Casinos invest a lot of energy selling the dream. One way to do this is by showing off people winning big in your casino. Everyone has seen those corny pictures of people holding human-sized cheques right? It’s a solid tactic, since empirical evidence shows that after a store has sold a large-prize winning lottery ticket, the ticket sales increase from 12 to 38% over the following weeks.

If we look at slot machine play, what exactly defines a big win? The first stab we took at this was quite sloppy. We took an arbitrary number and said wins bigger than 500 euro are impressive. This was quick and easy to implement, but when we observed the results we noticed that when you have players playing at high stakes, a win of 500 euro really isn’t that impressive, and we would see the exceptional high roller often dominate the results.

What defines a big win, is not the amount, but how many times the win multiplies your stake. Betting 1 euro to win 200 euro sounds like quite the return right? Coming to this conclusion, we had to define a multiplier threshold that indicates a big win.

Having each win correlate to a bet, we could project the multipliers, and look at the distribution.

In this example I’m using matlab, but we could do the same using Excel or code.

So first we load the multipliers data set.

multipliers = csvread('C:\data\multipliers.csv')

For then to look at its histogram, visualizing how the multipliers are distributed.

histfit(multipliers)

Here we notice that there is a skewness towards large values; a few points are much larger than the bulk of data. Logarithmic scales can help us here.

histfit(log(multipliers), 8)

This shows us a pretty fitting bell curve, meaning the multipliers are somewhat log normally distributed. We could now use the log standard deviation to pick the outliers.

But we can also tabulate the data set and hand pick the cut-off of normal wins.

tabulate(log(round(multipliers)))

    Value    Count   Percent
        0    54905     21.54%
 0.693147    68548     26.89%
  1.09861    29680     11.64%
  1.38629    16421      6.44%
  1.60944     8900      3.49%
  1.79176     8102      3.18%
  1.94591     2238      0.88%
  2.07944     5953      2.34%
  2.19722     1044      0.41%
  2.30259     3297      1.29%
   2.3979      625      0.25%
  2.48491     1128      0.44%
  2.56495      687      0.27%
  2.63906      544      0.21%
  2.70805      820      0.32%
  2.77259     1402      0.55%
  2.83321      364      0.14%
  2.89037      344      0.13%
  2.94444      185      0.07%
  2.99573     2406      0.94%
  3.04452      162      0.06%
  3.09104      139      0.05%
  ...

We could now write a rule in our projection of big wins which states that a log(multiplier) larger than 3 is considered to be a big win.

Matlab, Excel and the like are great domain specific tools for data exploration which can help you reach a better feel and understanding.