show me no mercy - tell me how wrong I am

I do not dispute the reality or the relevance of this: http://en.wikipedia.org/wiki/Gambler's_fallacy


but within 7,500 rolls - does This fall within the bounds of normal possibility? --->


(14% chance of losing each roll, within my first/last session of 7,500 rolls I hit 4, then 3, then 5 consecutive losses)



thanks

You would expect around 3 sequences of 4 losses in a row in 7,500 trials.

14/100^4 = 0.00038416 = 1 in 2603 that any new sequence of 4 attempts will end up in 4 losses. We don't divide 7,500 by 4 to get the number of sequences, as we are looking for LLLL. Any W means the next spin is a new sequence. As we have 7500 spins, about 86% are new potential sequences of LLLL, so about 6,500 events... at 1 in 2603, we'll get 4 Losses about 2.5 times in 7,500 trials.

Falls in the bounds of possibility. You'll get a 5 in a row loss about half the time when you have 7,500 trials.

Numbers are estimates, there are better techniques to find the exact likelihood of a string of 4 in 7,500 trials.