My intuition is that this is one of those cases where given t "evaluation on the left side of t" and "evaluation on the right side of t" give different results. It seems to me that at any given time decision is made about future actions (and not the past), thus "evaluation on the left side of t" seems to be more important and it is the one that makes me reluctant to play this game. It seems to me that using "evaluation on the right side of t" (in cases where they differ) might give some strange results, e.g. murder having no victims.

It seems that left side of t and right side of t differs whenever there is different number of people on both sides. E.g. if you make an exact copy of a person and their entire memory, the "left identity" and "right identity" (perhaps there are better terms) intuitively seem to become two different things.