# Gambler’s Fallacy

Original article was published on Artificial Intelligence on Medium

The safest way to double your money is to fold it over and put it in your pocket.” — Kin Hubbard

## Index

0. Dear Statistics Journal
1. Introduction to Probability
2. The Monty Hall Problem
3.
Gambler’s Fallacy

Let’s start, as most successful essays do, by asking a simple question.
Say I toss a fair coin 7 times and it leads to the following series of outcome:

`Head, Head, Head, Head, Head, Head, Head`

Now, if you had to bet on the next outcome, would you bet on it being a Heads or a Tails?

If you said Tails, well it sure seems like it should be Tails, because balance of probability! That every consecutive Head we flip incurs a debt to Tails and surely it must be much more likely for the next flip to be Tails.

Or perhaps, you’re a maverick, and you thought that the consensus would surely be Tails, but the fact that 7 heads showed up makes an even stronger case for the next flip to be Heads. *

Here’s the deal, it doesn’t matter what you picked. If you construed a pattern from the above series of flips and constructed an argument based on it to infer the next outcome, then you have committed to the Gambler’s Fallacy. In simple terms, the probability of the next outcome being a Heads or a Tails is still (50–50) and the fact that 7 consecutive heads showed up, doesn’t enforce any conditionality for the next outcome to be a Tails (or a Heads).

This is the case for all independent events.

`📖 In probability, two events are independent if the incidence of one event does not affect the probability of the other event. If the incidence of one event does affect the probability of the other event, then the events are dependent.`