2 Dice to Points

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thomasgolf

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Help: I need the 6 whole numbers for a 2 dice roll. If the roll is 7 n=, 6 / 8 n=, 5 / 9 n=, 4 /10 n=, 3 / 11 n=, 2 /12 n=. The numbers will be used in a board game for point totals.
 
thomasgolf said:
Help: I need the 6 whole numbers for a 2 dice roll. If the roll is 7 n=, 6 / 8 n=, 5 / 9 n=, 4 /10 n=, 3 / 11 n=, 2 /12 n=. The numbers will be used in a board game for point totals.
Click to expand...
The problem statement does NOT make any sense to me. Please explain the problem more - perhaps with numerical examples.
 
Are those '/' symbols division signs, periods, or something else?
 
OK, a numerical example would be if you roll a 7 with 2 dice you would get 1 point vs if you roll a 2 you would get 6 points. So the problem is coming up with what 6 whole numbers best represent the 11 dice combinations.

/ is = to or
 
thomasgolf said:
OK, a numerical example would be if you roll a 7 with 2 dice you would get 1 point vs if you roll a 2 you would get 6 points. So the problem is coming up with what 6 whole numbers best represent the 11 dice combinations.

/ is = to or
Click to expand...
If we expand [imath]{\left( {\sum\limits_{k = 1}^6 {{x^k}} } \right)^2}[/imath] you see the term [imath]6x^7[/imath] SEE HERE
The coefficient six tell us that there are six ways to roll a seven, the exponent.
Does that help?
[imath][/imath][imath][/imath]
 
thomasgolf said:
Help: I need the 6 whole numbers for a 2 dice roll. If the roll is 7 n=, 6 / 8 n=, 5 / 9 n=, 4 /10 n=, 3 / 11 n=, 2 /12 n=. The numbers will be used in a board game for point totals.
Click to expand...
Is this an assignment from your class - or a "game" simulation"?
 
thomasgolf said:
OK, a numerical example would be if you roll a 7 with 2 dice you would get 1 point vs if you roll a 2 you would get 6 points. So the problem is coming up with what 6 whole numbers best represent the 11 dice combinations.

/ is = to or
Click to expand...
I still can't tell which /'s are equal signs or OR signs.
You can use any symbol you like, but you need to define them!!!
I also would suggest that you do not use the same symbol to represent two things.
 
thomasgolf said:
OK, a numerical example would be if you roll a 7 with 2 dice you would get 1 point vs if you roll a 2 you would get 6 points. So the problem is coming up with what 6 whole numbers best represent the 11 dice combinations.

/ is = to or
Click to expand...
There is no "correct" answer. You have to decide what you want points to mean. What criteria do you have?

Possibly you want more points for a rarer result; or the nature of the game might imply some particular point values due to how they are used. And why should there be only 6 values?

thomasgolf said:
If the roll is 7 n=, 6 / 8 n=, 5 / 9 n=, 4 /10 n=, 3 / 11 n=, 2 /12 n=.
Click to expand...
Can you explain in English what this means? Your reply doesn't seem to express the same ideas. (It's generally not a good idea to use symbols if you aren't sure the reader will interpret them as you intend.)

I'm starting to see what you may have meant, though: You want one point value for a roll of 7; another for a roll of 6 or 8; another for a roll of 5 or 9; and so on. This implies that you are aware that the probability of 6 or of 8 is the same, and explains why you want 6 numbers. If all you want is a higher point value for a rarer roll, you could just use 1, 2, 3, 4, 5, 6 respectively; but I suspect there is more to it than that.
 
Help: I need the 6 whole numbers for a 2 dice roll.
If the roll is 7 n=,
roll a 6 or a 8 n=,
roll a 5 or a 9 n=,
roll a 4 or a 10 n=,
roll a 3 or a 11 n=,
roll a 2 or a 12 n=. The numbers will be used in a board game for point totals.
 
thomasgolf said:
Help: I need the 6 whole numbers for a 2 dice roll.
If the roll is 7 n=,
roll a 6 or a 8 n=,
roll a 5 or a 9 n=,
roll a 4 or a 10 n=,
roll a 3 or a 11 n=,
roll a 2 or a 12 n=. The numbers will be used in a board game for point totals.
Click to expand...
How many ways can you roll a 7 with 2 dice?

How many ways can you roll a 6 with 2 dice?
How many ways can you roll a 8 with 2 dice?
.
.
.
How many ways can you roll a 2 with 2 dice?
How many ways can you roll a 12 with 2 dice?
 
Subhotosh Khan said:
How many ways can you roll a 7 with 2 dice?

How many ways can you roll a 6 with 2 dice?
How many ways can you roll a 8 with 2 dice?
How many ways can you roll a 2 with 2 dice?
How many ways can you roll a 12 with 2 dice?
Click to expand...
Mr. Khan, that was my guess also. Hence my reply in #6.
Now I am left to conclude that Thomas is a non-English speaker or else a troll.
 
thomasgolf said:
Help: I need the 6 whole numbers for a 2 dice roll.
If the roll is 7 n=,
roll a 6 or a 8 n=,
roll a 5 or a 9 n=,
roll a 4 or a 10 n=,
roll a 3 or a 11 n=,
roll a 2 or a 12 n=. The numbers will be used in a board game for point totals.
Click to expand...
Okay. I have no idea what the game is or the purpose of it but if you want an answer without giving us more information then
If the roll is 7 n= 1
roll a 6 or a 8 n= 2
roll a 5 or a 9 n= 3
roll a 4 or a 10 n= 4
roll a 3 or a 11 n= 5
roll a 2 or a 12 n= 6

-Dan
 
pka said:
Mr. Khan, that was my guess also. Hence my reply in #6.
Now I am left to conclude that Thomas is a non-English speaker or else a troll.
Click to expand...
Actually, I formulated my questions after reading response (and going "o-h-h-").....
 
Using 1 through 6 seems less than precise when the odds are:
roll a 2 are 2.78%
3 are 5.56%
4 are 8.33%
5 are 11.11%
6 are 13.89%
7 are 16.67%
8 are 13.89%
9 are 11.11%
10 are 8.33%
11 are 5.56%
12 are 2.78%
 
thomasgolf said:
Using 1 through 6 seems less than precise when the odds are:
roll a 2 are 2.78%
3 are 5.56%
4 are 8.33%
5 are 11.11%
6 are 13.89%
7 are 16.67%
8 are 13.89%
9 are 11.11%
10 are 8.33%
11 are 5.56%
12 are 2.78%
Click to expand...
You have given the probability of each roll and not the odds.
For example: the probability [imath]n=5[/imath] is [imath]11.\overline{~11~}[/imath]
while the odds of [imath]n=5[/imath] are [imath]12.5[/imath].
 
thomasgolf said:
Using 1 through 6 seems less than precise when the odds are:
roll a 2 are 2.78%
3 are 5.56%
4 are 8.33%
5 are 11.11%
6 are 13.89%
7 are 16.67%
8 are 13.89%
9 are 11.11%
10 are 8.33%
11 are 5.56%
12 are 2.78%
Click to expand...
The unanswered question is, on what grounds do you want to assign point values? What is the goal? The word "precise" is meaningless without that. Points are used in different ways in different games.

Whether you calculated or looked up these probabilities (technically, they aren't "odds"), they don't help us until you answer that question. The probabilities, stated exactly as fractions, are 1/36, 2/36, 3/36, 4/36, 5/36, 6/36.

For example, it is possible that you want the score to be inversely proportional to the probability (though I'm not sure how that would be appropriate). In that case, you are looking for whole numbers that are (exactly? approximately?) proportional to the reciprocals of those numbers, namely 36/1 = 36, 36/2 = 18, 36/3 = 12, 36/4 = 9, 36/5 = 7.2, and 36/6 = 6. If you want it exact, you could multiply each of these numbers by 5 to get whole numbers.

But you have to tell us what you are trying to accomplish by your choice of point values; we can't tell you that.
 
OK, I understand.
Using 1 through 6 seems less than precise when the probability is:
roll a 2 are 2.78%
3 are 5.56%
4 are 8.33%
5 are 11.11%
6 are 13.89%
7 are 16.67%
8 are 13.89%
9 are 11.11%
10 are 8.33%
11 are 5.56%
 
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