# Shouldn't the utility function of two-player zero-sum games be in the range $[-1, 1]$?

In Appendix B of MuZero, they say

In two-player zero-sum games the value functions are assumed to be bounded within the $$[0, 1]$$ interval.

I'm confused about the boundary: Shouldn't the value/utility function be in the range of [-1,1] for two-player zero-sum games?

• Hi @nikos. The game will return either $+1$ or $-1$ to the agent to indicate whether it wins or not. I get that the agent is unlikely to take actions that cause it to lose, but I cannot see any guarantee that restricts the value function to positive. For example, if the agent is in a state where there is no way to win if its opponent acts optimally. Shouldn't the value function of that state be negative in that case? – Maybe May 8 '20 at 11:48