# 'Payback' most important number in casino games

July 01, 2014 3:00 AM
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I call payback the most important number to measure a game. It is the percent of the total wager a player can expect to have returned to him over time.

A 100% payback game would mean, over the long haul, the player will break even. He will have 100% of all his wagers returned to him. A game with a 99% payback means, over time, the player will lose 1% of his total wager.

Total wager should not be confused with the amount the player buys in for or the total amount of his initial wager. It refers to the total amount of dollars wagered at any point in a game. So, if a player plays 30 hands of \$5 blackjack, he can expect to wager about \$170. In blackjack, the average wager per hand is about 1.15 units when doubling and splitting are taken into account.

Of course, payback is a player term. Casinos care about house advantage which is really the same as payback, but looked at from the other side. The house advantage – also called the vig – is the amount the house can expect to win over time as a percent of the total wager.

Simply put, it is 100% minus the payback. So a game with a 99% payback has a 1% house advantage. But, in all honesty, this number has limited value to the casino. For the most part, you care only about your payback.

If you play correctly, you can play at the stated theoretical payback. But the casinos don’t care much about any one player’s payback. They care about everyone’s payback all put together. And, the reality is most players do not play anywhere near the correct strategy. I’d be surprised if more than 10% of the players really do.

This is why the casinos instead rely on a number called the Hold. This is the total amount won by the casino divided by the total amount bought in by the player. It’s not a perfect number because it is possible for a player to buy in for \$1,000, play one \$5 hand and then leave.

Over time it is a very useful number for casinos. No one expects the hold to be the same as the house advantage. Players don’t buy-in for their total wager.

The blackjack player I mentioned earlier who plays 30 \$5 hands, doesn’t buy in for \$170, but more likely \$20-\$40. If he buys in for \$40 and loses \$1, the hold will be 2.5% (\$1/\$40). This is about how much he might expect to lose if he uses the right strategy. But, if he uses something less than the correct strategy and loses \$5, then the hold is 12.5%.

So, the hold measures to some extent how players are playing relative to proper strategy.

Three Card Poker (ante/play) has a house advantage of right around 2%. Yet the game holds in the mid-20% range. I’ve always found this staggering. How can a game with a 2% edge and such simple strategy result in such a large hold for the house?

The answer was stated earlier – because my best guess says only 10% of the players play the right strategy. This is true even with games like Three Card Poker that have the simplest strategies.

I’ve often surmised if I were to stand outside a casino and hand out copies of my booklet Expert Strategy for Three Card Poker maybe 30%-40% of the players would attempt to follow the strategy in it. After an hour, I’m guessing half of these people would abandon it.

Why? Because too many people think a strategy implies you will win, and you’ll do it big and often. It simply doesn’t work this way.

The strategy for Three Card Poker couldn’t get any easier. Play with Q-6-4 or better. Fold if Q-6-3 or less. If you believe when you have a Q-J-5 hand you are in the driver’s seat when you play, then you don’t understand how the math behind the strategy works.

If you get Q-J-5’s all night, it is going to be a short night. This is not a winning hand in the long run. This is simply a hand in which you will lose less by playing than by folding. You will get a lot of these Queen High and King High hands that fall into this category.

If you get a bunch of them in a row and lose a lot of them (which you will do), and you don’t understand this concept then there is a strong chance you will lose confidence in the strategy and abandon it.

And, I can’t be more plain than this – when you alter from the correct strategy, the only possibility over the long run is you will lower your payback. Yes, over the short run, you might get lucky and win a few extra units. But you will pay the price over time.

This is why knowing more than just Q-6-4 is the right strategy is important. You need to get some understanding of why this is the right strategy and what to expect when you follow the strategy. It is this more complete knowledge that gets you to realize you should stick with the strategy no matter what.

If you are completely satisfied to simply go with Q-6-4, you can stop reading for this week. If, however, you want to learn more about the whys and the what, then I’m happy to report I have updated my booklet Expert Strategy for Three Card Poker, which will explain why Q-6-4 is the right play and what to expect out of many of the other hands.

The booklet explains about Ante/Play and Pair Plus, the two original parts of the game. It now also covers the 6-Card Bonus Sidebet that can be found on about half of the tables. If you are interested in ordering the new version, please send a check or money order for \$5.95 to Gambatria, P.O. Box 37464, Las Vegas, NV 89133. This price includes 1st class shipping and handling.

Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His book is Expert Strategy for Three Card Poker. His website is www.gambatria.com. Contact Elliot at ElliotFrome@GamingToday.com.