Having two possible outcomes does not mean it’s a 50:50 chance.
“So if I aim the arrow at the 1cm square from 100m away and shoot, I either hit it or I don’t. So basically I have a 50% chance of hitting it.”
My wife, father-in-law and I were playing a board game with my brother-in-law. In this game, we were playing as detectives who have to try to find his character, but each turn he could move in secret in one of several directions. We were a few turns in at one point and he could have been in any of dozens of places at this point. We drove him nuts by saying “he’s either in this spot or he’s not, it’s a 50-50 chance.” He kept arguing “I could be in a ton of places! It’s not a 50-50 chance!” But we just kept pretending we didn’t understand and arguing that there were only two possibilities, he’s there or he’s not, so it was clearly a 50-50 chance. He got quite angry.
I love Scotland Yard. We got it for a friend who loves detective stories. Then discovered that it’s a public transit simulator which is even better.
Letters from Whitechapel?
Either that or you buried the lede by failing to mention something rather significant about the hidden character, and you were playing Fury of Dracula. Or my boardgamegeek-fu isn’t as strong as I hoped.
Either I become president, or I don’t.
Therefore, the odds of me becoming president is 50%
Brb committing 34 felonies.
Very weird fun fact about arrows/darts and statistics, theres 0% chance of hitting an exact bullseye. You can hit it its possible to throw a perfect bullseye. It just has a probability of zero when mathematically analyzed due to being an infinitesimally small point. Sound like I’m making shit up? Here’s the sauce
How can an outcome both be entirely possible and have 0% probability?
Q.E.D
Key word here is “infinitesimally.” Of course if you’re calculating the odds of hitting something infinitesimally small you’re going to get 0. That’s just the nature of infinities. It is impossible to hit an infinitesimally small point, but that’s not what a human considers to be a “perfect bullseye.” There’s no paradox here.
Another lesson I the importance of significant digits, a concept I’ve had to remind many a young (and sometimes an old) engineer about. An interesting idea along similar lines is that 2 + 2 can equal 5 for significantly large values of 2.
The thing with that is that it’s actually a useful generalization to make in a lot of scenarios.
If you know nothing about the distinction between two possible outcomes, treating them as equally likely is a helpful tool to continue with the back of the envelope guess. Knowing this path needs 5 coin tosses to go right and this one needs 10 is helpful to approximate which is better.
Your example is obviously outside the realm where you have zero information, so uniform distribution is no longer the reasonable default. But the idea is from a reasonable technique, taken to extremes by someone who doesn’t fully get it.
