Re: Roulette.




Tudor Jones wrote:
Some years ago I read a book on how to win at roulette.

Pretend for the moment that the wheel has no 0 or 00.
Let p(X) be the pdf giving the probability you walk away
from your gambling session with amounts of $X. Then
you can fashion almost any such pdf you want(!) *provided*
its mean value equals your starting bankroll.

This is subject to certain constraints such as (a) X can't
go negative (casino won't give you credit) and (b) it will
be hard to win a lot, due to table limits.

There is a 0 and 00 on the American wheel (*) but this
doesn't affect the statement that you control the pdf;
it just means that the mean will be less than your
bankroll, by an amount related to the variance (and other
statistics) of the pdf you seek.

BTW, you will always get a better pdf at roulette by betting
a *single number*. For example, to double $350 you have
only a 18/38 chance if you bet it all on Red, but you have
a much better chance if you start by betting $10 on a single
number (and walking away if you get it on the first spin).

The classic martingale does indeed fulfill its promise --
you *almost always* walk away a winner. (But your occasional
losses over many sessions will exceed your aggregate winnings.)

You describe a reverse martingale in which you tolerate a
likely small loss in exchange for an occasional large win.
That is very easy to arrange and I'll tell you how, free of charge.
(But your *mean winning* will be negative.)

(1) Throw your book away.
(2) Walk up to the roulette wheel and make one (1) bet
on a *single number.* How much you bet is determined
by what you want to win and/or are willing to lose.
(3) Unless the amount you wanted to win was more than
35 times your bankroll (or more than maximum house payoff)
you're done. Go watch a show.
(4) After a few sessions of this your winnings (or more likely,
the reduction in your losses) compared with the system you
describe will more than make up for the cost of the book you
threw away.

(* - BTW, if the roulette book didn't explain that playing the
game in Europe or Asia where the wheel has 0 but not 00
was the one very useful step you could take, it sure wasn't
much of a roulette book!)

James Dow Allen

.



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