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.
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