If I am following, it seems like an agent which says “bet ‘higher’ if positive and ‘lower’ otherwise” does well
Robert Kennedy
Karma: 105
Neither
Thanks!
I do not believe that “any monotonically increasing bounded function over the reals is continuous”. For instance, choose some montonically increasing function bounded to (0,0.4) for x<-1, another function bounded to (0.45,0.55) for −1<x<1, and a third function bounded to (0.6,1) for x>1.
I did not check the rest of the argument, sorry
Please spoiler your edit
Could you explain why you are almost certain?
Could you explain why it’s clearly impossible to produce an algorithm that gives better than 50% chance of success on the first round? I think I follow the rest of your argument.
Good questions! It’s a forum with posts between two users “Iarwain” (Yudkowsky) and “lintamande”, who is co-authoring this piece. There are no extraneous posts, although there are (very rarely) OOC posts, for instance announcing the discord or linking to a thread for a side story.
In each post, either user will post as either a character (ie Keltham, Carissa, and others—each user writes multiple characters) or without a character (for 3rd person exposition). I usually use the avatars when possible to quickly identify who is speaking.
You don’t need to pay attention to history or post time, until your catch up to the current spot and start playing the F5 game (they are writing at a very quick pace).
By “better than 50% accuracy” I am trying to convey “Provide an algorithm such that if you ran a casino where the players acted as ROB, the casino can price the game at even money and come out on top, given the law of large numbers”.
(Perhaps?) more precisely I mean that for any given instantiation of ROB’s strategy, then for any given target reward R and payoff probability P<1 there exists a number N such that if you ran N trials betting even money with ROB you would have P probability to have at least R payoff (assuming you start with 1 dollar or whatever).
You can assume ROB will know your algorithm when choosing his distribution of choices.
Computability is not important. I only meant to cut off possibilities like “ROB hands TABI 1 and ‘the number which is 0 if the goldbach conjecture is true and 2 otherwise’”
You can restrict yourself to arbitrary integers, and perhaps I should have
I don’t see how 2 is true.
If you always answer that your number is lower, you definitely have exactly 50% accuracy, right? So ROB isn’t constraining you to less than 50% accuracy.
Actually, for any given P which works, P’(x)=P(x)/10 is also a valid algorithm.