Recent research by the NRGP for the Gauteng Gambling Board has considered the use of simulation to explore the extent to which gamblers are able to negotiate the conflict between demonstrable statistical principles underpinning games of chance and deeply held convictions which could be loosely termed "gambler's fallacies".  The spreadsheet below allows players to "play" the game of European Roulette for some fixed bet and determine their winnings, and then for multiple plays to interrogate the concept of casino house advantage. 

1. In the initial phase of the exercise, the simulated Roulette game first worksheet (tab: Play_Roulette) is used to examine the return one receives on (repeated) contrasting bets of one's choice. In order to demonstrate the fact that the expected return will remain constant but the variability of that return will differ greatly it is suggested that one tries contrasting bets; for example, play and compare the returns of a Red or Odd bet versus a Number bet.
   
   
2. In the second phase one may observe a large number of plays before reaching any conclusions about the efficacy of any betting strategy. One may then proceed to the second worksheet (tab: MultiplePlays) in the software which records and tabulates the results of large numbers of simulated plays. At this stage the cogent point about constant expected value across different bets generally becomes clearer. If one continues to use the contrasting bets suggested above, although the observed % profit/loss, referred to as the house advantage, varies across n plays, it is much more stable for the low risk bet (Red or Odd) than the high risk (Number) bet.
   
   
3. The software has a third worksheet (tab: CasinoAdvantage) which allows one to empirically build the distribution of the house advantage. The empirical results for selected bets can be observed, followed up by a demonstration that these findings in fact reflect the theoretical concepts of expected value and variance of a random variable. This level has been added in order to challenge those who have grasped the first two levels and who wish to pursue a deeper understanding of the statistical concepts.

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Please note that this roulette simulation currently works on Windows 10 and Windows 11 PCs running MS 365 or MS Office. It does not work on smartphones or tablets running iOS or Android.

1. Click the button below to download an Excel file to simulate a Roulette game.
2. Run the Excel file.
3. Enable Macro content in the security warning at the top of the screen before playing.
4. Make the file a trusted document in the security message that pops up.