Quote from: Azlan on May 05, 2014, 02:07:51 PM

Quote from: dooglus on November 26, 2013, 08:09:37 PM

Quote from: nicolaennio on November 26, 2013, 07:34:55 PM

Great! I was fearing you were in the gambler's fallacy :-)

May I ask you why you are so interested in the busting probability of funny martingales?

You can ask, but I don't know what to tell you.

I'm interested in mathematics, and this seems like it should have a neat solution.

I don't know that you can call it a "martingale" by the way, since it doesn't reset on a win.

If you are interested in martingale / gamblers fallacy / hothand (as I am) Its worth looking at the Fibonacci variants of Martingale. I havnt read all 216 pages of this thread but I did do a search for the term Fibonacci and nothing came up. For example:
Start with the Fibonacci series: 1,1,2,3,5,8,13,21 .... starting with 1:

a) Place 50/50 bet
b) If win, increase 1 step
c) If lose, go back 2 steps

The psychology is that you lose only 1 unit 50% of the time, but the other 50% of the time the sky is the limit! So the "bust" in this case is not losing your pot in a streak of bad luck, but rather, having a streak of good luck and hitting the just/dice limit.

From an entertainment point of view, i believe you can play fibonacci much longer then classic Martingale (assuming 1 unit as the initial bet). I dont think it changes the houses expected value, aside from possibly increasing the propensity for he user to play again through positive reinforcement.

Just a few years ago a psychologist (Daniel Kahaneman) won the nobel prize in economics for related work in behavioral economics. ANyhow.... great discussion, and I think the math behind the JD website is very very cool!

(Fibonacci caveat - Strictly speaking, you want to start with 1 unit, then multiply repeatedly by Phi [~1.68=sqrt(5)+1)/2] which quickly converges to the more popular integer series. Phi is one of those cool constants related to DaVinci, Pi, pythagoras and that 3x3 grid on your iphone camara. )

It is interesting to get the most excitement and fun out of your betting experience but it doesn't change the house edge

You should bet as you like and come up with your own fun way to do so since the goal should be to get entertained