Ignoring the Odds
Also: Appeal to Probability, Blind Optimism,
Against All Odds, Slam Dunk, Neglect of Probability
Class: Questionable Cause
Ignoring or exaggerating
the chance of something.
Probability is not intuitive. Just because something is improbable doesn’t mean it’s impossible:
There is no way you could have drawn all four aces. You must be cheating!
I swear I didn’t cheat! It’s a tiny chance, but it’s not impossible!
There is no way life could have evolved by chance from random mutations. That’s impossible!
Each step was incredibly unlikely, but over billions of years even the smallest chances add up.
Just because something is highly likely doesn’t means it’s definite:
There are billions of stars in the galaxy, so there definitely must be intelligent life out there!
That seems very likely, but it is not definite.
And a slight chance is not a strong chance:
To defeat the Empire all we need to do is sneak past all the guards, disable their shields, and fire a torpedo down a tiny vent shaft. It’s a slam dunk!
There are sooo many things that could wrong. That works only in movies.
We are in a movie! Pew, pew, pew!
Foolacy vs. Fallacy

The cognitive bias Neglect of Probability shows that people usually ignore or distort probability. This leads to faulty reasoning. However, there is no traditional fallacy that neatly covers this. Instead several different fallacies partly cover it:

Appeal to Probability/Possibility is treating a small possibility as a large one, and some sources say it also means treating a large probability as definite.
Appeal to Incredulity covers improbable events if they are hard to understand (like evolution).
Divine Fallacy covers improbable events if they are attributed to God or the supernatural (like ESP).
Spotlight Fallacy covers exaggeration of odds if they are sensational news stories.
Gambler’s Fallacy and Hot Hand Fallacy are a false assumptions that past events effect future luck.

The strong evidence of this cognitive bias justifies a corresponding foolacy.