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.  
Your outgoings will be:

   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/