Tag Archives: Independent Events

Don’t Fall for the Gambler’s Fallacy: List of Biases in Judgment and Decision-Making, Part 7

A little later in the day than I would have liked, but today’s cognitive bias is the gambler’s fallacy. The bias gets its name from, as you’d expect, gambling. The easiest example to think of is when you’re flipping a coin. If you flip a coin 4 times and each of those 4 times the coin turned up heads, you’d expect the coin to turn up tails on the next (or at least have a higher chance of turning over tails), right? WRONG!

The odds are exactly the same on the 5th turn as the 6th turn as the 66th turn as the 11,024th turn. Why? Because the two instances of flipping the coin are independent events. (Note: we’re ignoring, for the time being, any effects that quantum reality might have on a given event in the past and the future.) So, every time you flip a coin, that’s an independent event — unaffected by earlier events.

Another important example is the reverse fallacy. That is, if we think that heads are “hot” because it’s been flipped a number of time, thinking that there’s a better chance that heads will be flipped is also a fallacy. Again, this is an independent event — unaffected by previous events.

This fallacy is so named because there’s a famous example of the gambler’s fallacy happening at the Monte Carlo Casino where, on roulette, black came up 26 times in a row. A number of gamblers reasoned that red would come up because there had been such an unlikely number of blacks that came up in a row. As the story goes, they lost millions.

Other examples of the gambler’s fallacy:

  • Childbirth: “we’ve had 3 boys, so we’re going to have a girl now…”
  • Lottery: “I’ve lost 3,000 times, so I’m due for a win…”
  • Sports: “Player X is playing really well, they’re bound to start playing bad…”
  • Stock market: “Stock X has had 7 straight down days, so it’s bound to go up on this next trading day…”

Ways for Avoiding the Gambler’s Fallacy

1) Independent Events vs. Dependent Events

The biggest way to avoid the gambler’s fallacy is to understand the difference between an independent event and a dependent event. In the classic example, the odds of a coin landing on heads or tails is — negligibly — 50/50 (I say negligibly because there are those who contend that the “heads side” weighs more and thus gives it a slight advantage). An example of a dependent event would be picking cards from a deck. There are 52 cards in a deck and if you pick one card without replacing it, your odds of picking one of the other 51 cards increases (ever so slightly).

If you liked this post, you might like one of the other posts in this series: