Bunco Probabilities
January 13th, 2013 at 1:36:19 PM
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I am working on probabilities for a game where three dice are rolled to establish points, and then subsequent rolls are made to match the original numbers rolled. Our rules will say that each match is worth 1 point, a pair will be worth more, and rolling trips is worth even more. We have not set how much yet because we can't pin down the probabilities.
The probability for matches when the original roll is trips is fairly easy: 1 way to make trips, 15 ways to make a pair, and 75 ways to make one match. (Right?)
The probabilities of when they player rolls a pair or three unique numbers are failing us. We've been working out probabilities for three unique numbers and can't hit the magic 216 combinations.
Any help y'all can provide is appreciated!
'Brian
The probability for matches when the original roll is trips is fairly easy: 1 way to make trips, 15 ways to make a pair, and 75 ways to make one match. (Right?)
The probabilities of when they player rolls a pair or three unique numbers are failing us. We've been working out probabilities for three unique numbers and can't hit the magic 216 combinations.
Any help y'all can provide is appreciated!
'Brian
January 13th, 2013 at 1:40:38 PM
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Wouldn't it be (3/6)*(2/6)*(1/6) for matching three unique numbers?
At my age, a "Life In Prison" sentence is not much of a deterrent.
January 13th, 2013 at 3:12:13 PM
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You're calculations are correct so far.
1/216 trips
15/216 pair
75/216 singleton
The probability of everything else (no matches) is 5^3 = 125.
This accounts for all possibilities (1+15+75+125 =216).
If you attempt to calculate other pairs, keep in mind that some of them have already been counted in the singletons above. For instance, if you are trying to match the number 6, rolling 655 will count as a singleton and as a pair of fives.
1/216 trips
15/216 pair
75/216 singleton
The probability of everything else (no matches) is 5^3 = 125.
This accounts for all possibilities (1+15+75+125 =216).
If you attempt to calculate other pairs, keep in mind that some of them have already been counted in the singletons above. For instance, if you are trying to match the number 6, rolling 655 will count as a singleton and as a pair of fives.
I heart Crystal Math.
January 13th, 2013 at 3:12:14 PM
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You're calculations are correct so far.
1/216 trips
15/216 pair
75/216 singleton
The probability of everything else (no matches) is 5^3 = 125.
This accounts for all possibilities (1+15+75+125 =216).
If you attempt to calculate other pairs, keep in mind that some of them have already been counted in the singletons above. For instance, if you are trying to match the number 6, rolling 655 will count as a singleton and as a pair of fives.
1/216 trips
15/216 pair
75/216 singleton
The probability of everything else (no matches) is 5^3 = 125.
This accounts for all possibilities (1+15+75+125 =216).
If you attempt to calculate other pairs, keep in mind that some of them have already been counted in the singletons above. For instance, if you are trying to match the number 6, rolling 655 will count as a singleton and as a pair of fives.
I heart Crystal Math.
