Re^3: Fractional dice (buckets)

averaging the results of 2 random floats yields what appears to be a parabolic distribution

I believe you are probably seeing a side effect of the pseudo-random sequence algorithm. If you add two (independent) uniform random distributions, you get a 'tent' distribution with straight sides. The results of adjacent calls to rand() are not as independent as one might hope.

Simulating the situation with increasingly fine buckets by using "dice" doesn't change the shape of the graph.

- tye

Comment on Re^3: Fractional dice (buckets)

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Re^4: Fractional dice (buckets) by Roy Johnson (Monsignor) on Jan 30, 2004 at 18:45 UTC
Mea culpa (again). The results from my original function are tent shaped, except the two extreme values are half as big as they would be expected to be. It's more likely the result of rounding slop on my part than it is an artifact of using random numbers. No such effects are seen when the function is this straightforward 2-dice method: `sub roll_dice { my ($low_end, $range) = @_; int(rand(int $range/2)) + int(rand(1 + $range - int $range/2)) + $lo +w_end; }` [download] And here's dice-rolling code generalized to let you choose a range and number of dice, and it will figure how many sides each die needs. (No fractional dice, here.) `sub roll_dice { my ($low_end, $range, $dice) = @_; my $sidesneeded = $range + $dice - 1; my $r = 0; for (0..$dice-1) { my $sides = int($sidesneeded / ($dice-$_)); $sidesneeded -= $sides; $r += int(rand $sides); } $low_end + $r; }` [download] The PerlMonk `tr///` Advocate	[reply] [d/l] [select]

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Re^4: Fractional dice (buckets)
by Roy Johnson (Monsignor) on Jan 30, 2004 at 18:45 UTC

It's more likely the result of rounding slop on my part than it is an artifact of using random numbers. No such effects are seen when the function is this straightforward 2-dice method:

sub roll_dice {
  my ($low_end, $range) = @_;
  int(rand(int $range/2)) + int(rand(1 + $range - int $range/2)) + $lo
+w_end;
}
[download]

sub roll_dice {
  my ($low_end, $range, $dice) = @_;
  my $sidesneeded = $range + $dice - 1;
  my $r = 0;
  for (0..$dice-1) {
    my $sides = int($sidesneeded / ($dice-$_));
    $sidesneeded -= $sides;
    $r += int(rand $sides);
  }
  $low_end + $r;
}
[download]

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