Consider a simplified version of the game Yahtzee. In this game, we have 3 dice with 4 sides each (numbered 1-4) and the game begins by rolling all 3 dice. At this point, a player can make a decision: pick one of the 3 dice to reroll, or don’t reroll anything. Then, points are assigned as follows. the score is equal to the sum of all 3 dice. A reward of 10 points is given for two-of-a-kind; a reward of 15 is given to three-of-a-kind; and a reward of 7 points is given for rolling a series (1-2-3 or 2-3-4). If a special roll is achieved (series or two-of-a-kind) but the sum of dice is higher, the max is always taken. Now suppose the human player does not understand how to play the game, and as a result, they choose any action with uniform probability, regardless of the initial roll. We employ the use of a 'helpful robot' that has the power to perform the action selected by the human. Given a configuration of dice and the desired action from the human, this robot either actually implements the human's action (with probability 1 — p) or overrides it with a 'no reroll' action (with probability p).

Your friend Ethan (again) argues that our "helpful robot" should not only override the human player's "reroll" choice with probability p (and replace it with a "no reroll"), but also override the human player's "no reroll" choice with probability p (and replace it with the outcome of selecting one of the 3 dice at random and rerolling that dice) Ethan claims that "Ethanbot", equipped wth this new feature, will help a random human player achieve better end reward in expectation than our "helpful robot."

Required:
Give an example where "Ethanbot" is better (or worse) than our "helpful robot" in helping a random human player, if they override the human player's choice with the same p.
Describe a procedure to find the pe where the "Ethanbot" will be the most helpful increasing the end reward the most in expectation).