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Post subject: WAS probability calculator - possibly another bug
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G'day all,
I just had a go at calculating the probability of x hits (4&5 = 1 hit, 6=2 hits) for 7d6 and then compared it to the AAForuMINI calculator and came up with teh below:
Rolls* Total Hits Prob 7d6 aaForumMini
7831 0 0.8% 99.95%
36617 1 3.7% 99.22% 99.22%
90761 2 9.1% 95.56% 99.32%
153959 3 15.4% 86.48% 95.49%
194169 4 19.4% 71.08% 82.72%
190425 5 19.0% 51.67% 57.40%
150029 6 15.0% 32.62% 26.40%
96038 7 9.6% 17.62% 5.87%
49411 8 4.9% 8.02%
21075 9 2.1% 3.08%
7338 10 0.7% 0.97%
1896 11 0.2% 0.23%
400 12 0.0% 0.05%
41 13 0.0% 0.01%
10 14 0.0% 0.00%
1000000 Total 100.0%
I know that the web site calculator doesn't work for more hits that dice - but teh above probabilities are so different that either I'm wildly wrong (not unknown) or there may be a another bug in teh web calculator.
Comments?
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all the best
David |
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 Fri Jun 19, 2009 3:43 am |
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SOCCEROO FEVER
Posts: 6808
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i hate maths
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| Fri Jun 19, 2009 3:48 am |
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Posts: 9282
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Let's check for one of your examples
prob(successes>=2) = 1 - (prob successes = 1) - prob (successes = 0) = 1- 0.5^7 - 1/3*7*(0.5^6) = 95.57%
So, your computations are correct.
Still, you computed them numerically with 1 million iterations, which isn't practical on the web. The prob. calculator uses the binomial distribution formulas with the assumption that the prob of success for one dice is the expected number of successes per dice (4/6). That's why inaccuracies are introduced in some cases, especially when there is the same number of successes as rolls.
I wouldn't mind changing the code of the prob. calculator if someone wrote it in a better way.
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My new blog, specialised in the military equipment of Greece (1821-today). |
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| Fri Jun 19, 2009 6:46 am |
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Posts: 110
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G'day all,
What about a lookup table?
(instead of a coded calculation)
True it would be best to actually calculate the underlying numbers (rather than my lazy generated numbers).
Notting that I have absolutely no idea about setting up functions in web pages (I can barely navigate them!).
In the interum I can post three table based on 50K replicants that at least give an idea of the probability of more successes than dice... (4-6, 5-6 and 6) anyone interested? (Would it be better as an excel email attachment to an administrator?)
| NeuralDream wrote: | Let's check for one of your examples
prob(successes>=2) = 1 - (prob successes = 1) - prob (successes = 0) = 1- 0.5^7 - 1/3*7*(0.5^6) = 95.57%
So, your computations are correct.
Still, you computed them numerically with 1 million iterations, which isn't practical on the web. The prob. calculator uses the binomial distribution formulas with the assumption that the prob of success for one dice is the expected number of successes per dice (4/6). That's why inaccuracies are introduced in some cases, especially when there is the same number of successes as rolls.
I wouldn't mind changing the code of the prob. calculator if someone wrote it in a better way. |
_________________
all the best
David |
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| Fri Jun 19, 2009 7:29 am |
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Posts: 9282
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You can use the "attach file" option when you post a reply here.
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My new blog, specialised in the military equipment of Greece (1821-today). |
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| Fri Jun 19, 2009 8:01 am |
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Why is the rum always gone?
Posts: 237
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See my new post on WaS Tables.
They're built and ready for prime-time!
Cheers...
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| Fri Jun 19, 2009 4:28 pm |
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