The Stratosphere offers a craps variation called “crapless craps

Homework Feb 1

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The Stratosphere offers a craps variation called "crapless craps." On the pass line bet in this game the player can not lose on the come out roll. If the player rolls a 7 on the come out roll he wins. Any other number becomes the point. If the player rolls the point before another 7 then he wins. If a 7 is rolled before the point he loses.

The player can make a place bet on the 2 or 12. Both bets pay 11-2.

1. What is the probability of rolling a 2?

1/36

2. What is the probability of rolling a 7?

6/36

3. What is the probability of rolling a 2 before a 7?

1/(1+6) = 1/7

4. What is the player’s expected value on this bet?

(1/7)*(11/2) – (6/7) = 11/14 – 12/14 = -1/14 = -7.14%.

The player can also make a place bet on the 3 or 11. Both bets pay 11-4.

5. What is the probability of rolling a 3 before a 7?

2/(2+6) = 2/8 = 1/4

What is the player’s expected value of this bet?

(1/4)*(11/4) – (3/4) = (11/16) – (12/16) = -1/16 = -6.25%.

To determine the house edge on the pass line bet complete the following table. The first two rows are filled out to get you started. The total in the lower right cell should be the expected value.

Event	Probability	Pays	Return
2 on come out roll then win	0.003968	1	0.003968
2 on come out roll then loss	0.023810	-1	-0.023810
3 on come out roll then win	0.013889	1	0.013889
3 on come out roll then loss	0.041667	-1	-0.041667
4 on come out roll then win	0.027778	1	0.027778
4 on come out roll then loss	0.055556	-1	-0.055556
5 on come out roll then win	0.044444	1	0.044444
5 on come out roll then loss	0.066667	-1	-0.066667
6 on come out roll then win	0.063131	1	0.063131
6 on come out roll then loss	0.075758	-1	-0.075758
7 on come out roll	0.166667	1	0.166667
8 on come out roll then win	0.063131	1	0.063131
8 on come out roll then loss	0.075758	-1	-0.075758
9 on come out roll then win	0.044444	1	0.044444
9 on come out roll then loss	0.066667	-1	-0.066667
10 on come out roll then win	0.027778	1	0.027778
10 on come out roll then loss	0.055556	-1	-0.055556
11 on come out roll then win	0.013889	1	0.013889
11 on come out roll then loss	0.041667	-1	-0.041667
12 on come out roll then win	0.003968	1	0.003968
12 on come out roll then loss	0.023810	-1	-0.023810
Total	1.000000		-0.053824