OT: Home Sick for the Holidays, or Probability and Yahtzee

[Kamog]

OK, I did some more searching around and discovered that Excel can, in fact, do this calculation.

There is a handy pre-built function called BINOMDIST(number_s, trials, probability, cumulative).
Now this is easy.

The probability of getting 182 or more 6's in 1000 rolls is:
P = 1 - BINOMDIST(181, 1000, 1/6, TRUE)
P = 0.105008

I needed to subtract from 1 because the cumulative function adds from 0 to 181. To get the portion for 182 and above, we subtract from the whole (1) the part we don't want, the stuff at 181 and below.

OK, so there's about a 10.5% chance of getting 182 or more.

The probability of getting 326 or more 6's in 1000 rolls is:

P = 1 - BINOMDIST(325, 1000, 1/6, TRUE)
P = -0.5.08482E-14

Obviously there's something wrong. The answer can't be negative. I think Excel still can't handle this kind of big / small number.

Does anybody have a better program and/or calculation method that can do this? Or am I doing something wrong?

[David E. Gervais]

Originally posted by spoon:
I plugged those numbers into a RISK calculator... odds of you winning were 0.99999978. That's some streak of luck!

I remember he was defending with 2 dice and I was attacking with 3. I vividly remember when I rolled 3 six's and expected certain victory but he rolled boxcars to counter my attack. I really don't want to know the odds on that happening.

When people say there is no such thing as luck, I don't believe them. I have faced luck and lost too many times playing RISK. LOL

Cheers!

[Krsqk]

Obviously there's something wrong. The answer can't be negative. I think Excel still can't handle this kind of big / small number.

I think that's because 1000! comes out to...

4.02387260077093773543702433923e+2567

Anyone want to put a name to that number?

The BINOMDIST function (with the TRUE parameter) gave me values steadily approaching 1 all the way up to 167, at which point Excel decided they were close enough to round to 1 (when I subtracted them from 1, the values were things like .1E-77 and the like). The odds of having no more than 167 sixes when rolling 1000 dice shouldn't be ~100%, should it?

The problem apparently occurs at 260 successes. The function calculates that the probability of having no more than 260 successes is slightly more than 1. This may be due to the rounding limitations of this function.

[ December 27, 2003, 21:46: Message edited by: Krsqk ]

[Kamog]

Since Excel can't handle 1000 events in the calculations, I have settled for something less ambitious.
I calculated the probability for each of the results for the 100 dice rolls for David and Claude.

The numbers are cumulative, so for example the first entry means that there's a 80% chance of getting 14 or more 6's out of 100 dice rolls.

code:

---

David	Probability	Odds		        Claude	Probability	Odds

14	0.7999947521	1 in 1.25		34	0.0000190716	1 in 52434

12	0.9222807788	1 in 1.1		32	0.0001238040	1 in 8077

17	0.5058410243	1 in 2.0		35	0.0000070251	1 in 142347

20	0.2197498431	1 in 4.6		37	0.0000008412	1 in 1188738

17	0.5058410243	1 in 2.0		28	0.0031013887	1 in 322

16	0.6123424483	1 in 1.6		31	0.0002957849	1 in 3381

21	0.1518878479	1 in 6.6		36	0.0000024818	1 in 402926

32	0.0001238040	1 in 8077		27	0.0062087189	1 in 161

18	0.4005925583	1 in 2.5		33	0.0000496373	1 in 20146

15	0.7125790826	1 in 1.4		33	0.0000496373	1 in 20146

---

From this, it appears that what Claude did is very, very, improbable!

[Gryphin]

I had a friend who played miniatures who said:
"I rather be lucky than good any day"

[Kamog]

Claude should play SE4. He'll beat your fleet of 50 dreadnaughts using 3 escorts armed with DUC's.

[David E. Gervais]

I just think my friend Claude's karma is dice based while mine is pixel based. This would explain why I'm good at computers and he is good at dice.

with this anaolgy, what kind of karma would you all say you have? (you must all be good at something. )

Cheers!