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Roulette Betting "System"

```
Date: 08/09/97 at 11:35:38
From: Connie
Subject: Roulette betting "system"

One roulette system is to bet \$1 on black. If black comes up on the
first spin of the wheel, you win \$1 and the game is over. If black
does not come up, double your bet (\$2). If you win, your net winnings
for two spins is still \$1. Continue this doubling procedure until you
eventually win; in every case your net winnings amount to \$1. What is
the fallacy with this betting "system"?
```

```
Date: 08/09/97 at 12:41:41
From: Doctor Anthony
Subject: Re: Roulette betting "system"

Consider how much 'doubling' your stake amounts to after a few turns.

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 +
(total is 2047 to here)
+ 2048 + 4096 + 8192 + 16384 + 32,768 + 65,536 + 131,072
+ 262,144 + 524,288 + 1,048,576 + ...

You need a very deep pocket to stand these losses.  In theory you
cover your losses by doubling, but in practice your nerve will crack
long before your total wealth has gone down the tubes.

Remember that at each stage you have an even chance of winning or
losing. What happened on the last ten or more throws has no bearing on
what happens next. If there were 20 reds in a row, the probability
that the next throw would be red is still 1/2.

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Probability

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