A common dice game called craps is played in several variations, resulting in an infinitely large probability tree. To see some of the results associated with large probability trees, consider the following single die game, similar to craps, which we will call scraps.

A player rolls a single die, if the player rolls 2 or 6, he wins. If the player rolls a 1 he loses. With any other result the player rolls again. If his second roll matches his first roll, he wins. If the 2nd roll is 1, 2, or 6, he loses. If the player does not win or lose on his second roll he continues to roll, using the same criteria given for the second roll.

i.e. 6 wins
3 4 6 loses
1 loses
3 5 2 loses
3 5 4 3 wins
3 3 wins
2 wins
5 3 3 3 3 4 5 wins

1. Play 100 games of scraps and empirically determine an estimate for the probability of winning.

2. Using classical methods discussed in class, try to estimate the probability of winning. (You will likely not be able to get this exactly because of the nature of the problem, just make the best estimate you can).

3. How close is the calculated value to your experimental value?