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

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
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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

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Re: Re: Re: Re: check my logic & a random number issue
by rmckillen (Novice) on Oct 11, 2002 at 17:21 UTC

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%
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Thanks for the continued help!

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