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?