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If I bet on red vs. black, I need to double the money on every loss to keep getting profit:

1 * 2 = 2 - 1 = 1
2 * 2 = 4-3 = 1
4*2 = 8 - 7 = 1

etc. etc.

Now my question is, what formula should be considered when you bet on 2to1 when chances of wining are 1/3 (excluding 0). how should you progressive bet in this place? there is no need to double the money, correct?

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  • $\begingroup$ What do you mean by "excluding zero" ? $\endgroup$ – true blue anil Feb 9 '17 at 16:52
  • $\begingroup$ Also, I presume you mean 2 to 1 against ? $\endgroup$ – true blue anil Feb 9 '17 at 17:00
  • $\begingroup$ let's assume there is no 0 in roullete, yes 2 to 1 $\endgroup$ – Testing man Feb 9 '17 at 17:01
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To attempt to win $1$ unit (the first bet, if it wins, pays $2$ units but after that, I assume you will settle for $1$), the bet after the $k$-th loss must be $$ \left(\frac32\right)^{k-1} $$

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