## Monday, April 1, 2013

### Dice Gambling System

We all know that Las Vegas was built with gamblers’ losses. The casinos love gamblers who think they have foolproof systems. So, when I was introduced to a new system for playing the dice game craps, I first ignored it. Then after hearing more, I decided to simulate it to prove that it is worthless. The amazing thing is that I didn’t get the results I expected.

The system involves only playing the simple pass-line in craps; it ignores all the other more complicated bets. It’s well known that the odds of winning this bet are 244 out of 495. So, out of 495 plays you expect to lose 7 more times than you win. On each bet, you either double your wager or lose it. So, after 495 plays, you expect to be down by 7 times your bet size.

I wrote a little simulator for craps and tested it first on a simple case. Start with \$10,000 and wager \$100 at a time and see what happens after many bets. The expected result is to lose all your money, eventually. With a bankroll of 100 times the bet size, the expected number of bets before losing all the money is

100 x 495 / 7 = 7071.

I ran a million trials on my simulator. In every single one of them all the money was lost eventually. The average number of bets before the money ran out was 7066, which lines up nicely with the expected answer above. There was some variation, though. The shortest trial was 344 bets, and the longest 110,188 bets.

So far, everything was going according to theory.

The System

Then I tried simulating the new craps system to prove it doesn’t work. The system involves starting at \$100 bets and adjusting the next bet size based on the previous result. When you win, you bet a dollar more the next time. When you lose, you bet a dollar less the next time. Another rule is that you never put more than 1% of the bankroll at risk each bet (rounded down to the nearest dollar).

The result I expected was that the betting would stop when the bankroll hit \$99 and the next bet size became \$0 because of the 1% limit rule. However, that’s not what happened.

On the first simulation, after 100,000 bets, the bankroll grew to \$510,610! This was totally unexpected. How could the bankroll grow so much? I decided to run 10,000 simulations of each of 4 cases: 1000 bets, 10,000 bets, 100,000 bets, and one million bets. Here are the results:

1000 bets: \$8715
10,000 bets: \$6580
100,000 bets: \$598,949
1,000,000 bets: \$85,587,100!

The system starts out losing money, but then gradually begins winning and produces explosive growth. It takes a while, but this system would eventually break a casino.

As many have guessed already, this post is an April Fools joke.  However, the simulation results are real.  See tomorrow's post for an explanation.

1. Wow, this is a good one! A real head-scratcher.

Did your simulation allow negative bets?

2. @Patrick: I was hoping that someone would figure it out. Well done!

3. a good one :)
Given your hard-core math reputation I was astonished ... till I looked at calendar again.

4. Excellent research.

And now that you have done the number-crunching for the rest of us, this will be the perfect system for people with no interest in mathematics.

Any thoughts of creating a stock-picking system based upon this model?

1. @Andy: It's tricky when it comes to stocks because it's hard to pick losers to short. Perhaps some sort of arbitrage would work where you short a high-fee closet index fund and use the proceeds to buy the index.