The Gambler’s Fallacy

Take a red or black bet in a game of European Roulette – an 18 in 37 chance (or roughly 50/50 bet).

Each outcome is totally independent of past outcomes.

Yet for some reason players will turn to the game history display as if it’s some kind of oracle and expect that a long string of red’s increases the likelihood of the next color being black (and vice versa).

Their belief is this: there should be an even spread of red/black outcomes so if you can observe a significant historical deviation from this, then it follows that future outcomes should reverse this deviation.  See plenty of red on the board and anytime soon a flood of black should come.  See plenty of black and the reds are soon to have their turn.

This is such a common misconception that it even has a name – the Gambler’s Fallacy and it is the undoing of many a gambler.  It applies to any game of chance where bets are placed on independent events but roulette is perhaps where it causes most damage.

And at the risk of pointing out the obvious casinos aren’t exactly working overtime to correct this misconception.  In fact they well and truly encourage it.  Why else do you think they include game history displays for most roulette tables?  They certainly aren’t there to help advantage players identify a wheel bias.  Some even go further and provide complicated statistics like ‘hot’ or ‘cold’ numbers presented in chart form…like these are going to help you with the next spin!

Let’s again take a red or black bet in a game of European Roulette – an 18 in 37 chance. Now let’s assume we’ve been patiently stalking the casino floor (or live casino lobby) watching the game history at a bunch of tables.  We find a table where the ball has dropped on red a staggering 21 times in a row!

The odds of this happening are remote indeed… or 1 in 3,728,323.

The odds of ANOTHER red coming up next spin… 18 in 37

The odds of a black coming up next spin… 18 in 37

The chance some punter will do their nuts increasing their stake and/or doubling up on successive black bets…almost certain.