Thread: How to work out the probability of a specific sized win?

I wonder if someone can help me with this probability problem.

The following is based on using European single zero roulette as an example which has a house advantage of 2.7%. There are 37 numbers on said roulette wheel consisting of 18 red numbers, 18 black numbers, and one green.

If I were to place a £100 bet on red (which pays out even money, the chances of that bet hitting are 18/37 = 48.6%.

Therefore the chances of me doubling my money are 48.6%.

However.....how would I work out the chances of quadrupling my money if I use the same bet size?

Obviously if I bet £100 on red and it won, I would then have £200, and if I bet THAT £200 all on red, the chances of that happening are;

48.6% x 48.6% = 23.66%.

But what would the chances be of hitting the £400 if I kept the bet size at £100 ?? (and how do I calculate that?).

Thanks

I've actually just done this with a probability tree, and I worked out that to hit the £400 target, you would need to win 3qty £100 bets in a row, therefore the probability of this happening is (I think)

48.6% x 48.6% x 48.6 = 11.51%

However this assumes that all three bets win. Does this probability change, for example, if you were to win a bet, lose a bet, then win etc etc.... ??