If I am randomly put into a 2d grid of rooms, assuming that “random” means that I have an equal probability of ending up in any room, then shouldn’t I be equally likely to end up in the border rooms as in the middle rooms?
More likely actually*. The trick is people are using middle, to mean** ‘middle rooms, or close to middle rooms’, and are trying to riff off the central limit theorem or something.
*The actual probability depends on whether the grid has an even or odd number of columns/rows (and if it’s big enough that the middle and the border are different).
1 2 3
4 5 6
8 9 0
Odd both ways, probability of having a border room is actually a lot larger.
1234
5678
9012
3456
The ‘middle’ is larger for an even number of columns and rows. But the border is still bigger than the center. The bigger it gets, the more this is the case.
**Above this is clarified to something very different: middle as any ‘non-border room’.
If I am randomly put into a 2d grid of rooms, assuming that “random” means that I have an equal probability of ending up in any room, then shouldn’t I be equally likely to end up in the border rooms as in the middle rooms?
I mean by “middle” a large region of rooms which are not on borders, like between 20 and 80, not exactly room 50. Should clarify it in the post.
More likely actually*. The trick is people are using middle, to mean** ‘middle rooms, or close to middle rooms’, and are trying to riff off the central limit theorem or something.
*The actual probability depends on whether the grid has an even or odd number of columns/rows (and if it’s big enough that the middle and the border are different).
1 2 3
4 5 6
8 9 0
Odd both ways, probability of having a border room is actually a lot larger.
1234
5678
9012
3456
The ‘middle’ is larger for an even number of columns and rows. But the border is still bigger than the center. The bigger it gets, the more this is the case.
**Above this is clarified to something very different: middle as any ‘non-border room’.