# The truth about EV

Oct 26, 2004 3:19 AM

The phrase "expected value" has become common with respect to gambling over the past decade or two. It wasn’t always that way. Although it has always applied to a variety of casino games, it really caught on when video poker came on the scene.

Although sometimes difficult to calculate, expected value is not really a difficult concept. In simple terms, it’s how much money you can expect back from your wager, in the long run, when all possible outcomes are considered. For a game like video poker, expected value is the number of coins, on average, you will get back once you determine which of the five initial cards you plan on holding. The calculation is done by looking at all possible outcomes of the draw. So, for the following example:

3 3 4 5 6

There are 32 different ways that any hand can be played, and the above example is no different. About 28 or 29 of these are obviously wrong plays, but they exist nonetheless. Most people who look at the above hand would figure it can be played in one of three ways:

1. Hold the pair of 3s

2. Hold the 3-card straight flush

3. Hold the 4-card straight

To decide what is the proper answer, we need to calculate the expected value of each of these choices. To do this, we use a simple computer program that looks at every possible draw. Total coins is calculated by multiplying each hand type by the payback for that hand and adding them up. The expected value is calculated by dividing total coins by total draws. The results are in the table at left:

From this table, we learn that the pair of 3s has the highest expected value, and thus, is the proper play. In expert strategy we ALWAYS play the hand that results in the highest expected value. We acknowledge that in the short run, most anything is the short run, most anything is possible, but in the long run, following this strategy will enhance our bankrolls.

There may be some who feel that holding the pair of 3s is the obvious play. However, if the 6 was a 10, and option three was a 4-card flush instead of the 4-card straight, we would find that the 4-card flush is actually the proper play. We would find that there are nine ways to complete the flush, resulting in total coins equaling 54, and the expected value equaling 1.15.

What do these expected values mean in the long run? An expected value below 1.0 means that in the long run, the hand is a loser. If you were to play 100 hands with one coin each and each time get a low pair, you could expect to get back approximately 82 of those coins. If, on the other hand, you were dealt a 4-card flush (with no high cards), for each of the 100 hands, you could expect to get back about 115 coins. Obviously, you’re not going to get dealt the same hand 100 straight times, but over several hours of play, you might. Playing this hand wrong can cost you 33 coins. If you were playing five quarters, this would really be 165 coins, or more than \$40.

By playing every hand using expert strategy, you can achieve 99.5 percent or more payback from a full-pay jacks or better machine. No human can play with computer efficiency, but even a few mistakes are not likely to cost you much.