A common dice game (sometimes called “You blew it”)consists of:
Any number of players
Each in turn rolls 5 dice
A “1” scores 100 points, a “5” 50points, others none
After each roll the player can score and keep any of the“1 or 5” and roll the remaining die or dice.
If any roll does not contain a 1 or 5, the player“busts” and the total score for that turn becomes zero.Play moves to the next player.
The player can stop or continue any time.
If all 5 dice are scored the player can continues with another 5dice roll
Scores accumulate and an arbitrary total (say 500) is thegoal.
(a) If on my first roll I get 5,3,1,5,1 what is my score ifI stop? If I continue and roll the 3 again:
(b) What is the probability of a 1 or 5?
(c) What is my expected score if I get a 1 or 5? (onenumber)
(d) What is the probability of losing all my points?
(e) What is the total mathematical expectation ofcontinuing? Given the choice of stopping or rolling the 3 again,which is the better strategy? Why?
(f) If I hold the 1, 1 and roll the other threedice, what is my probability of busting?
(g) Of not busting?
(h) Why is this a better strategy?
(i) What is the chance (expressed as 1 in ?)of busting on the first roll?
(j) If I hold 1,1,1 should I stop or roll theremaining two dice again? Discuss the options.