Sort of OT: Dice odds  Printable Version + HP Forums (https://archived.hpcalc.org/museumforum) + Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum1.html) + Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum2.html) + Thread: Sort of OT: Dice odds (/thread194469.html) 
Sort of OT: Dice odds  Dave Britten  09122011 I'm already familiar with calculating the odds of getting a certain number of specific individual results when rolling an arbitrary number of dice (simple binomial distribution). But a fair amount of Google searching and working out numbers by hand hasn't led me to a general formula for calculating the odds of getting a certain total when rolling an arbitrary number of dice. (e.g. What are the odds of rolling a total of 17 or greater using four standard 6sided dice?) This looks like some form of binomial expansion, but I'm drawing a blank putting it all together.
And I can always post a 15c implementation of the calculation, since that's the hot topic at the moment. ;)
Re: Sort of OT: Dice odds  M. Joury  09122011 Try this page: Chance of total with 'x' dice From the above page: This section endeavors to answer the frequently asked question on the probability for any given total over the throw of multiple dice. ... My method was a recursive computer program. No, I don't know of an easy nonrecursive formula. Hope this helps. Cheers,
Marwan
Re: Sort of OT: Dice odds  Dave Britten  09122011 I was afraid I might have to resort to that. Now, to really complicate things, I also want to be able to do this with nonstandard dice. For example, a 6sided die with faces reading 0, 0, 0, 1, 1, 2, or something like that, and maybe even mixtures of different dice. I'll have to see how far I can take this on the 15c LE when it shows up, though honestly I think this would be easiest to implement with SQL and liberal use of cross joins.
Re: Sort of OT: Dice odds  M. Joury  09122011 SQL? If you end up going that route I would love to see how you do it. Although I would not consider myself a SQL programmer (C, C++, C#) I do program SQL on a regular basis for my job and solving this using SQL would never (never did) even occur to me! Cheers,
Marwan
Re: Sort of OT: Dice odds  Egan Ford  09122011 This smells of Project Euler. I'm afraid you are going to have to tough it out like the rest of us have. :)
Re: Sort of OT: Dice odds  Dave Britten  09122011 Ha ha, I was wondering if there might have been one on there like that. I should check my Project Euler source code and see if I solved it and forgot about it.
Actually, I'm more interested in game play and/or design at the moment, and figuring these things out mathematically could come in handy.
Re: Sort of OT: Dice odds  Dave Britten  09122011 Sure, here's what I slopped together for SQL Server (I'm assuming you have access to that, with C# background). The memory/CPU usage gets really out of hand with a large number of dice. Doing 7 sixsided dice takes about 10 seconds on an 8core server with 32 GB RAM. But you can mix and match types of dice, and do nonstandard dice. http://dave.brittens.org/Dice.sql You'll also need to have my string split function in the current database.
http://dave.brittens.org/fn_split.sql
Re: Sort of OT: Dice odds  M. Joury  09122011 Thanks Dave!
Re: Sort of OT: Dice odds  Thomas Klemm  09122011 Quote: There's a function glob in Perl that does the cross joins. For example, this produces nine strings, one for each pairing of fruits and colors: @many = glob "{apple,tomato,cherry}={green,yellow,red}";
That's the program I came up with: #!/usr/bin/perl And that's the result it produces when the script is started with time:
4 1 I hope it is useful and you can modify it to your needs. It's not optimized for speed (the function eval is used often), but for small n it might be fast enough.
Kind regards
Edited: 12 Sept 2011, 5:14 p.m.
Re: Sort of OT: Dice odds  Kiyoshi Akima  09132011 Here's an unoptimized, bruteforce implementation on the 15C:
001 . 012 LBL 3 023 ISG 0 It runs in just under ten seconds on my HHC2010 15C+. It did take a little longer to key it in on the fly...
All sorts of time optimizations are possible. For example, if you total up the first three dice, you can immediately calculate the number of ways the fourth die would push the total to 17 or above, eliminating the fourth loop.
