A Fun Problem

[mondaymother]

This is a fun problem I came up with last night while I was thinking about trading strategies. Using roulette as a metaphor:

Suppose there is a rigged roulette table: the ball lands red 35% of the time and black 65% of the time.

You have $1000 and you are only picking between red and black. Choosing correctly pays out double your stake.

What is the most efficient sized bet you can make on black to ensure the fastest return on your $1000 while minimizing the risk of losing your $1000 entirely to under 1%.

To add a twist to this problem: what if the payout is not always double; if it was only 10% what would be the most efficient bet in this case?

I hope this is a fun problem for all of you and i look forward to seeing your solutions!

 

[Romsek]

How about you share your solution, or thoughts regarding how you might find such, with us first.

 

[mondaymother]

what kind of maths problem starts with the solution?

first I would look at the extremes: clearly betting $1000 on black in one go will not keep your risk below 1%.
what is the worst case scenario with a likelihood closest to 1% 1%: 35%^5 < 1%
after losing every stake in this scenario how much would you be left with?
how many times (and with what stake) must you bet again to make back your losses

using a probability tree would be my recommendation

 

[Steven G]

We really do not want to know your recommendation We want to see your work. This way we can help you arrive at the correct solution.
Also what does 1% 1%: 35%^5 < 1% mean??