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At the center of every decision made while in a casino is the expected value or EV for short. The expected value is what portion of our wager we can expect to win back at any decision point in the long run. Thus, even the overall payback of a game is really the expected value of that game in the long run. Part of our decision making process to play game A over game B is likely to be that game A has a higher payback (i.e. EV) than does game B. It doesn’t matter if we are comparing video poker to a table game or two table games or two video pokers.

The payback of any game is really the sum of all the expected values of every possible hand played the best way multiplied by the frequency of each hand. What this really means is – if you want to earn the theoretical payback of the game, you have to make the right decision all along the way. Of course, this is not an ‘all or nothing’ type situation. If you accidentally hold a Low Pair over a 4-Card Flush, it doesn’t mean that you completely forfeit your 99.5% payback. It means you might only be at 99.49%!

For those of you who are new to the concept of Expected Value, allow me to try to and explain it a bit better. The expected value is calculated by looking at every possible outcome from a particular point and determining what the average return will be. So, if a player holds a Low Pair in a full-pay video poker game, there are 16,215 possible 3-card draws. We use a computer program to play out all 16,215 draws and tabulate how many of each type of winning hand might occur. By doing this, we learn exactly how many Two Pairs, Three of a Kinds, Full Houses and Four of a Kinds the player can expect to get over the long run by holding this Low Pair (and taking into account the three discards).

We multiply the occurrences of each of these winning hands by the payout of these hands and sum up the values. We then divide this value by the total number of possible draws to arrive at an expected value of 0.82. This means that if the Player has wagered $1 on his video poker game and he holds a Low Pair, he can expect on average to get back 82 cents, or in other words, lose 18 cents, on average.

If the player has no choice to make, then this value is meaningless. If, however, he is playing a game like video poker where he has to choose to hold the Low Pair or a 4-Card Straight or a 4-Card Flush or a 3-Card Straight Flush then he needs to choose the hand that provides the highest expected value. This is the critical decision made every time someone gambles. Do they stick or hit on that 14 into a dealer’s 2? The answer lies in whether the expected value to hit is higher or lower than it is to stick. Should a player fold or play a Q-7-2 in Three Card Poker? The expected value of playing is higher than the expected value of folding, so the player plays this hand.

Thus, the expected value is like the basic building block of every casino game. Every decision made to play or fold, to check or to raise, which cards to play are all based on this expected value. You don’t need to memorize expected values to play correctly – you only need to learn the strategies that are generated based on these expected values.

Understanding that the strategies are based on expected values, which are in turn based on pure math is what we use to realize that these strategies are absolute and should be used all the time. They are not based on hunches or luck or hot and cold streaks. They are based on the exact same math that was used to create the game in the first place.

When we put all these expected values together, they add up to the payback of the particular game. The very first decision we make is which game to play. This decision should also be made with the expected value in mind. Playing video poker and its 99.5% payback seems like a much smarter move than playing slots and its 92.8% payback. That is, unless you believe that splitting 10’s in blackjack is a good move because today is your lucky day.

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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