yewler: forum

My spouse has informed me that they are going to go inactive so I'm looking for someone new. Preferably I'm looking for someone with a maxed PI. I'm willing to pay upkeep or go halvsies on it, and I'm active every day.

I'm in :)

Manual Labor: 79

Intelligence: 224

Endurance: 243

I'm a new player with low stats but I'm online every day.

No longer looking for a job

Oh that is beautiful. I like that a lot.

Let me know if I'm missing something here (I'm appealing to the uncountability of the rationals but in a different way) but I've been thinking about this for the past 30 mins or so and want to put some thoughts out. I do think Bob can always win, but I don't have all the details fleshed out.

In step k, Bob is given an interval by Alice and obviously has many different possible choices, but I want to restrict Bob to just consider the two choices where he selects exactly the first third or exactly the last third. We can call the former choice L and the latter choice R and consider the choices that Bob makes through the entire game. Games from Bob's perspective can be represented as the infinite strings of L and R. For example, the game where Bob chooses to alternate between the left and right choice might be represented as the following string:

LRLRLRLRLRLRL...

Suppose we had two strings S1 and S2 that differed at any place along the string. We can assume that at the place of discrepancy, S1 has the L and S2 has the R. If Bob followed S1 for a game, then xi must be in L, and if he followed S2, xi must be in R. Now, L and R are disjoint, and so the final xi will be different.

A diagonalization argument shows that the set of games Bob can play (and therefore the set of xi he can zone in on) is uncountable, and therefore he's got lots more options than just the measly set of rationals.

I have not figured out a precise strategy for Bob yet, but this is my rough thought process for why I think there is one for him.

Good stuff. Was quite quick.