Gene G. answered • 03/15/17
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(257)
You can do it! I'll show you how.
The first roll can be any number. Probability = 1
The second roll has to match the first roll. Probability = 1/6
Probability of a double at this point is 1/6.
For a triple, the third roll has to match the first and second rolls (one number). Probability = 1/6.
Probability of a triple is 1/36.
The third roll can form a double by matching either the first or second one. Probability = 2/6 = 1/3.
This only applies to the case where there is no double yet. Probability = 1 - 1/6 = 5/6
The additional probability of a double is 1/3 * 5/6 = 5/36
Net probability of a double is 1/6 + 5/36 = 11/36.
That would return 2 * 11/36 = 11/18 on average.
Net probability of a triple was 1/6. That would return 3 * 1/6 = 1/2 on average.
Net return would be 11/18 + 1/2 = 20/18 = 5/9 = 0.56 on average.
On average, a $1 bet would return $0.56.
Riley M.
And for the net return, how does 20/18=5/9?
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03/15/17
Gene G.
Oops! You're right. Thanks for catching my goof!
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03/15/17
Riley M.
So with that in mind how would it change the final answer?
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03/15/17
Riley M.
I am still confused on how to get the net return
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03/15/17
Gene G.
You're right again.
I was really focused on how to combine things and I loused up the simple arithmetic!
I found a typo in the triple probability and more errors.
I'll pick it up here:
The additional probability of a double is 1/3 * 5/6 = 5/18
Net probability of a double is 1/6 + 5/18 = 8/18 = 4/9
That would return 2 * 4/9 = 8/9 on average.
Net probability of a triple was 1/36. That would return 3 * 1/36 = 1/12 on average.
Net return would be 8/9 + 1/12 = 32/36 + 3/36 = 35/36 = 0.97 on average.
On average, a $1 bet would return $0.97.
Net probability of a double is 1/6 + 5/18 = 8/18 = 4/9
That would return 2 * 4/9 = 8/9 on average.
Net probability of a triple was 1/36. That would return 3 * 1/36 = 1/12 on average.
Net return would be 8/9 + 1/12 = 32/36 + 3/36 = 35/36 = 0.97 on average.
On average, a $1 bet would return $0.97.
Turns out to be more like real casino odds. Just a little in favor of the house.
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03/15/17
Riley M.
03/15/17