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Expected Value, Part 3

by Lou Krieger

This is the third and final installment in our series on expected value, or “EV” as players call it [read Part 1 and Part 2]. In this installment we’ll do a little arithmetic—nothing complex or off-putting; I promise—and by the end you should be able to incorporate the notion of EV into your poker game and make much better decisions at the table.

 Last time we used an example based on flipping a coin, which is a 50-50 proposition. It had neutral EV if you and your opponent were willing to pay the other $5 per coin flip, but turned into an enormously positive EV for you if your opponent would shell out $10 whenever you won the flip, but you only had to pay him $5 when you lost.

 Without doing any math at all, it’s pretty clear to see that this was a +EV bet for you. For your opponent, it’s just the opposite. Each flip has a –EV of $2.50. In other words, each time you flipped that coin, it’s theoretical value to you would be $2.50, regardless of whether you won that particular flip or not.

 If you flipped 10,000 times, your +EV for each flip would remain $2.50, and you’d expect to win $25,000 at the end of your flipping marathon.

 That’s why having an edge is so important. If you can repeat it a large number of times, you can expect to win a lot of money.

 This is how aisles of small, 25-cent slot machines, each with a small edge, can yield enough money to construct incredibly large casinos. It’s all in the edge… that +EV that builds fortunes over long periods of time. And in poker, that’s precisely how you win money—by making bets that show a positive expectation. Suppose you’re playing no-limit Texas hold’em and have a flush draw. You’re holding As-9s and the community cards are Ks-4sTd-7h.

 We’ll assume the pot contains $250 and your opponent moves all-in for his remaining $50. Your option is to fold, or call $50 for the chance of winning a total of $300—the $250 already in the pot plus his $50 wager. If we assume the only way you can win this pot is by calling and catching a flush with the last card, what’s the expected value of a call? Is calling profitable, or is it a –EV play?

 The odds against catching a flush card on the river are 4.1- to-1, which we’ll round off to 4-to-1. Another way to express these 4-to-1 odds against completing your hand is to say that you have approximately a 20 percent chance of catching your flush card.

 If you call and miss your flush, you will lose $50, and you figure to miss about 80 percent of the time. If you call, you will either win $300 (the size of the pot) or lose $50 (the cost to call your opponent’s bet). Let’s do some simple arithmetic.

Here’s how it all works out:

 EV = Hitting the flush + Missing the flush
EV  = ($300 x 0.2) + (-$50 x 0.8)
EV = ($60) + (-$40)
EV = $20 EV

 Each time you call that bet you gain $20 on average. This is a +EV call, and if you make it, you’ll win money in the long run. But if the pot contained only $150 instead of $300, calling would have an EV of minus $10, and under those circumstances, you should fold.

 Please remember that EV is seldom a perfect calculation. Any time you have to assign a percentage to the chances of an opponent calling, it’s a judgment call at best. Even so, EV is still one of the best tools we have to help guide our poker decisions. In fact, just to think in terms of engaging in hands only when it affords a +EV to you, is a major addition to your poker tool box.

 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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September 4, 2014 - 9:31am
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