Another maths puzzle for anyone wanting to work their brain.

One of the big betting sites are offering a £5 bonus to their customers. The catch being that you have to stake 10x the amount on the roulette wheel. for example: you can bet 50x £1 or 100x 50p.

Its a European Roulette wheel so has 36 numbers + 0 (everyone loses if the ball lands on 0)

Assuming average luck, how much money will you have left from the £5 bonus after you have wagered the required 10x amount. Get yourself a pen and paper (and a calculator). Once you’ve figured it out scroll down to see if you got it right.

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The solution:

The first thing to do is figure out what % advantage the casino has in this game. Most of the bets on a roulette wheel are even money (red/black odds/evens). You’ll win half the time and break even in the long run. However if the ball lands on 0, everyone loses (This is where the casino make their profit.)

there are 37 segments on the wheel, so the odds of the ball landing on 0 are:

(1/37)*100 = 2.7%

Now that we know the casino’s edge we can figure out how much we expect to lose over the course of trying to earn this bonus.

As we need to bet a total of £50 to get the bonus we can expect to lose 2.7% which is:

50*0.027 = 1.35

Now that we know that we expect to lose £1.35 we can take that away from the bonus to figure out how much we can expect to have left:

£5 – £1.35 = £3.65

So on average, people taking part in this offer can expect to get £3.65 in free cash.

 

Note : I went through with the bonus and ended up with £4.50 left which suggests I has slightly better than average luck.