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Bob Dancer writes a video poker column for beginners to experts. He also writes a column with Jeffrey Compton, "Player's Edge", featuring information on promotions at various Las Vegas casinos. Player's Edge is published each Friday in the Neon section of the Las Vegas Review-Journal. Click here to send Bob Dancer an e-mail.

For more details and a schedule of Bob's free classes, visit www.bobdancer.com.

May 05, 2009

Sampling the Evidence

Let's assume I opened up a restaurant called Dancer's Diner near you. Let's further assume that you've heard the type of food and the price range fits in with what you normally purchase, at least some of the time. You decide to go in and give the Diner a try.

If the first meal I serve you is lousy, there's a good chance you will never come back. Some people will give me the benefit of the doubt and try the place twice. But even these folks follow a "two strikes and you're out" rule. On the other hand, if the food and atmosphere are good, there's a good chance Dancer's Diner has earned a repeat customer.

Gathering information in this manner is often described as "sampling" in the statistics books. The general idea behind sampling theory is how many trials (i.e. meals, in our example) are needed in order to support or reject a specific proposition. One possible proposition you could be testing would be "Dancer's Diner serves great food" and another equally valid proposition might be "Dancer's Diner serves food only fit for dogs."

In everyday life most of us intuitively do such sampling for a large variety of products. We don't do it very scientifically, but nevertheless we tend to go back to places or things where we've had positive experiences and we tend to shy away from those places or things where we've had negative experiences.

Now let's shift the discussion to video poker. Let's assume the best game in our casino of choice is 9/6 Jacks or Better, returning 99.54%. Let's further assume they are having a super promotion and we get 2% in cash back on top of our normal results. This makes it a 101.54% machine, which we'll assume will be the best return anywhere that we know about.

The first two hours we play this game, however, we go down 500 coins, i.e. $25 for a nickel player, $125 for a quarter player, $500 for a dollar player, etc. The amount we've earned at cash back doesn't come close to making this up. Assume further that bankroll is not an issue. You don't like losing this much (who does?) but there's no realistic chance of running out of money. What do we do?

There are people who consider this an exercise in sampling. They'll use the sample of losing 500 coins in order to decide to quit. They will use such phrases as "the machines are cold today" or perhaps "the machines won't even give me some play." However they justify it, they will change machines or games or leave the casino.

Smarter gamblers realize this isn't an exercise in sampling at all. They have already determined that 101.54% represents the best game around. Changing games will only amount to playing a lesser game. Changing machines within the same game doesn't change the 101.54% figure. Why bother? These smarter gamblers will continue to play. There are always up-and-down swings in every gambling game. These 101.54% games don't come around every day. If you refuse to play the game today, there's a good chance tomorrow's best game will be worse.

So what's the essential difference between sampling the food at Dancer's Diner and sampling the games at the casino? The essential difference is that at Dancer's Diner you have no good outside information as to whether the food will be good or not according to your taste buds. Yes you can read restaurant reviews. Yes you can listen to friends. But this is really something you have to do yourself.

In video poker, however, 9/6 Jacks or Better is a solved game. It's not a mystery. The math behind it is very solid. Once you've learned the game (it's one of the easiest games to learn), it's just a matter of playing and over the next million hands or so, you're results will be very close to 99.54%, discounted by your errors.

How you do in a few hundred or few thousand hands is largely irrelevant. There will be times that you hit more than one royal flush in a session. There will be times where you lose, lose, lose. So what? It's the nature of the game.

The key numbers that should drive your play are the return of the game and the value of the promotions. If those numbers say it's the best game in town, keep going. It's always wise to go back and verify the numbers on games and promotions in case you've made a mistake, but letting a minus score scare you away from a profitable situation is, in the long run, a very costly proposition.