Many events can’t be predicted with total certainty. The best we can say is how likely they are to happen using the idea of probability. Probability does not tell us what will happen or when it will happen.  Instead, it tells us the likelihood that something will happen.  Think of it more as a “guide”.

For example, we all know that there are two outcomes of flipping a coin (heads or tails), and that the probability of getting either heads or tails when flipping a fair coin is ½.  The probability of an event happening is “the number of ways it can happen” divided by “the total number of outcomes”.  Probability is always a number between 0 and 1, with 0 meaning “it will never happen” and 1 meaning “it will always happen”.  A probability of 0.5 is like saying “there’s a 50% chance that the event will happen”.

One of the key’s to understanding probability is understanding that probability is just a guide.  For example, if we ask, “Flip a coin 100 times.  How many heads will show up?”, we know the probability of heads turning up is ½, or 0.5, so the number of times we would expect heads to come up in 100 flips is half of 100, or 50.  But if we actually ran this little experiment, we might get 42 heads, or 56, or 61… It will likely be somewhere around 50.  In fact, if you increased it to 1,000 flips, then you’d be pretty close to 500 heads.  The more flips, the closer you’ll get towards “half” of your outcomes being heads.

A Practical Example

Imagine you are at a casino and you’re approaching the roulette table.  You notice that the         last eight numbers were black… so you think to yourself, “What are the odds of that?”.  So you bet everything you have left on red, because surely, the odds of a ninth black number coming up are really small.

You might think that the odds of another black coming up are:

(½)^9 = ½ X ½ X ½ X ½ X ½ X ½ X ½ X ½ X ½ = 0.001953

Ah, but you would be mistaken, and you’d be wasting you precious money.

The “trick” is that a roulette table – if fairly constructed – has no “memory”.  That is, one outcome does not depend on the previous outcome’s result. For each spin, the odds for a red number or black number to appear are just about equal (in actuality, they are just shy of 50% each since there are one or two green spaces on a roulette table depending on American or European versions).

Continuing with our example above, 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).  This is a far cry from the 0.00195 number above (a miscalculation that is roughly 243 times too small).

The Gambler’s Fallacy

This incorrect way of thinking has a name – 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.  This is just like our coin flipping example:  the more times you flip, the closer you’ll get to hitting the natural average of 50%.

How can this help you win at the casino?  If you understand that every individual spin (or “event”) has its own probability which never changes, you’ll be less likely to get sucked into bad bets.  So you can go to  and check how understanding the odds for the game you’re playing helps you make smarter bets.

The next time you’re at a casino and you see a string of the same color coming up at the roulette table, 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.