In European Roulette there are 37 pockets in the wheel numbered from 0 to 36 inclusive – 18 black, 18 red, and 1 green.
There are many possible bets that can be placed in the game of roulette. One of the simplest is just to bet on the ball finishing in the pocket of specific number.
If you bet £1 on 5, if the ball finishes on 5, you win £35 plus the return of your £1 stake (35-1 odds). If the ball finishes on any other number, you lose your stake.
Your bankroll is the amount of money that you start off with. If you bet on a number and it comes up, your bankroll increases by £35. Any other number comes up and your bankroll decreases by £1.
So, what are the possible outcomes if you go to the casino with £100 in your pocket and decide to play 100 spins of European Roulette at £1 per spin.
Below are some charts showing possible outcomes. Blue sees the bankroll jump to 216, red sees it fall to 36, and green sees it jump to 180.
I ran an Excel data table Monte Carlo simulation to see what could be the outcomes of 200,000 visits to the casino.
Logical when you think about it, but a surprise at first…with 100 roulette spins there are only certain discrete amounts of money which it is possible to walk away with from the casino…£0, £36, £72, £108, £144, £180, £216, £252, etc. Each possible value is £36 more than the previous.
This is always the case if the number of spins is equal to the number of betting units in the bankroll.
If the number of bankroll betting units and the number of spins are not equal, the possible amounts of walkaway money are still separated by £36, except that if the bankroll is small, it is also possible to finish with £0 before finishing all the spins.
Running another 200,000 trials, and tabulating the data shows the following:
- The average loss came out as 2.673% – very close to the expected loss of 1/37=2.703%.
- There was a 51% chance of finishing in profit, and the median bankroll after 100 spins was £108.
- Although the chance of making a profit was greater than the chance of making a loss, the expected value of any loss is higher than the expected value of any win.
- The simulated estimation of the chance of being wiped out (bankroll goes to £0 – in this case all 100 bets being losing bets) is 6.46%.