**Next message:**Mike Stilson: "Re: Dice Function"**Previous message:**Mythran: "Class Section Complete For coding.doc"**Next in thread:**Mike Stilson: "Re: Dice Function"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

On Sun, Jul 07, 2002 at 04:56:39AM -0700, Mythran wrote: > > The probability graph of 2-12 is different for "2d12" vs merely "2-12". > > Take a closer look at my post. You will see that it is not a disadvantage > at all.... > > 2d12 using the my dice() function has the same probability....it will not > return just 2-12. Let's evaluate the probabilities. For simplicity, we'll take a simple case, 2d3, which has 5 possible values: { 2, 3, 4, 5, 6 } There are only 5 values, but 9 possible rolls: { 1+1, 1+2, 1+3, 2+1, 2+2, 2+3, 3+1, 3+2, 3+3} This set evaluates to: { 2, 3, 4, 3, 4, 5, 4, 5, 6 } Now the probability matrix... { 2, 3, 4, 5, 6 } : { 1, 2, 3, 2, 1 } This means that out of 9 possible *equal* chances there is a 1:9 probability or rolling either a 2 or 6, 2:9 probability of rolling a 3 or 5 and 1:3 (or 3:9) probability of rolling a 4. Yes, when rolling evenly weighted 2d3 you are 3 times as likely to get a 4 as you are to get a 6. Your dice() function does not emulate this behavior because, among other things, you aren't generating enough random numbers: > int dice(int num, int size) > { > if (num <= 0 || size <= 0) > return (0); >· > return (number(num, num * size)); > } If we assume that the number() function has an even distribution, then your number(2, 2 * 3) would evaluate to an even (though discreet) gradient between 2 and 6 where there is an even probability of each. This is analagous to 1d5+1 which has the same range as 2d3 but *not* the same distribution. Rolling one die gets you (with a balanced die) even chances. Consider the uses of 1d20 in TSR games for saving throws, to-hit rolls, and the like. Rolling a 16 or better on 1d20 is a 25% chance, 17 or better is a 20% chance, 18 or better is 15%, 19 or better is 10% and 20 is 5% because you have a 5% chance of rolling any one value, always. Now compare to rolling 3d6 for ability scores. Similar range (3-18) but *totally* different distribution. There are 16 possible values but you have less than a 1% chance of rolling an 18 (or a 3) because it only comes from one possible combination (6+6+6) out of 216 (6^3). The middle values, 9-12, are each an order of magnitude more likely. This was chosen, as I understand, to simulate ability distribution in the typical population where half are average (9-12), a quarter are below (3-8) and a quarter are above (13-18). And the higher (or lower) the ability the less "common" it is. Rolling multiples of the same sized die results in what statisticians call the "normal distribution" (or "bell curve") and is used for modelling entirely different sets of characteristics than an even distribution. -- { IRL(Jeremy_Stanley); PGP(9E8DFF2E4F5995F8FEADDC5829ABF7441FB84657); SMTP(fungi@yuggoth.org); IRC(fungi@irc.yuggoth.org#ccl); ICQ(114362511); AIM(dreadazathoth); YAHOO(crawlingchaoslabs); FINGER(fungi@yuggoth.org); MUD(Nergel@mud.yuggoth.org:2325); WWW(http://fungi.yuggoth.org/); } -- +---------------------------------------------------------------+ | FAQ: http://qsilver.queensu.ca/~fletchra/Circle/list-faq.html | | Archives: http://post.queensu.ca/listserv/wwwarch/circle.html | | Newbie List: http://groups.yahoo.com/group/circle-newbies/ | +---------------------------------------------------------------+

**Next message:**Mike Stilson: "Re: Dice Function"**Previous message:**Mythran: "Class Section Complete For coding.doc"**Next in thread:**Mike Stilson: "Re: Dice Function"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

*
This archive was generated by hypermail 2b30
: 06/25/03 PDT
*