Try playing without angst

Jun 18, 2007 4:15 AM

By now, if you’ve been reading my columns, you know that there are three parts to expert strategy — play the right games, play the right strategy and know what to expect. The last one, could fill up volumes and volumes of books.

There really is no end to how many different ways you can explain what to expect about any particular game. Knowing what to expect is important because it is what makes us realize that the game is controlled by math in the long run, and what appears to be a very unusual event (or even cheating by the house) is not really the case.

”˜Volatility’ is one of the know-what-to-expect items that fall into this category. If you were to play for an infinite amount of time (or at least a very long period of time) with an infinite bankroll, then volatility would be meaningless.

First of all, we need to explain the term volatility. I could pull out a math book for that, but I doubt that’s what you want to hear. In simple terms, it’s the thrill ride you get from the ups and downs in your bankroll while playing.

To liken it to an amusement park ride, a Ferris wheel would be low volatility, a simple wooden roller coaster would be medium volatility and the corkscrew with your feet dangling while you do loops at 65 MPH would be high volatility.

How does volatility affect you while you play? Generally speaking, it affects the size of the bankroll you need to show up with. You need to make sure you have enough money to ride out the long droughts that may occur with a high volatility game. Keep in mind, this may be the case even with games that have a high payback. Let’s take a look at an example.

I created simulations for two very simple games. The first is the coin-flip. You bet 1 unit. If the coin lands on your choice (heads/tails), you win even money. The game has a payback of exactly 100%.

The second game is a modified form of roulette. In this version, there are 36 numbers on the wheel (no zeros). If your number comes up, you win 35 to 1. Again, the payback is exactly 100%. So, here we have two games with identical paybacks, but whose volatilities vary greatly. What will this do to the results?

I ran 100 million wagers for each game. The overall payback of coin-flip was 100.0013% and the overall payback of the roulette was 99.9972%. As should be no surprise, the detailed results for each game were vastly different when looking at a 100-wager session, which for many games represents about three hours of play. The table below shows these results:

Result

Coin-Flip

Roulette

Lose > 40

0.0005%

23.03%

Lose 21 — 40

1.77%

24.19%

Lose 1 — 20

44.24%

0.00%

Push

7.96%

0.00%

Win 1 — 20

44.26%

22.61%

Win 21-40

1.76%

0.00%

Win > 40

0.0008%

30.17%

Total Wins

46.02%

52.78%

Total Losses

46.02%

47.22%

As I expected, the results for the coin-flip are very even. We can expect to win as much as we lose. The likelihood of a big loss is the same as a big win. Fully 72.87% of all sessions ended within 10 units of even. If you showed up to play with 20 units, you could probably play for hours, if not days on end with this game.

The roulette game is radically different. First of all, 5.95% of all sessions resulted in the player winning ZERO units back. This means that in 100 straight spins, the player’s number did not come up.

That never came close to happening in our coin-flip game. Because in this game, the player wins 35 to 1 if his number comes up, the player will tend to either lose big or win big.

In roulette, 30% of the time, the player won more than 40 units, while this occurred only 0.0008% of the time in coin-flip. In coin-flip, the largest win was 44 units, while in roulette it was 368 units. If you showed up with 20 units to play roulette, there is a very good chance that you will go home bankrupt after 20 spins.

Which is the better game? No one can answer that. The only question that can be answered is, which is the better game for YOU. I can’t answer that one, either. Only you can.

The important part is to know what to expect. If you were playing coin-flip and you lost 100 straight hands, I’d seriously wonder if the coin was fair. If, on the other hand, you were playing roulette and you lost 100 straight spins, this would not be all that unusual. Sometimes, it’s not the destination, but the ride that matters.