No Formulas or Advanced Math

Responding to your own post 4 times. Good work!


On the other hand, you didn't do such a good job with the, "No formulas or advanced math" part. [img]/images/smile.gif[/img]

Because you have a one third chance of losing on any given bet, the odds that you will lose three times in a row are one third to the 3rd power, or one third times one third times one third with equals one eighteenth. This means that you will have a five and a half percent chance of going broke.

Opps, My math was wrong. 3*3*3 = 27. 1/27 = .037 which rounded up is 4%

I think the probability for you to go broke is 6.7%

Call the probability of going broke with one dollar x. That means the probability with two dollars is x squared and with three dollars its x cubed. Why? Because the probability that a guy with two bucks falls to one buck is exactly the same as falling from one to zero when the opponent's bankroll is limitless. So to go from two to zero is x times x.


When you have one buck you can go broke two different ways. Either immediately, which has a probability of 1/3, or win the first bet and then go broke, which has a probability of 2/3 times x squared. Together the chances add up to x. x = 1/3 + (2/3)(x squared). So x is 1/2. X cubed is 1/8.

x = 1/3 + (2/3)(x squared) sure looks like a formula. So this is not an acceptable answer to your own problem!

its not a formula or advanced math, its a simple algebraic equation [img]/images/smile.gif[/img]

Go back to Day 1 of Introduction to Calculus and review limits. Well, to be fair, maybe this has an added dimension that makes it a bit more complicated than Day 1 stuff. Still, it should be intuitively obvious what the answer is once you combine terms infinite and probability.