To phrase it better: You find yourself in room N, how many total rooms are there?
I know UDASSA accounts for the description length of the room address, but remember that given a number of rooms, each room will have the same description length. If there are 64 rooms, then room 1 will have address “000000” and not simply “0″ or “1”.
This way if you find yourself in a room, without knowing how many total rooms there are, and only knowing your room number, then you write it out in binary and take 2 to the bit-length of your room’s address. For ex, you find yourself in room number “100111”, 6 bits. So with 50% chance, there will be 64 rooms in total. Then you add an extra bit with 50% of the remaining measure (25%), 128 rooms, and repeat. If the payout doesn’t scale with the number of rooms, then 64 rooms would be the most profitable bet. It’s easy to test this either irl, or with a python script.
After doing so, I got unexpected results: given your room number, the most likely number of total rooms is a number whose description length is one-bit longer than the description length of your room. Weird.
The experiment is commonly phrased in non-anthropic way by statisticians: there are many items getting sequential unique numbers, starting from 1. You get to see a single item’s number n and have to guess how many items are there, and the answer is 2∗n. (Also, there are ways to guess count of items if you’ve seen more than one index)
To phrase it better: You find yourself in room N, how many total rooms are there?
I know UDASSA accounts for the description length of the room address, but remember that given a number of rooms, each room will have the same description length. If there are 64 rooms, then room 1 will have address “000000” and not simply “0″ or “1”.
This way if you find yourself in a room, without knowing how many total rooms there are, and only knowing your room number, then you write it out in binary and take 2 to the bit-length of your room’s address. For ex, you find yourself in room number “100111”, 6 bits. So with 50% chance, there will be 64 rooms in total. Then you add an extra bit with 50% of the remaining measure (25%), 128 rooms, and repeat. If the payout doesn’t scale with the number of rooms, then 64 rooms would be the most profitable bet. It’s easy to test this either irl, or with a python script.
python script: https://pastebin.com/b41Sa6s6
After doing so, I got unexpected results: given your room number, the most likely number of total rooms is a number whose description length is one-bit longer than the description length of your room. Weird.
The experiment is commonly phrased in non-anthropic way by statisticians: there are many items getting sequential unique numbers, starting from 1. You get to see a single item’s number n and have to guess how many items are there, and the answer is 2∗n. (Also, there are ways to guess count of items if you’ve seen more than one index)