Math Is Fun Forum

mrpace

Member

Registered: 2012-08-16

Posts: 88

Calculating the probability of a system being profitable

Hi all.

Let's take blackjack.
In blackjack, your expected return on each bet you place is about 98% (depending on the rule variants).
So for a $1 bet, you expect to lose 2 cents

Someone then tells you that they have a winning system to beat the game.

You try the system and your results are as follows.

You played 4500 hands, betting $1 each time
After 4500 hands, you are up $60

What is the probability that this is a better than break even system?

I'm interested to know any theorems which have been developed to answer this question.

At the moment I am merely running computer simulations to get an estimated probability.

Thanks

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Calculating the probability of a system being profitable

Each hand you either win to get two bets back or lose to get nothing back.
So 98% return means you have 49% chance to win
49% * 2 + 51% * 0 = 98%
This is definition of "Expectation" in probability

using similiar logic: Suppose you win X hands in 4500:

2*X + 0 = 4560
X = 2280
Thus the new system gets you winning probability of 2280/4500
And you can compare it to 49%

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