# The power of the payback tables

May 2, 2005 1:26 AM

How much is payback worth? I don’t mean "payback" as in revenge. I mean payback as in how much you can expect to get back from your gambling investment. The first rule of expert strategy is to know which games to play.

Generally speaking, this means playing games with higher returns, or paybacks. Of course, these paybacks are the theoretical long-term paybacks of the machine, and nearly anything can happen in a short session.

Because of this, some folks out there have turned this around to mean that payback really isn’t all that important, and that you can just as easily win at a lower-paying video poker machine. I don’t think so.

Last week, I introduced my concept of a computer simulated roulette wheel game. In that case, I created an overly generous version in which the player won if the "0" came up.

For this week’s column, I’ve reverted to more normal versions of the game. In order to show just what the payback can mean to you, I simulated two versions of the game.

In the first one, the player bets "even" numbers each time, and if a "0" comes up, it’s a push. The payback of this game is exactly 100%, as the player will be paid even money each time an even number comes up.

In the second scenario, I’ve used the traditional payouts, in which the player wins even money when a even number comes up, and loses half of his wager when the "0" comes up. The payback on this version is 98.65 percent.

So, the difference is about 1.35 percent or a bit less than the difference between a full-pay (9/6) jacks or better and an 8/5 jacks or better (the difference is just over 2 percent).

So, we all know that over the long run, the first version of the game will return 1.35 percent more than the second version.

What is the impact for a normal session? The results are staggering! I simulated one million sessions of 1,000 games each and recorded the results. They are shown in the accompanying table.

I have to admit that even I was surprised by the impact. With only a 1.35 percent difference in payback, the game changed from one in which you had a 50 percent chance of walking away a winner after a session to one where you were going to lose twice as many times as you win!

When I first got the results, I went back to check the program and make sure there wasn’t a mistake. But then I began to think about it. On average, in 1,000 rounds, the "0" will come up (on average) about 27 times.

For each of these 27 times, the player would lose half a unit or 13-14 units per session. This means that every session that in the first version would end up anywhere from a push to the player winning 13 units would now likely become a loss.

When looking at the detailed results (not part of the table), it turns out that this accounted for about 17 percent of all sessions. Lo and behold, an additional 17 percent of our sessions were turned into losers in the second version of the game.

Of course, video poker is a bit different than our roulette game above. First of all, it has a much longer cycle than the roulette game. With only 37 different outcomes as compared to the millions in video poker, we cannot expect the results to be so clearly defined so quickly.

Video poker is also much more volatile than roulette, especially when we’re just betting "even" all the time. In a short session of two to three hours, hitting a four-of-a-kind just once more than "average" will almost guarantee a winning session. Hit a royal in a short session and you can be sure to walk away a big winner.

At the same time, some of the same concepts apply. When you play 8/5 jacks or better video poker instead of a full-pay machine, you will get one less unit every time you hit a flush or a straight.

On average, these hands will each occur about once in 90 hands. In a 1,000 hand session, you’ll hit these hands a total of about 22 times on average. This means you won’t be receiving those additional 22 units.

Playing maximum quarters, this would translate into 110 quarters or \$27.50. This means that many of the sessions that you would play on a full-pay machine where you would walk away up \$25 or less will now be losing sessions.

A session on a full-pay machine in which you would win \$50 is reduced to a \$25 winning session. So, not only does playing lower-paying machines decrease your chances of having a winning session, it also decrease the amount you will win in a winning session, and increases the amount you will lose in a losing session. Yikes!

This example used a 1.35 percent difference in payback. Imagine what you’re doing to your bankroll when you sit down and play a 96 percent game when perfectly good 99.5 percent games can be found nearby!