How do fruit machines work? Do they operate on a fixed mathematical model which governs payouts using probability or are they totally random? — TS, Norfolk, UK
I assume that you are referring to the gambling machines that spin several wheels when you pull a lever and that pay you amounts that depend on the patterns of symbols that show on the faces of the wheels when they stop. While the final arrangement of symbols that appear on such a machine when it stops is entirely random, the patterns that pay and the amounts they pay are calculated to ensure a slight financial advantage for the house. The mathematics of probability is well developed for such gambling machines and it’s relatively simple to determine what fraction of your money you should expect to lose if you play the game for a very long time. If you do play long enough to sample the full statistics of the game, you are certain to lose money. It’s only if you play briefly that you can take advantage of statistical fluctuations to leave with more money than you had when you started.