Stats with random numbers - algorithm

Question

I want to create 7 stats for a character, randomly generating a value from 3-21, with the stat's sum being no higher than 91. I've tried arranging the stats into an array, and just going through them like this:
1) add random(15) to each array member
2) computing the total, subtracting from the 91 maximum
3) dividing this difference by 7
4) do step 1 with random(difference) adding it to the stat
5) Until I hit the 91 total.
Doing this a few hundred times I seem to get a curve where the 5,6, and 7th stats tend to be higher. And sometimes I hit the 4 or 5th stat and there are no more numbers to be added, meaning then that the first few stats get the most points. I think I am approaching this the wrong way to begin with. Any ideas? I have tunnel vision at this point I think.

Answer 1

It sounds like you're overthinking this. I might do something like this :
const
STAT_QTY = 7;
STATSUM_MAX = 91;
STAT_MIN = 3;
STAT_MAX = 21;
type
TStatArray = Array [0..STAT_QTY-1] of integer;
Then in implementation :
function GenerateStats : TStatArray;
var statArr : TStatArray;
i, statSum, excess, debit : integer;
done : boolean;
begin
Randomize;
done := false;
while not done do begin
done := true;
statSum := 0;
for i := 0 to STAT_QTY - 1 do begin
statArr[i] := STAT_MIN + Random(STAT_MAX - STAT_MIN);
statSum := statSum + statArr[i];
end;
if statSum > STATSUM_MAX then begin
excess := statSum - STATSUM_MAX;
debit := excess div STAT_QTY + 1;
for i := 0 to STAT_QTY -1 do begin
statArr[i] := statArr[i] - debit;
end;
end;
for i := 0 to STAT_QTY -1 do begin
if statArr[i] < STAT_MIN then done := false;
end;
end;
result := statArr;
end;
This generates a list of random stats in the range 3-21. If the sum is more than 91 then divide the excess by the number of stats (use div then round up the answer) and subtract an equal number from each. In the rare case that you end up with stats less than three, just do it again. Job done.
Tested over 2000 iterations I get average stats of :
[1] : 11.13893053
[2] : 11.15692154
[3] : 11.16141929
[4] : 11.11444278
[5] : 11.10194903
[6] : 10.9800100
[7] : 10.86856572
That's a total average of 11.07 with a standard deviation of 0.11 - certainly about what one would expect from a generally random set with your construction parameters.

Answer 2

Here's C-ish pseudo code for a slightly different approach, assuming a suitable random(N) function that returns numbers in the range 0 - N-1.
int stats[7], deficit = 70;
for (int i = 0; i < 7; ++i)
stats[i] = 3; // initial assignments of the minimum to each stat
while (deficit)
{ int tmp = random(7); // pick a random stat to bump
if (stats[tmp] == 21) // but not if it's already at max
continue;
++stats[tmp];
--deficit;
}
Assuming your random() is uniformly distributed, that should give pretty good results.