Dodecahedron Scraps

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IlanH

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A modified version of the dice game craps is played with two regular (i.e., perfectly symmetrical) dodecahedrons. Each die has its sides numbered from 1 to 12 so that any sum from 2 to 24 would be showing on the top surfaces of the two dice after each throw. If a player gets the sum 13 or 23 on his first throw (a natural), he wins. If he gets the sum 2, 3, or 24 (craps), he loses. If he gets any other sum (his point), he must throw both dice again. On this or any subsequent throw, the player loses if he gets the sum 13 and wins if he gets his point but must throw both dice again if any other sum appears. The player continues until he either wins or loses. To the nearest percent, what is the probability at the start of any game that the dice thrower will win?
 
IlanH said:
A modified version of the dice game craps is played with two regular (i.e., perfectly symmetrical) dodecahedrons. Each die has its sides numbered from 1 to 12 so that any sum from 2 to 24 would be showing on the top surfaces of the two dice after each throw. If a player gets the sum 13 or 23 on his first throw (a natural), he wins. If he gets the sum 2, 3, or 24 (craps), he loses. If he gets any other sum (his point), he must throw both dice again. On this or any subsequent throw, the player loses if he gets the sum 13 and wins if he gets his point but must throw both dice again if any other sum appears. The player continues until he either wins or loses. To the nearest percent, what is the probability at the start of any game that the dice thrower will win?
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