Expected Value Explained For Casino Games

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As far as I know, my father, Lenny Frome, was the first person to coin the term Expected Value with regard to casino gaming. In fact, in some of his earliest columns he used the term “win power.” That term probably makes more sense to the lay person. But, in the end it was the term Expected Value, or EV for short, that wound up sticking for going on three decades.

So, what is Expected Value? It is the win power of the hand! Just kidding. Well, it is an accurate description, but that probably doesn’t explain much. The Expected Value is the portion of the original wager we can expect to receive back, on average. So, an expected value of 1.00 would be a wager we would expect to push on in the long run.

We will wager one unit and get back 1.00 of that wager. This can be thought of as a percentage as well, where 1.00 equals 100% So, an EV of 0.50 would mean we can expect to only get half of our initial wager back on average. An EV of 2.00 would mean we can expect to double our wager.

Let’s look at a couple of very easy examples. If you are dealt a Blackjack and the dealer has a 2 through 9 as an upcard, your Expected Value is 2.5. You can expect to be paid 3 to 2 for your wager. If he has a 10/Face as an upcard it will be a bit less as the dealer may have a Blackjack as well. It will be even lower if he has an Ace up. If you don’t know what his upcard is yet, then your Expected Value will only be a bit below 2.5 for the 4-plus percent of the time he will get a Blackjack.

Every hand in blackjack has an Expected Value. You have a hard 20 looking into a 5, this has a specific EV that has been calculated taking into account every possible outcome and how often you can expect to win, lose or push. Obviously, a 20 vs. a 5 has a much higher expected value than a 17 against a 10! In blackjack, the expected value cited assumes the player will play the hand the proper way, which ironically is determined by which way has the highest expected value.

A Player 16 vs. a Dealer 10 doesn’t truly have an expected value until we take in to account what the player will do. If he sticks on the 16, then the hand has one expected value. If he hits on it, then it has another. And, if he surrenders, it has yet another. This is how we decide how he should play his hand. We review the Expected Value of each option and go with the one that provides us the highest expected value.

Why? Well, I think it is fairly obvious. The hand is a clunker. In the long run, it is a losing hand for sure. But if you have your choice of playing it so you will get back 50%, 55% or 60% of your money, which one will you choose? I know I’m going with the one that is 60%. Getting back $3 of my $5 wager is better than getting back only $2.50!

In the situation I used, those three options are about the only ones that could be picked with a Hard 16 vs. a Dealer 10. In blackjack, that is about how many options you generally have – you can hit, stick, double, split or surrender. Most of the time, at least one will clearly not apply. You’re not going to stick on a Soft 15. (Although we’ve probably all seen someone do it!)

In video poker, each hand has 32 different ways it can theoretically be played. This ranges from holding zero cards to holding all five. When you hold all five, it means you have a pat hand and the expected value is rather straight forward. If you are dealt a Straight, your EV is 4.00 as a Straight pays 4. If you hold three cards because you have Trips, the calculation becomes a bit more complex. For many video poker hands, what to hold is obvious, just as the decision in blackjack is. But for a significant number of hands, you are left with two or three realistic choices. When this happens, we need to turn to expected value to tell us what to do.

More on this in two weeks! I recently found out March 2 is Blackjack Day. Why? Because it is 3/2 and this date was picked to honor the 3-to-2 payouts for blackjack that have become so rare. So, next week, I’ll have a special column about this topic.

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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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