Farkle is a dice game played with 6 six-sided dice. There are many rules and variations...

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Farkle is a dice game played with 6 six-sided dice. There are many rules and variations to the game so let's stick with the simplest version: Each die showing a 1 is worth 100 points and each die showing a 5 is 50 points. Any other number (2,3,4,6) does not score. This is how the game is played: You first roll all 6 dice. If you do not roll any scoring dice then your turn is over and you get 0 points (This is called a FARKLE). Otherwise, you will set aside all of your scoring dice (1's and 5's) and then roll the remaining dice. The play continues in the same way. If on your next roll, you do not roll any scoring die then your turn is over and you get 0 points (FARKLE). Otherwise, you will set aside all of your scoring dice (1's and 5's) and then roll the remaining dice. If, eventually all of your dice are scoring dice then your turn is over and you earn that score. (a) (18 points) Design a dynamic programming algorithm that computes the probability of playing FARKLE with n dice and successfully ending with all 1's and 5's. (b) (2 point) What is the expected score for 6 dice? Farkle is a dice game played with 6 six-sided dice. There are many rules and variations to the game so let's stick with the simplest version: Each die showing a 1 is worth 100 points and each die showing a 5 is 50 points. Any other number (2,3,4,6) does not score. This is how the game is played: You first roll all 6 dice. If you do not roll any scoring dice then your turn is over and you get 0 points (This is called a FARKLE). Otherwise, you will set aside all of your scoring dice (1's and 5's) and then roll the remaining dice. The play continues in the same way. If on your next roll, you do not roll any scoring die then your turn is over and you get 0 points (FARKLE). Otherwise, you will set aside all of your scoring dice (1's and 5's) and then roll the remaining dice. If, eventually all of your dice are scoring dice then your turn is over and you earn that score. (a) (18 points) Design a dynamic programming algorithm that computes the probability of playing FARKLE with n dice and successfully ending with all 1's and 5's. (b) (2 point) What is the expected score for 6 dice?