The Inverse Gambler's Fallacy Explained

What the hell is the Inverse Gambler's Fallacy? It's easy to explain with an example:

Suppose a man walked into a room and saw someone rolling a pair of dice. Furthermore, imagine that the result of this dice roll is a double-six. The man entering the room would commit the Inverse Gambler's Fallacy if he said, "You've probably been rolling the dice for quite a while, since it's unlikely you would get a double-six on your first attempt."

This is a fallacy because, regardless of whether the dice have been rolled once or a million times, the odds of a double-six on that particular occasion are 1 in 36.

The Inverse Gambler's Fallacy in cosmology?

I discuss elsewhere an argument that the fine tuning of our universe is evidence for multiple universes. A universe fit for life is remarkably unlikely, unless there are a great many universes. However, some suggest that this line of reasoning commits the Inverse Gambler's Fallacy.

Here's why it doesn't. (I'm essentially following John Leslie's well-known paper.)

If we were standing outside the universe looking in, and we found that it happened to contain life, this would be no argument for other universes. The odds of one particular universe having life should be the same regardless of whether there are others.

However, we are actually in such a universe, and therefore can't help but find that the universe we're looking at contains life. If it didn't, we wouldn't be here. So, our situation is not analogous to the man in the example above.

A better example

Leslie gives another example of reasoning from an unlikely event; one which more closely matches our own position in the universe.

This time, suppose that the man is told that he will not be allowed to enter the room until a double-six has been rolled. At some point, he is told that he may now enter. He enters and sees that, indeed, a double-six has been rolled. In this case, he does not commit a fallacy if he concludes (with a probability of 35 in 36, or 97.2%) that this was not the first dice roll.

The point is that he does not witness a random dice roll, but rather is only allowed to witness a double-six. By analogy, we do not experience a universe chosen at random, but rather are only "allowed" to experience a universe where life is possible.

References

allancrossman.com