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Introduction:

Average Joe play a gamble game with 40% of bet *2
He will start his bet at 5€. And double his bet each time he looses. Restarting his bet at 5 each time he win.

Starting with 2000€, Average Joe find that the more consecutive looses the more he "wins" money.

Average Joe decide to play 20 000 times. And dreams about a 13 loose streak.
Yes, that's a 5*(2^14)-5 = 81915€ bet.

Question:

What are the probabilty of 13 consecutive failures in 20000 trials with 40% winrate?

1 Answers 1

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Plugging $m=13$, $p=.6$, and $n=20000$ into the formula in my answer here, we find that the chance of a losing streak of 13 or more losses is .9999729409. It is practically guaranteed!