# Poker card odds vs pot odds can earn you \$\$\$

Mar 31, 2009 5:09 PM
by George “The Engineer” Epstein |

A student in my poker lab admitted that he shied away from using the poker odds. "Oh, that’s higher math," he complained. "I can’t handle that." Well, I assured him that he doesn’t have to be an expert in math to use such a valuable tool.

There are two categories of poker odds: card odds and pot odds.

In previous columns, we discussed the pot odds – essentially how much money you need to "invest" to stay in the pot, compared to the amount already in the pot or anticipated at the showdown. Now, let’s try to better understand the card odds.

Using your two hole cards and the board, what is the chance that you will make the hand to which you aspire? And what are the odds – the card odds – against making that hand, hopefully a winner?

To illustrate, you have been dealt J-J in the hole. What is the chance that the very next card will be a third jack, giving you a set of jacks? Wow! There are two jacks remaining in the deck; you have seen just two cards (your hole cards); so there are 50 (that’s 52 - 2) unseen (unaccounted for) cards.

The chance the next card will be a jack, then, is two out of 50 – or one out of 25. It will happen once out of 25 times – on the average, in the long run. (You can never be sure in the short term; that’s a matter of luck.)

So there are two cards that can help you, and 48 that won’t. Hence the card odds are 48-to-2; that’s 24-to-1 against making the set on the next card. But the flop affords you three opportunities to make the set. A rigorous mathematical calculation would show that the odds of making the set on the flop are 7.5-to-1 against you. We can approximate that simply by dividing our 24-to-1 by three (since the flop gives you three shots at it); that gives us approximately 8-to-1 against making the set on the flop. Close enough!

Another Typical Case

You hold A-10 of hearts and the turn brings a fourth heart (see chart):

What are the odds against making the nut flush on the river? With four hearts, there are nine more remaining in the deck. You have seen six cards (your two hole cards plus the four on the board); so there are 46 (that’s 52 - 6) unseen cards. Since nine of these are hearts (you need just one more for the nut flush!), then 37 cards (46 - 9) would miss your flush. Therefore, the odds are 37-to-9 against you; that’s 4.1-to-1.

Now that’s really not so difficult to understand. As we noted in a previous column, when the pot odds are higher than the card odds, you have a Positive Expectation, and are bound to be a winner – at least in the long run.

Hopefully, that makes it easier to grasp the use of card odds, used in conjunction with pot odds.

Next week, we examine "nut" hands – how to get them, and then make the most of them.

Try out your poker strategy with our new poker odds calculator.