Last week I did a pyschology experiment in gambling. I got to keep my winnings as a way of thanking me for my participation.  The experiment was a simple slot machine with the setup was as follows:

• I started with £5.
• Each spin cost £0.25.
• Every time I won I got £1.50.
• The chance of winning a particular spin was 1/6.

I had to play for about 30 minutes in order for the experimenters to get enough information about what they were interested in and then I could choose to stop whenever I wanted. If I hit £0 I had to stop.

The question is: When should you stop?

I stopped at £6.50 which I was pleased with at the time since I had started with only £5. However afterwards thinking about it I realised there was an equal chance of hitting zero and getting £10 (moving £5 down or £5 up). And therefore a higher chance of hitting £9 than there was of hitting £0. I felt robbed. Should I? When it is the optimal time to stop?

Thanks to Scott Murphy for thinking through this.