# How to improve your odds at the casino: The Gambler’s Fallacy

October 22, 2018Imagine 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.