Re: Re: check my logic & a random number issue

[Daruma]

Greetings!!

PPS: FWIW in the interests of not installing more stuff, my roll function came out to be:

sub rolldice()
{
        my $roll = int(rand(12)) + 1;
        return $roll;
}

After reading your node, jarich, I began wondering how different Math::Random, int(rand(6)) and int(rand(12)) might be... I noted your suggested rolldice() subroutine quoted above. To appropriately spread the roll result to mimic a table craps game, there should be a curve peaking at seven. I decided to slap together a quick test...

#!c:\perl\bin\perl.exe

use strict;
use warnings;
use diagnostics;
use Math::Random;

my $num_rolls = 10000;

my @rollhashes;
for (my $i=0; $i<4; $i++) {
  $rollhashes[$i] = { 2 => 0, 3 => 0, 4 => 0, 5 => 0, 6 => 0,
         7 => 0, 8 => 0, 9 => 0, 10 => 0, 11 => 0, 12 => 0
        };
}

for (1 .. $num_rolls) {
  my $m1 = random_uniform_integer(1,1,6);
  my $m2 = random_uniform_integer(1,1,6);
  my $math =  $m1 + $m2;
  $rollhashes[2]{$math}++;

  my $m0 = random_uniform_integer(2,1,12);
  $rollhashes[0]{$m0}++;

  my $r1 = (int(rand(6) + 1));
  my $r2 = (int(rand(6) + 1));
  my $rand = $r1 + $r2;
  $rollhashes[3]{$rand}++;

  my $r0 = (int(rand(12) + 2));
  $rollhashes[1]{$r0}++;
}

print "\nUSING TWO DICE:\n";
print "\nMath::Random\t\tint(rand)\n";
for (my $i = 2; $i <= 12; $i++) {
  my $n = sprintf("%02d",$i);
  print "$n = $rollhashes[2]{$i}\t\t$n = $rollhashes[3]{$i}\n";
}

print "\nUSING ONE DIE:\n";
print "\nMath::Random\t\tint(rand)\n";
for (my $i = 2; $i <= 12; $i++) {
  my $n = sprintf("%02d",$i);
  print "$n = $rollhashes[0]{$i}\t\t$n = $rollhashes[1]{$i}\n";
}

And here is the output:

USING TWO DICE:

Math::Random            int(rand)
02 = 271                02 = 270
03 = 533                03 = 606
04 = 876                04 = 849
05 = 1129               05 = 1172
06 = 1364               06 = 1362
07 = 1640               07 = 1632
08 = 1390               08 = 1402
09 = 1101               09 = 1079
10 = 876                10 = 838
11 = 540                11 = 535
12 = 280                12 = 255

USING ONE DIE:

Math::Random            int(rand)
02 = 862                02 = 852
03 = 853                03 = 835
04 = 795                04 = 865
05 = 849                05 = 876
06 = 817                06 = 772
07 = 801                07 = 836
08 = 822                08 = 801
09 = 809                09 = 814
10 = 856                10 = 821
11 = 891                11 = 841
12 = 823                12 = 848

So, using one die rather than two has a tremendous impact on the spread of the numbers! Additionally, I noted that the differences between using Math::Random and int(rand(6)) were fairly slight. After running the above code over numerous tests, I found them to be quite comparable. In the interest of not installing more than is necessary, I would go with the int(rand(6)) rather than slurping in the Math::Random goodies.

Craps is my favorite Vegas game... I find it to be the most fun and exciting of all the games I've tried. (Probably more fun than it should be!)

-Daruma

Update: formatting changes and fixed reference to jarich's rand(12) usage... Thanks, jarich!!
Update2:Reworked my unnecessarily long code with a few loops...

[jarich]

You're quite right. When you use a single dice (twelve sided) the probability of getting any number (1 to 12 inclusive) is just 1/12. When you use two dices of 6 sides each the probability of each number is markedly different.

Value      Probability      Combinations
   1            0
   2           1/36            1:1
   3           2/36            1:2, 2:1
   4           3/36            1:3, 2:2, 3,1    
   5           4/36            1:4, 2:3, 3:2, 4:1
   6           5/36            1:5, 2:4, 3:3, 4:2, 5:1
   7           6/36            1:6, 2:5, 3:4, 4:3, 5:2, 6:1
   8           5/36            2:6, 3:5, 4:4, 5:3, 6:2
   9           4/36            3:6, 4:5, 5:4, 6:3
  10           3/36            4:6, 5:5, 6:4
  11           2/36            5:6, 6:5
  12           1/36            6:6

Of course, if you're not using a truely random or very, very convincing pseudo-random generator you probably won't quite get these probabilities.

Considering that 7 is a bad number to get in Craps, it'd be nicer to use just a 12 sided dice, but then the Casinos would have to rig the game another way to get their money. ;)

It's good to know that for this kind of example rand() is as good as Math::Random.

jarich

[rmckillen]

If you look at the dice rolls that generate these losses you'll find that they're all different.

Jarich: I think that explains the issue I was seeing. You can lose with a craps roll on the come out roll, and then win the next round with a winning odds bet on a 6 OR a winning odds bet on an 8, and the net win will still be the same. Basically different roll combinations are likely to yield the same net win/loss result. I'm sure I'll find some to be fairly common.

Daruma: Thanks for putting up the results of Math::Random vs. int(rand). When you look at the probabilities of the various outcomes, and compare them with the actual real-life probabilities, although they both have fairly normal distributions, the Math::Random yields a better result.

Math::Random                int(rand)        
roll    occ    prob        roll    occ    prob
2    271    2.71%        2    270    2.70%
3    533    5.33%        3    606    6.06%
4    876    8.76%        4    849    8.49%
5    1129    11.29%        5    1172    11.72%
6    1364    13.64%        6    1362    13.62%
7    1640    16.40%        7    1632    16.32%
8    1390    13.90%        8    1402    14.02%
9    1101    11.01%        9    1079    10.79%
10    876    8.76%        10    838    8.38%
11    540    5.40%        11    535    5.35%
12    280    2.80%        12    255    2.55%

real life    
roll    prob
1    2.78%
3    5.56%
4    8.33%
5    11.11%
6    13.89%
7    16.67%
8    13.89%
9    11.11%
10    8.33%
11    5.56%
12    2.78%

Thanks for all the help so far. Now I guess it comes down to a random number issue. Are there any perl modules, or different techniques I can use to get the rolls as random and close to real-life as possible, or is Math::Random likely as good as it will get?

Thanks for the continued help!