Imagine you are at a Las Vegas casino and you’re approaching the roulette table. You notice that the last eight numbers were black… so you think to yourself, “Holy smokes, what are the odds of that!” and you bet on red, thinking that the odds of another black number coming up are really small. In fact, you might think that the odds of another black coming up are:
0.5*0.5*0.5*0.5*0.5*0.5*0.5*0.5*0.5 = 0.00195 (a very tiny number)
Or are they?
The problem is that a roulette table – if fairly constructed – has no “memory”. That is, one outcome does not depend on the previous outcome’s result, and so the odds for a red number or black number are just about equal (actually, just shy of 50% each, since there is one or two green spaces on a roulette table depending on American or European versions).
Keeping with our example, if you bet on either red or black for each spin, this type of outside bet pays 1 to 1 and covers 18 of the 38 possible combinations (or 0.474). A far cry from the 0.00195 number above (a miscalculation that is roughly 243 times too small). Now your odds of a red coming up aren’t so good anymore…
This fallacy is called the Gambler’s Fallacy, and it’s what the city of Las Vegas is built on.
Random events produce clusters like “8 black numbers in a row”, but in the long term, the probability of red or black will even out to its natural average.
The key to your success at the casino? Understand that every individual spin (or “event”) has its own probability which never changes. In this case, 18 in 38.
So the next time you’re at a casino and you see a string of the same color coming up, remember that the odds of that color coming up again are exactly the same as the other color… it might save you a few bucks so you can play a bit longer.