These are silly. In a game you can't lose, you should invest no resources into your decision making and play as many instances of this game simultaneously as possible to maximize return. The worst I can do is 3 points per game as Blue. The best I can do is 6 points per game as Blue. If I play two games simultaneously without devoting any decision to either of them, the worst I can do as Blue is 6 points, which is the former best. Because there are no resources devoted to deciding how to play, this can scale infinitely and with untrained players.
The point of the exercise is to determine the best strategy on each turn. Blue may not be able to play as often and rapidly as desired. The payoffs are all positive for Blue just to make the analysis simpler. The same strategy would apply if all the payoffs were five points lower: R1 B2: no points R2 B1: Blue gets 1 R2 B2: Red gets 1 R1 B1: Red gets 2