To maximize utility when you can play any N number of games, I believe you just need to calculate the EV (not EU) through playing every possible strategy. Then, you pass all those values through your U function and go with the strategy associated with the highest utility.
<Tried to retract this comment since I no longer agree with it, but it doesn’t seem to be working>
To maximize utility when you can play any N number of games, I believe you just need to calculate the EV (not EU) through playing every possible strategy. Then, you pass all those values through your U function and go with the strategy associated with the highest utility.