Question

3. Suppose you’re playing a game where you consecutively roll 3 dice. After each roll you may choose to either roll the next dice or sacrifice one die to reroll any number of the previous dice. If you get a number greater than 5 you win, but if you roll doubles or a number less than 6 you lose.
   1. Considering each roll a separate state what is the approximate branching factor? Justify.
   2. Draw the full state space considering only the number of distinct dice that have been rolled, not what’s on the dice (so if you have rolled one dice and have a 6 that is the same state as if you had rolled a 2). What is the approximate branching factor of this space?
   3. Evaluate the probability of winning for each end state only considering the end state, not the path there.
   4. Using the probability of winning as a heuristic highlight the path of a best first search.

this is all question

Answer 1

Winner Case:

case1.

with the 1st dice i get 6

case 2

with the 1st dice i get less than 6 and I take Dice2. and I get 6.

Case 3,

I skip 2nd Dice. i kept rolling 1st dice. I get 6

case 4

with the 1st, 2nd dice i get less than 6 and I take Dice3  and I get 6.

or, Dice1 gave less than 6, Dice2 gave less than 6, but I skiped Dice3 and rolled Dice2 and got 6

state transition diagrams of different winning cases (given above) are shown below:-

• best case, case 1
• ---------------------------------------------------------------------------------
• case 2
• ---------------------------------------------------------------------------------------------------------------
• case 3
• ----------------------------------------------------------------------------------------------------------------------------------------------------------

case 4

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