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Say you are making a roulette bet and you want to double your bet every time you lose in an attempt to recover what you lost. So, if you lose repeatedly you'd have spent:

first round = $10$,

second round = $10\times 2$,

third round = $10\times 2\times 2$,

forth round = $10\times 2\times 2\times 2$ ... and so on...

I am trying to create a formula for that, without success.

Given the variables:

  • Amount to start: $10
  • Multiply between rounds: 2
  • How many rounds: 4

How do I create a formula to calculate how much money I spent after 4 rounds? I know, by calculating manually, that it would be $150(10+20+40+80)$.

But how to do that with a formula so that I can calculate for any number of rounds?

Thank you so much for your help.

Luis Novo
  • 111

1 Answers1

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Found the answer here: https://en.wikipedia.org/wiki/Geometric_progression

For:

a: total amount I am betting r: how I'd multiply it every time n: how many times it's done

a(1-r^n)/(1-r)

So, to answer my question:

10(1-2^4)/(1-2) = 150

Luis Novo
  • 111