an extra card to get your hand, one of the most important abilities is to figure out the pot odds. In other words, how much is the pot offering, compared to the amount you have to pay.

Some basic terms first:
Outs – the number of cards left in the deck that will improve your hand. For example: if you hold Ah, 5h and the flop is Kh, 4h, 3c. It seems that you have 13 outs - 9 hearts that will make you a flush and another 4 two’s that will give you a straight. But pay careful attention not to count the 2 of hearts twice. Therefore you have only 12 outs.

Odds – calculating the odds of getting one of the outs is quite simple. You divide the number of outs by the number of cards you haven’t seen yet. If we take the previous example, the odds of getting the winning hand in the turn is 12/47 = 25%. Because there are 52 cards in the deck and you’ve seen 5 of them, it leaves 47 cards you haven’t seen yet. Phil Gordon developed a simple rule of “four and two”: he calculated the approximate odds of getting the winning card on the turn, by multiplying the number of outs by two. And for getting it on the turn or on the river, he multiplied the number of outs by four. This is not the exact percentage, but it’s almost always good enough because rarely do you need the specific calculation.

Pot odds – the final calculation you’ll need is checking if the pot is big enough for you to call with a hand that needs to be improved in order to win. If the pot is $100 and your opponent bets $50 after the turn, this means you have to pay $50 in order to get the chance of winning $150. This means you get 3 to 1 odds on your call. If you win one time for every 3 times you lose, you’re even. So you must win at least one out of every 4 games in order to make the call the right decision. The final calculation you’ll need to make is to see if your odds of getting the winning card are above 25% (1 out of 4). You should call if they are higher than 25%, and fold if lower.

Example: you hold 8d, 7c and the board is Ad, Qs, 6h, 5h. You have 8 outs to make a straight. If the pot is $300 and a player bets $100, you have to bet $100 to win $400, and your pot odds are 20%. Since you have 8 outs, by the rule of 2, you have approximately 16% of making your straight. Therefore you are not getting enough pot odds and should fold.