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Expected Value, PART 2

By Lou Krieger

This is the second part [read Part 1] in a series of three columns about expected value, commonly called “EV,” and how understanding this notion can dramatically affect your results at poker. Using EV at the Table. EV is generally used to understand and express the value of a particular play, such as betting or raising. A multitude of factors influence the EV of any given poker play, and they include: position, number of opponents, playing style, table image, pot odds, and more.

 Some of these factors are easily measured, such as the odds against completing a flush on the turn whenever you flop a four flush. Other factors are estimates, at best, such as reckoning how often your opponent will call your bluff. With a mixture of measurable facts and estimates going into a decision, figuring your EV is not always going to be precise.

 Here’s an example. You have Ac-Jc and are first to act when the flop is Th-5c-3c. You don’t have a hand that’s likely to win if you went to showdown right now, but you can calculate the chances of completing your flush on the turn, or calculate your chances if you were going to consider both the turn and river cards too. And if you were to come out betting your flush draw, you’d have another way to win too, because your opponent might fold. The chances of him raising, calling, or folding to your bet are not measurable, but you can estimate them—even if that estimate is no more accurate than a good guess—based on how well you are able to read your opponent, and how accurately you are able to figure the range of hands he might play. You might also win if you caught an ace or a jack to pair-up on the turn or river, so you can consider that a bit of lagniappe.

 How to Figure EV. While no one really likes doing arithmetic at the poker table, and it can be distracting from the decisions at hand, it really helps if you understand how to compute EV. Once you know how to do this, you can do some calculations away from the table, and take that knowledge into the game with you.

 Here’s how to figure the amount of money, on average, that you will win or lose on a bet. Let’s say you and a friend agree to flip a coin, each paying the other $5 if he wins. Since the expectation is that the coin with come up heads half the time and tails the other half, it’s a neutral EV bet, and neither side has the better of this wager in the long run—although one of you could get very lucky in the short run and win a bundle. But suppose your opponent is willing to pay you $10 every time you win, but you only have to pay him $5 every time you lose. Without doing any math at all, it’s pretty clear to see that this is a +EV bet for you and a –EV wager for your friend.

 Let’s See How This All Works Out. You’ll still win approximately half the coin flips in the long run, but when you win, you’ll win $10; when you lose, the cost is only $5. If you flipped that coin 100 times, and it came up heads half the time, you’d win $500 (50 x 10) when you won. And when the coin came up in favor of your opponent, you’d only lose $250 (50 x 5). So if you flipped 100 times, you’d figure to be ahead $250. If you divide your expected win of $250 by each of the 100 times you flipped, each flip would have an EV of $2.50 for you.

 But there’s a lot more to EV than this simple example, and we’ll reveal it all in the third and final piece in this series. Stay tuned.

 Visit Lou Krieger online at www.loukrieger.com, where you can read his blog, and check out all of his books. Write directly to him at loukrieger@aol.com.

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