part 2: We roll a fair die until 3 number 4s are thrown. Determine the expected value of the total number of 2s and 3s obtained along the way.

this question came from this questionthe only difference i want to change is, lets assume the game stops once I roll 3 dice in a row with number 4. how would the problem change?the solution that caught my attention is this because it is solve using recurion, and i am curios how this equation will change once hte condition becomes getting 3 4's in a row instead of just 3 4's.thanks