What about the case that instead of rolling two dice simultaneously, rolling of the dice in the game is this:
The player rolls the dice.
The player is asked whether he/she want to roll the dice again.
If the player want to roll the dice again, he/she will roll the dice again and the points obtained will be the final score; if the player does not want to roll the dice again, he/ she will have the dice roll points in 1. as the final score
The purpose of the game is to get the as high score as possible.
Am I correct that the expected value of the game score is also 4.47 (as in the question mentioned at the beginning of this question)? Am I correct that the optimal strategy is that if a player get a dice roll point smaller than 5, he/ she should roll it again?
If yes, does that mean this game is equivalent mathematically to the game mentioned at the beginning of this question?
Is such result extensible to more than 2 dice (e.g. 3 dice and rolling a die for 3 times)?