On August 18, 1913, something very strange happened at Monaco’s Monte Carlo casino: for the twentieth time in a row, the ball had fallen into a black pocket. More and more people gathered at the table and started betting like crazy for red — they were convinced that the time for red was more than overdue. Well, most of them lost a lot of money because it took another seven spins of the wheel until red finally arrived.
Today, I present a little Groovy program that I wrote in order to get insight into Roulette probability, to save us from what is now known as the Monte Carlo Fallacy.
When you call ‘runSimulation’ you can specify how many number of times you want to spin the wheel. With every spin, the method ‘spinWheel’ returns either 0 (for black), 1 (for red), or 2 (for Zero).
‘runSimulation’ keeps track of the length of a certain color series in three associative arrays (i. e. maps), one for every color (including the color Zero). The key into these maps is the length of the series and the associated value is the count of how often this series length was encountered during the experiment.
To make accessing these color length maps generic, their references are stored in a plain list (‘seriesMaps’). By using the color value returned from ‘spinWheel’ as an index, one can easily obtain the length map for a particular color. This list of length maps is returned at the end of the simulation. As an example, after 100 spins, the list might look like this:
[ [2:6, 3:3, 1:14, 5:1], [3:5, 1:8, 2:9, 4:1, 5:1, 7:1], [1:3] ]
In this simulation, for black, a series of length 2 was encountered 6 times, and a length of 5 one time. For red, there was one series length of 7, and our virtual ball landed three times on Zero, but there was never a series of Zeros (i. e. longer than 1). (Aside: in one experiment I did with the bug-fixed version, I spun the wheel more than 100 million times; I got a maximum series of 30 for black and — believe it or not — I once got a series of four times Zero in a row.)
But the program, as it is presented to you, contains a bug. It just doesn’t work as it is supposed to. Can you spot it? (Note: the bug has nothing to do with any Groovy idiosyncrasies.)