Opponents are not all equal.
Nor is their inequality linear. You should also reject it if you’re near-even with this person, and there is a larger gap between you and the other players (in either direction). But really, it’s all down to expected value—take your distribution of possible paths through the game, conditional on each side of this decision. Take the one with the highest mean.
Aside: you are misusing “utility” in this example. What is offered is not utilons, but resources that (may or may not) impact the utility you get from the final position of the game.