tag:blogger.com,1999:blog-5179649506981851979.post2371815533776750401..comments2024-01-14T05:19:08.074-06:00Comments on Troll and Flame: Hackmaster / Exploding Dice AnalysisNorman J. Harman Jr.http://www.blogger.com/profile/01319655075997712313noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-5179649506981851979.post-42525821242973658772024-01-14T04:40:09.536-06:002024-01-14T04:40:09.536-06:00The average roll for an exploding n-sided die (wit...The average roll for an exploding n-sided die (with n>1) is n/(n-1) + n/2. I reduced the problem to an infinite series and reduced it using Wolfram Alpha. Paul Asa Burchetthttps://independent.academia.edu/PaulBurchettnoreply@blogger.comtag:blogger.com,1999:blog-5179649506981851979.post-7078343478816361822024-01-14T04:36:50.827-06:002024-01-14T04:36:50.827-06:00The closed formula for the average roll on an n-si...The closed formula for the average roll on an n-sided exploding die is n/(n-1) + n/2. I reduced the problem to an infinite series and then put the series into Wolfram Alpha. This assumes of course that n>1.Paul A Burchetthttps://independent.academia.edu/PaulBurchettnoreply@blogger.comtag:blogger.com,1999:blog-5179649506981851979.post-60365356891824300742014-04-14T16:37:07.157-05:002014-04-14T16:37:07.157-05:00@dither I don't think it's worth it / neve...@dither I don't think it's worth it / never bother having players subtract 1 from exploded dice in *my houserules*. But, HackMaster / Kenzer & Co are sticklers for accuracy and what they think of as "realism". So, running HM I do the -1.<br /><br />btw the average increases by much less than 1. 'p'enetration dice are math correct (subtract 1), 'x'ploding dice don't subtract 1<br /><br />d4p 3.00 27<br />d6p 3.99 25<br />d8p 5.05 35<br />d12p 6.97 55<br />d20p 10.68 38<br />d100p 50.10 135<br /><br />d4x 3.34 30<br />d6x 4.18 35<br />d8x 5.15 36<br />d12x 7.07 55<br />d20x 11.14 72<br />d100x 51.32 243Norman J. Harman Jr.https://www.blogger.com/profile/01319655075997712313noreply@blogger.comtag:blogger.com,1999:blog-5179649506981851979.post-23834046927775264112014-04-14T16:15:50.897-05:002014-04-14T16:15:50.897-05:00I've been looking for information on the math ...I've been looking for information on the math of exploding dice from Hackmaster and this post was very informative, thanks! I have a question about the math for exploding versus penetrating dice, which was mentioned in an above comment.<br /><br />I understand the desire for a flatter range of damage values (the d4-1 penetrating) and I would assume that without that, the change in average damage from using exploding dice increases from 0.5 to 1.5.<br /><br />Given bonuses from classes, feats, ability scores, and whathaveyou, the "missing" numbers from the range of potential damage results seems... "trifling?" I realize that means without the -1 you would never actually deal 6 damage from rolling a d6, but is that really worth the conflation of addition and subtraction when determining damage?<br /><br />Thanks!<br />--Ditherditherhttps://www.blogger.com/profile/16636135891319380870noreply@blogger.comtag:blogger.com,1999:blog-5179649506981851979.post-43725314633024513862009-10-29T04:39:56.073-05:002009-10-29T04:39:56.073-05:00> Man, that's some in-depth analysis!
Ah, ...> Man, that's some in-depth analysis!<br /><br />Ah, actually that was just a quick knock-off. Was curious about effect of shield/armor/weapon and how it seemed it was foolish to ever use two-handed weapon over sword and board. So, I made a HackMaster Basic Combat simulator. The summary output of a couple matchups is below. Detailed output is more... I'm not too much of a nerd am I?<br /><br /><br />Fight Silent<br />The Dude(33) in scalemail with longsword and medium shield<br /> vs<br />Hammertime(33) in scalemail with warhammer and medium shield<br /><br />The Dude 598(59.8%) wins(48.7% by death, 51.3% by ko), killed 173 and ko'd 229 times. hit/miss: 2725/2331 (53.9%), 231/48hp crits/max, 202/277 a/d fumbles, 270/215 p/n defences, 229/0/60 k/r/l<br /><br />Hammertime 402(40.2%) wins(43.0% by death, 57.0% by ko), killed 291 and ko'd 307 times. hit/miss: 2912/2660 (52.3%), 262/39hp crits/max, 267/251 a/d fumbles, 241/213 p/n defences, 308/0/60 k/r/l<br /><br /><br /><br />Fight Silent<br />The Dude(33) in scalemail with longsword and medium shield<br /> vs<br />Compensator(33) in scalemail with two-handsword and no shield<br /><br />The Dude 540(54.0%) wins(46.7% by death, 53.3% by ko), killed 146 and ko'd 314 times. hit/miss: 2824/386 (88.0%), 159/44hp crits/max, 74/109 a/d fumbles, 105/80 p/n defences, 318/0/60 k/r/l<br /><br />Compensator 460(46.0%) wins(31.7% by death, 68.3% by ko), killed 252 and ko'd 288 times. hit/miss: 1196/994 (54.6%), 109/68hp crits/max, 89/164 a/d fumbles, 82/57 p/n defences, 290/0/60 k/r/lNorman J. Harman Jr.https://www.blogger.com/profile/01319655075997712313noreply@blogger.comtag:blogger.com,1999:blog-5179649506981851979.post-60494007700039490032009-10-29T00:54:09.351-05:002009-10-29T00:54:09.351-05:00Man, that's some in-depth analysis!
Thanks fo...Man, that's some in-depth analysis!<br /><br />Thanks for sharing!Aaron E. Steelehttps://www.blogger.com/profile/07789462075611254929noreply@blogger.comtag:blogger.com,1999:blog-5179649506981851979.post-53674715201990794412009-10-28T14:35:04.897-05:002009-10-28T14:35:04.897-05:00That's really cool. I have been thinking about...That's really cool. I have been thinking about grabbing this. I will have to nowrmckee78http://darjanix.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-5179649506981851979.post-14308674887155349442009-10-28T12:21:06.333-05:002009-10-28T12:21:06.333-05:00The d4, then d4-1 used to be the mechanic for grev...The d4, then d4-1 used to be the mechanic for grevious wounds in hackmaster as I recall, don't know about currently.Zzarchovhttps://www.blogger.com/profile/07714805545939725730noreply@blogger.comtag:blogger.com,1999:blog-5179649506981851979.post-87383475094628911562009-10-28T12:12:54.469-05:002009-10-28T12:12:54.469-05:00@mckee78
Be satisfied! Hackmaster penetrating di...@mckee78 <br />Be satisfied! Hackmaster penetrating die is indeed dX-1. d4p possible values are 1,2,3,4,5,...<br /><br />The program is doing actual rolls with pseuudorandom generator so numbers won't always add up exactly.<br /><br /><br />@zzarchov<br />Interesting alternative.Norman J. Harman Jr.https://www.blogger.com/profile/01319655075997712313noreply@blogger.comtag:blogger.com,1999:blog-5179649506981851979.post-59874014465806045222009-10-28T11:52:21.422-05:002009-10-28T11:52:21.422-05:00I have a question, and I am sure this comes out of...I have a question, and I am sure this comes out of ignorance of how Hackmaster's exploding dice work on my part, how do you get any result of 4 on a 1d4 (or 6 on a 1d6 etc.)? If I am understanding it correctly, if you roll a 4 you roll again and add the second die in. So your set of possible numbers would be {1,2,3,5...}. <br /><br />Initially I thought that your program was counting the die roll of 4 and then also counting the final tally after the reroll. But when I added up your numbers I got 100.2%, which is clearly within the rounding error introduced by having only 2 decimal places. <br /><br />The only way I could see for those results to be possible would be for the secod die roll to be a 1d4-1 that allows for a 0 result. This would allow for the results you got. I have only played the game once at GenCon along with a million other demos so I have no idea if that is true. <br /><br />As an engineer I would find the idea of rolling 1d4-1 on the second die pretty satisfying because it keeps there from being a gap in the original die's range. However this kind of thought is not something you see often in an RPG's mechanics. The trade off is that for many people this will mechanically be a pain in the butt. Is it possible that Kenzer and Co. is actually filled with non-English majors?rmckee78http://darjanix.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-5179649506981851979.post-77476620845778077392009-10-28T11:37:46.002-05:002009-10-28T11:37:46.002-05:00That is some hardcore math. One of the reasons I ...That is some hardcore math. One of the reasons I like Hackmaster, and likewise one of the reasons I'd not want to play it (or at least, run it - maybe I'd play it with a good GM).Jack Badelairehttps://www.blogger.com/profile/10932441028544500024noreply@blogger.comtag:blogger.com,1999:blog-5179649506981851979.post-1492468910720278662009-10-28T10:51:03.258-05:002009-10-28T10:51:03.258-05:00With fighters re-rolling damage I stick that to sp...With fighters re-rolling damage I stick that to specialization with a weapon. When combined with repeating dice, I count them as getting two rolls, not two rolls per "explosion".<br /><br />So if I roll 2d8, and get an 8 and a 4, I choose the 8 and roll it out (one die)<br /><br />If I roll double 8's, then I keep going with 2 more d8's until one of them (or both) stop exploding and pick the higher number.Zzarchovhttps://www.blogger.com/profile/07714805545939725730noreply@blogger.com