In my post http://www.neilmcniven.co.uk/european-roulette-simulation/, I looked into the amount of money you could expect to win or lose with a given bankroll and number of spins at European roulette.
Here instead I will look at the number of spins of the wheel you can expect to survive before your bankroll is down to zero – gambler’s ruin.
Again using the Excel data table Monte Carlo simulation method, I set everything up so that a trial will last for up to 10,000 spins of the wheel, but will be stopped immediately if/when the bankroll hits zero. I then ran the trial 10,000 times, keeping track of the number of spins after which the bankroll hit zero each trial.
The chart above shows the results of the simulation when starting with a bankroll of 100 betting units. Apparently there is a good chance at hanging out at the casino for a long time before losing the whole bankroll….a 50/50 chance of still being there after around 600 spins of the wheel. There is a 38% chance of still being there after 1,000 spins of the wheel, and 8% chance after 10,000 spins.
At 40 spins of the roulette wheel per hour, >10,000 spins is >250 hours of very repetitive betting on the same number every time.
Starting with a bankroll of only 20 betting units is a much better way to hit gambler’s ruin quickly. A less than 93% chance of seeing fewer than 1000 spins, and a 58% chance of seeing fewer than 50 spins.