Hi, I need help figuring out the following statistics:
Player A rolls aX amount of d10 dice.
Player B rolls bX amount of d10 dice.
X = between 2-10 dice.
After the roll, each player checks what "sets" he got, aka how many die results show the same number. One set can be 2,2 or 4,4,4 or 2,2,2,2 etc, several dice with one number is one set. the leftover dice not in any sets, are "loose dice".
The number of dice in a set is the sets width (2,2 = width 2 / 5,5,5 = width 3).
The number on the dices in each set is the sets height (2,2 = height 2 / 5,5,5 = height 5)
1:
What is the probability (in %) that Player A rolls at least one set that is of greater height than any set Player B rolls? This would result in a table of course, where X-axis is aX, and Y-axis is bX. I'm seeking the mathematical formula that I can use to create this table.
2:
What is the probability that Player A (or B) gets P amount of dice included in any set? Aka, if he rolls 6 dice, what is the probability that he gets 2 dice in a set (1 set), and the rest loose dice, 4 dice (2 sets), 5 dice (2 sets of with 2 and 3), 6 dice (3 sets of width 2)? I need a formula to create a table where X-axis is X, and Y-axis is P.
Any help is appreciated.
Player A rolls aX amount of d10 dice.
Player B rolls bX amount of d10 dice.
X = between 2-10 dice.
After the roll, each player checks what "sets" he got, aka how many die results show the same number. One set can be 2,2 or 4,4,4 or 2,2,2,2 etc, several dice with one number is one set. the leftover dice not in any sets, are "loose dice".
The number of dice in a set is the sets width (2,2 = width 2 / 5,5,5 = width 3).
The number on the dices in each set is the sets height (2,2 = height 2 / 5,5,5 = height 5)
1:
What is the probability (in %) that Player A rolls at least one set that is of greater height than any set Player B rolls? This would result in a table of course, where X-axis is aX, and Y-axis is bX. I'm seeking the mathematical formula that I can use to create this table.
2:
What is the probability that Player A (or B) gets P amount of dice included in any set? Aka, if he rolls 6 dice, what is the probability that he gets 2 dice in a set (1 set), and the rest loose dice, 4 dice (2 sets), 5 dice (2 sets of with 2 and 3), 6 dice (3 sets of width 2)? I need a formula to create a table where X-axis is X, and Y-axis is P.
Any help is appreciated.
