''frequency'' vs ''probability'' of occurence
His statement was to the effect that if the win prob for one event was 0.48, then the prob of 5 consecutive events would be 0.48^5.
The difference here is between the "probability" of occurence and the "frequency" of occurence.
From any given starting point, the FREQENCY of occurence of 5 consecutive wins would be approximately 0.0138; NOT 0.48^5 = 0.02548.
The probability of occurence involves considering all 2^5 possible sequences of 5 events, while *frequency* of occurence only looks at how often, from any starting point, you will win EXACTLY 5 events.
Thus the sum of all the probs I mentioned WOULD have to total 1.0; for there cannot be any overlaps. I.e., either you win 5 in a row or you don't; and winning exactly 4 in a row has a different, and entirely separate frequency of occurence; and either could be followed by anywhere from 1 to infinity consecutive losses.
I believe the original post clearly implied the contemplation of some kind of money management system; and if that is the case, the *frequency* of occurence is FAR more relevant than the *probability* of occurence.
I should have made that clear in my original post; for his was not a *mathematical* error, but merely one of using what is, IMHO, the wrong yardstick.
I therefore retract and apologize for the allegation of error, and restate my difference of opinion solely on the basis that I think he's using the wrong "yardstick."