EV class: cliff notes

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In chemistry, the basic building blocks are the elements from the periodic table. In casino games, the basic building block is something called the Expected Value, or EV for short.

It is what should determine the strategy for virtually every decision made by the player. Yet, it can frequently go ignored in favor of hunches, guesses and rabbit’s feet.

The term ‘expected value’ was initially used by my father, Lenny Frome, when assigning relative values to video poker hands. In this context, the concept of expected value can be somewhat complex to grasp, even when explained in detail.

So, to try and make it even more simplistic to understand the importance of EV, I’d like to try and use a simpler example.

Let’s say you walk up to a single-zero roulette wheel. It has 37 numbers (0 through 36) with 18 are red, 18 black, one is green.

If you bet red, it pays even money. In this case, we’ll assume that if it comes up green, it is a loss. What is the EV of this wager? This is a relatively simple calculation.

There are 37 possible outcomes, 18 result in a win, paying you a total of two units (one won plus the original wager), for a total of 36 units. All others result in a loss.

The expected value is total units returned divided by total units wagered (36/37 or 97.3%). Over the long haul we can expect to lose 2.7% of the total amount we wager if were to just sit down and keep playing this wager.

What if we decide to play a single number instead, paying 35-1? In this case, only one of the 37 possible outcomes would result in a win – and a return of 36 coins. Again 36/37 is 97.3%. The expected values of these two wagers are identical!

It should be noted, of course, that the volatility of these two wagers varies greatly and this will make a significant impact to the bankroll one requires to repeatedly play each of these wagers. But, this concept is for a different day.

In fact, we will find that most of the wagers on a roulette table have the exact same expected value. Thus, the notion that playing certain wagers are better than others is really not so true.

However, the lesson of expected value can be quickly understood looking at a double-zero roulette wheel, with 38 numbers (0, 00 and 1 through 36). In this case, two numbers are green, 18 red and 18 black.

If we assume that the payouts don’t change, then we find that the expected values of the wagers described earlier become 36/38 or 94.7%. This will impact all of the wagers on the table. So, where is the lesson to be learned?

Let’s say you walk into a casino and to the left is a single-zero roulette wheel and to the right is a double-zero roulette wheel. Assuming you want to play some roulette, which one are you going to go over to? The one whose wagers pay 97.3% or the one whose wagers pay 94.7%? Did any of you answer the lower paying one? I doubt it.

By deciding to play the single-zero roulette wheel, you’ve in essence made the same decision that should be made every time there is a decision to be made while playing. You pick the one with the higher expected value!

When you’re deciding which cards to hold/draw in video poker, you play the hand in the way that results in the highest expected value.

When you’re deciding what to do at a blackjack table, the play or fold at Three Card Poker or Ultimate Texas Hold’em, you do what will give you the highest expected value.

The calculation to determine the actual EV might become more complex in these situations, but how you use it to decide what to do remains the same. Expected value is the basic building block for all casino gaming strategies.

Check out my website at www.gambatria.com or my blog at gambatria.blogspot.com.

About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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