You're a contestant on a game show.
There are infinity doors in front of you, behind just one of those doors is a sports car.
You choose a door and the gameshow host opens infinity-1 doors, leaving behind just two doors - one that doesn't have the car behind it and one that does.
You've probably heard this question before so I'm not going to ask if you would stick or switch. However, is the chance of the car being behind the door you didn't choose literally 100%?
well you said that host opens two doors and one of them has the car behind it. So you would switch, and have a 50% shot of getting the car. Plus you can't just do infinity-1. instead use n-1.
This is a prime example of the clash between statistics (which operate on the assume that all variable are known and the world is perfect) and human heuristics we tend to rely on while making predictions.
There very well could be patterns in what door the car ends up behind, that you aren't aware of. Your intuition could be correct. There are myriad at work beyond what the host tells you, so blindly switching to "increase muh odds" isn't something I'm fond of.
In truth I would likely view it as little above random odds and side with intuition. Whether that meant switching or not, depends.
Infinity is not a countable set, so the question is flawed; operations like infinity - 1 are not meaningful.
That being said, for games with large n you 100% should switch, because the odds you picked the correct random natural number are 1/n, which approaches zero as n approaches infinity.
ofc its meaningsful, infinity + 1 is bigger than just one infinity. And a infinity can have different sizes. For example: Between 1 and 2 are there endless of numbers, but between 1 and 100, it is even more numbers but also infinitely.