tag:blogger.com,1999:blog-2170237526012357403.post2127194755088477191..comments2024-03-15T11:16:44.045-04:00Comments on Delta's D&D Hotspot: Arena – Man vs. MonsterDeltahttp://www.blogger.com/profile/00705402326320853684noreply@blogger.comBlogger28125tag:blogger.com,1999:blog-2170237526012357403.post-86970702397480035832014-10-18T00:11:59.114-04:002014-10-18T00:11:59.114-04:00Thanks for posting! On that particular assessment ...Thanks for posting! On that particular assessment I actually come down on the other side of the issue, as I've written about in the past. <br /><br />To summarize the main points: (1) multiple D&D rulebooks explicitly state that Int × 10 = IQ; (2) there's no need for the fantasy population to have the same distribution (stdev) as the real world; (3) you otherwise miss several categories of real-world IQ deficiency; (4) you have problems converting D&D animal Ints of 1 or 2 to comparatively high IQs; (5) the classic D&D max Int of 18 likewise misses several categories of real-world high IQs.<br /><br /><a href="http://www.superdan.net/gaming/dnd3/dndmisc/int_iq.html" rel="nofollow">http://www.superdan.net/gaming/dnd3/dndmisc/int_iq.html</a>Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-81981392147523582422014-10-17T06:08:28.949-04:002014-10-17T06:08:28.949-04:00Slightly off topic, but mathematical, so hopefully...Slightly off topic, but mathematical, so hopefully you'll appreciate it.<br /><br />The often used mapping of Int onto IQ by multiplying by 10 does not match how IQ works. In IQ, the mean is 100, and the standard deviation is 15. The StdDev on 3d6 is approximately 3, so a much better mapping is to peg Int 10 at IQ 100, and then adjust up and down by 5 for every 1 Int.<br /><br />This means that your "drooling, barely aware" fighter actually has an IQ of 75, and a (wisdom quotient?) of 80. Not great, but hardly crippling (although as a fencer I'd say Int and Wis are probably far more useful, and strength is really only good for hacking through the thick hide or shell of a particularly tough enemy).<br /><br />Interestingly, this also means that the Int ranges of up to about 30 as seen in 3e much better resemble IQs seen in the real world.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-90707582074109155772014-09-04T10:48:05.324-04:002014-09-04T10:48:05.324-04:00I agree that "aging out" characters afte...I agree that "aging out" characters after a particular time is one of the things I think would be interesting to add to the simulation, if I get time and there's other people interested. I'm prone to possibly using what Gygax stipulated in the old Conan article; not simply death or minor ability-score losses, but steady loss of levels with advancing age. Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-42556343013748638852014-09-02T20:30:50.376-04:002014-09-02T20:30:50.376-04:00The additional monsters would keep the larger part...The additional monsters would keep the larger party size in check, but not completely negate its effect. Actually, the additional fighters may become a hindrance at higher levels, since they won't progress as quickly as the leader and replacements would be at a lower level than survivorsHolly Oatshttps://www.blogger.com/profile/01703437987958922954noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-30469131295071009322014-09-02T01:16:48.453-04:002014-09-02T01:16:48.453-04:00Yeah, going over it, I noticed some of that. That ...Yeah, going over it, I noticed some of that. That doesn't explain the 9th level drop (which occurs, though we don't yet have a clear idea of how much), though, and only partially explains why 11th and possibly 12th increases slightly over the previous level. The deep dive at 13 I imagine has to do with the maximum number of encounters that can occur and therefore the maximum amount of XP.<br /><br />It might be interesting to know the average "age" of characters at the various levels, by counting the number of encounters they engage in. Which brings up the idea of giving different SimFighters different numbers of encounters per year, and letting them go through a typical adventuring career of however many years, but I'm not sure that there's a simple way to do that, and even if there was a simple method to set the length of a "typical adventuring career", or to determine the distribution of average number of encounters per year.faoladhhttps://www.blogger.com/profile/03691952430041394614noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-16657852019554724692014-09-01T23:35:19.929-04:002014-09-01T23:35:19.929-04:00Glad it caught your interest! The simulation does ...Glad it caught your interest! The simulation does handle arbitrarily high level advancement (e.g., the run at a normal d6 roll produced some 16th-level fighters). Generally what happens is some fighters survive to higher levels, and can then reliably cruise along earning steady XP; the limit is however many cycles it runs (currently 200 combats). If we let it run more they'd achieve any level you like (e.g., the initial 2000-cycle run that produced 45th level fighters). <br /><br />Notice that if you compare those step ratios to the "monster determination" chart, they sort of track each other. Level 6 is conspicuous because it's the only tier that suddenly opens up a new monster level on 2 die pips (with -3 modifier max is 3; and either 2 or 3 reveals a level-5 monster, impossible at lower levels); so this sudden upsurge in difficulty would be expected to cut down the survival rate to a low level. Level 7 is the same tier, so once you survive 6th level, you won't see any new threats at 7th, and survival swings back up. So that coarseness in the encounters gets reflected here. Also effects of XP awards and increasing requirements play a role.<br />Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-70006551219641044322014-09-01T18:49:14.029-04:002014-09-01T18:49:14.029-04:00Looking at the -3 charts for the 100K and 1M runs,...Looking at the -3 charts for the 100K and 1M runs, I see the following correlations:<br /><br />Level 100K 1M<br />2 18% 17%<br />3 31% 30%<br />4 29% 28%<br />5 69% 71%<br />6 52% 50%<br />7 88% 91%<br />8 85% 83%<br />9 68% 77%<br />10 86% 85%<br />11 101% 101%<br />12 101% 87%<br />13 3% 4%<br /><br />So, I think I am most concerned about the big variations at 9th and 12th levels, but more importantly why the numbers go up and down so reliably. That isn't simple variation due to sampling error, that's consistency (except for 9th and 12th levels, which I expect are due to sampling error, which might be smoothed away by further runs to increase the sample size).faoladhhttps://www.blogger.com/profile/03691952430041394614noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-37698550052237912652014-09-01T18:38:22.561-04:002014-09-01T18:38:22.561-04:00Wait, where am I? Oh, sorry, I forgot for a minute...Wait, where am I? Oh, sorry, I forgot for a minute! This is Delta D&D, which has its own precise methods. The numbers should generally hold for other D&Ds, of course.<br /><br />I see that there is a general upward trend in the ratios, but I am trying to account for the fluctuations. With a sample size that large, it seems as though it should be smoother, rather than jumping around like it does (why 91% at 7th level? Or, for that matter, 50% at 6th?) Then I notice that the trend sort of plateaus from 7th through 12th level, jumping around 89%±12%. I want to understand why it does that. (I am currently assuming that the sudden drop at 13th level is due to other factors related to the simulation parameters. Does the simulation allow for higher levels and none of the SimFighters make it, or is that a hard cutoff?) I figure that, by understanding why the simulation gives the sort of results it does for Fighting Men, we can work out roughly what the other classes should look like, even if we can't simulate them for various reasons, taking into account their varying experience point charts and abilities.<br /><br />No problem! As you can probably tell, this subject interests me considerably.faoladhhttps://www.blogger.com/profile/03691952430041394614noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-50333717736599658892014-09-01T02:09:45.709-04:002014-09-01T02:09:45.709-04:00Yeah, the simulation already includes the +1 per l...Yeah, the simulation already includes the +1 per level increment to-hit. It doesn't include any extra attacks for these fighters. <br /><br />My guess is around level 10-11 then mean Constitution is right around 14.5, and one or the other in this run happened to come out a shade higher or lower than the population by standard sampling error. (I'm almost surprised there aren't more of those visible.)<br /><br />If you look at the stepwise ratios in graph form, it becomes evident that they're following a linear upward trend; i.e., the chance of continued survival increases with advancing level (which is sensible). I wouldn't expect it to be perfectly smooth simply due to the coarseness of the d6-based monster level table (and arbitrary power of monster on each level chart). <br /><br />See the last link which I updated with a chart for the stepwise ratios. Thanks for the questions!Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-42618199256404112362014-08-31T19:51:38.607-04:002014-08-31T19:51:38.607-04:00I think that, in general, the modifier to the d6 r...I think that, in general, the modifier to the d6 roll simulates the matter of multiple party members and multiple monsters.faoladhhttps://www.blogger.com/profile/03691952430041394614noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-7614538882369408662014-08-31T19:49:51.706-04:002014-08-31T19:49:51.706-04:00That does seem to clear up most of the difficultie...That does seem to clear up most of the difficulties, except that annoying anomaly in CON at levels 10-11. Judging by the previous results, it seems that both should be 15. That's why there are meta-analyses!<br /><br />I should add that I'm actually somewhat surprised that there is such an uneven result in the numbers of characters at each level. I'd expected quite a bit more smoothness in the result, even if not perfectly smooth. I wonder if the AD&D optional rule increasing "to hit" chances by 1 per level instead of 2 per 2 levels would smooth things out at all. I doubt it, since the general tendency of the increase is still the same. I forget if D&D includes the multiple attacks vs. low hit die monsters rule that AD&D has in the alternative combat system. I know that it was assumed in the Chainmail system.<br /><br />I'm sorry to keep bringing up issues. I hope that they improve the simulation, though I am not actually sure that it can be improved much further.faoladhhttps://www.blogger.com/profile/03691952430041394614noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-41504671902890937872014-08-31T15:18:26.306-04:002014-08-31T15:18:26.306-04:00Well, how you'd really compute the margin of e...Well, how you'd really compute the margin of error is by E = z(alpha/2)*sqrt(p^(1-P^)/n). At the 95% confidence level, z(alpha/2) = 1.96, p^ is the sample proportion, n is the sample size (100,000 here). For example, in a sample bin of bin of 200, it works out to E = 0.0003 = 0.03%, or about +/-30 men out of 100,000. <br /><br />So I did a run of the d6-3 model with 1 million men involved, and linked below you can find the results. Includes the margin of error and 95% C.I. for actual population range based on this Monte Carlo simulation. (e.g., it's 95% likely that the number of 12th level fighters per million is somewhere between 1690 and 1854, etc.)<br /><br /><a href="http://www.superdan.net/download/blog/deltasdnd/Arena-BigRun.pdf" rel="nofollow">http://www.superdan.net/download/blog/deltasdnd/Arena-BigRun.pdf</a>Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-49219683864831924642014-08-31T12:41:26.500-04:002014-08-31T12:41:26.500-04:00The simulation is currently always one fighter ver...The simulation is currently always one fighter versus one monster. If we were to simulate larger parties, but those parties fight more monsters, then it seems like that would just cancel out and effectively have one fighter per monster anyway.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-82886455536832551192014-08-30T18:39:45.191-04:002014-08-30T18:39:45.191-04:00I'd be interested in seeing how the results ch...I'd be interested in seeing how the results change once the effects of Charisma are included. That'd give the fighter a party to properly tackle dungeon levels equal to his level, plus we could see how Charisma differs by level<br /><br />Did you vary the number of monsters based on the level on which they're encountered? I'd imagine that would impact the results. If you add Charisma later, remember that larger parties attract more monstersHolly Oatshttps://www.blogger.com/profile/01703437987958922954noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-86436722371434362362014-08-30T17:57:17.765-04:002014-08-30T17:57:17.765-04:00Ah, very good, and why didn't I remember that?...Ah, very good, and why didn't I remember that? :) Now the little bit of statistics I do know is coming back to me.<br /><br />OK, ±300 is a pretty huge margin, especially at the higher levels there, where sample sizes are around 200 (or less!), but wouldn't we calculate the margins on the order of 1/sqrt(200) for those? That'd be an error margin of around 7%, or ±14 or so up at the higher levels (10-12) under the -3 assumption. That's an assumed range of 186-214 (matching the observed numbers, close enough), which leaves a ratio range for levels 11 and 12 of about ±0.15. For myself, I'd like to see that range narrowed a bit. If the sample size were increased 10x, then that should result in a variation of ±2.24% or ±44.7, giving a range of 1955.3-2044.7, or a ratio range of ±0.046 or so. Since, I think, the ratios are very nearly the most important result of this (since they can be plugged into a spreadsheet to give results of value for a given setting, for fighting men at least).<br /><br />Now, what will be the real project for the future is to figure what variables affect the results, so that we can build a model (a Monte Carlo simulation being out of the question, as we've previously discussed) that might include spellcasters and perhaps other classes.<br /><br />Hm. Thieves could perhaps be simulated by giving them a chance to avoid combats based on their abilities and thus gain experience from the imputed treasure without fighting. Which brings up the possibility of such things occurring for fighting men, now that I think on it. Not that I can think right away of how to simulate that statistically. Sorry to open another can of worms! D&D is not a simple game, which is perhaps why we love it so.faoladhhttps://www.blogger.com/profile/03691952430041394614noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-21165598844145614542014-08-30T12:14:05.723-04:002014-08-30T12:14:05.723-04:00Good point. See above for discussion under faoladh...Good point. See above for discussion under faoladh's post: I have found in the past that the 3E formula +/-2 challenge levels for each double-or-half of party numbers works surprisingly well. So that argues for run a fighter level N at dungeon level N-4 or something, which actually does make for a halfway decent model.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-26760671637961454872014-08-30T12:06:45.603-04:002014-08-30T12:06:45.603-04:00Well, of course, I'm a statistics professor my...Well, of course, I'm a statistics professor myself. :-) At the 95.44% confidence level, the maximal margin of error for a proportion like this is E = 1/sqrt(n) = 1/sqrt(100,000) = 0.3%, or about +/-300 men in any category (or less if we use the actual sample proportion in any one category, but this serves as an upper bound). Statistically there's no need for separate runs, just crank up the sample size to wherever you're happy with the margin-of-error. <br /><br />Although I think I misinterpreted the results of the half-level-round-up method above; it's a bit more top-heavy because the 3rd level fighters are now running into 5th-level monsters (minotaurs and superheroes) and getting cut down at that point. But the difference from round-down is fairly small.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-67405366835298172562014-08-30T01:33:11.627-04:002014-08-30T01:33:11.627-04:00That's excellent stuff. With those ideas in mi...That's excellent stuff. With those ideas in mind, then it does seem, again, as though -3 or -4 works best as a simulation. What it comes down to is that a certain percentage (20% or 40%) of level 1s will make it to level 2, and then some fraction make it to each higher level. It might be worth running the simulation a number of times (I am thinking on the order of 500 separate runs should do it, since that would be a total of 100,000 cycles to match the size of the world of fighters, which should almost completely eliminate random fluctuations; actually, it should work with fewer repetitions of the experiment, but I'm not sure of exactly how many - any statisticians want to weigh in?) and averaging the results of the various ratios per level.faoladhhttps://www.blogger.com/profile/03691952430041394614noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-88749021923515809632014-08-30T00:56:30.508-04:002014-08-30T00:56:30.508-04:00Good ideas. I let the program round down (truncate...Good ideas. I let the program round down (truncate) just because that's what computer division does by default, with a cap to use the 1st row at a minimum.<br /><br />Here's what happens if you round up instead (levels 1-2 roll on dungeon level 1, etc.): It actually gets even more top-heavy (fewer high-levels), because the 2nd level fighters are that much further away from the lucky big XP scores. <br /><br />But this does suggest other ways of modifying the "dungeon level" input. Like, I'm fond of 3E's formula for modifying difficulty by -/+2 per half-or-doubling of party size, which I've found to be surprisingly robust in the past. So if average party size was 4 then a solo fighter would be at -4 difficulty levels, or if average party is 8 then -6 difficulty. When I run this subtraction method through simulation, the model does seem best at around the -4 subtraction level, where the numbers do tend to decrease by about half per level. (Although I think the -3 of the d6 roll is a somewhat better model.)<br /><br />I've updated the link above with these runs, see pages 5-14. Also I added a "ratio" column to make it a bit more obvious where the steps are decreasing by a half or a third or whatever.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-26448588320269246182014-08-29T18:30:30.945-04:002014-08-29T18:30:30.945-04:00If you're rounding down, what chart are the 1s...If you're rounding down, what chart are the 1st levels rolling on? I picked "round up" so that they'd get to roll on the dungeon level 1 chart. Basically, the progression I imagined goes levels 1-2 roll on dungeon level 1 (up to monster chart 4), 3-4 on dungeon level 2, 5-6 on dungeon level 3, 7-10 on dungeon level 4-5, and so on.<br /><br />Hm, if 1st levels are rolling on dungeon level 1, maybe having to face up to monster chart 4 might have a deleterious effect. This does bring to mind, though, that most characters explore dungeons in parties. Perhaps, then, the reduction of the d6 roll might be the best approximation of that unless and until it could be modified for parties encountering monsters on expeditions (yeah, this is starting to get elaborate, and possibly not worth the effort when simply reducing the d6 roll can approximate encountering critters in parties, both by reducing the strength of the critter per fighter and the experience awarded similarly).<br /><br />On the whole, after consideration, I am thinking that your method of subtracting 3 or 4 from the monster dice result is the best approximation that suits most or all of the important variables. So, barring further complicated coding that will likely only verify what you already have, I think that you've probably reached a reasonable approximation of the results, confirming for the most part Gygax's (and Arneson's?) intuitive approximations. Go figure that an insurance adjustor would manage that!faoladhhttps://www.blogger.com/profile/03691952430041394614noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-74090257378706663982014-08-29T17:28:05.540-04:002014-08-29T17:28:05.540-04:00Great stuff, this.
Most dungeon-diving isn't ...Great stuff, this.<br /><br />Most dungeon-diving isn't performed solo, though. (As you allude to above...) Usually you gang-up. <br /><br />So I wonder if there isn't a sliding scale that relates (the presumably inverse-relation of) the <em>number of adventurers</em> to the <em>number of pips subtracted</em>. <br />... sort of a <a href="http://en.wikipedia.org/wiki/Lanchester's_laws" rel="nofollow">Lanchester's Laws</a> for Dungeon Diving.<br /><br />welbohttps://www.blogger.com/profile/00234798241485093836noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-44351351181142188632014-08-29T13:19:36.714-04:002014-08-29T13:19:36.714-04:00Great suggestions, those are excellent ideas! With...Great suggestions, those are excellent ideas! With the -4 modifier, the first couple steps are about 1/3, then a couple at 1/2, and then the relation continues to diminish after that.<br /><br />When I run it with dungeon level = 1/2 fighter level (round down, no modifier to the roll), there are actually many more fighters stuck at 1st level (94K out of 100K), 3K at 2nd level, and then steps of about 1/2 after that. I'm guessing that's because no one gets the big lucky XP boost out of 1st level? And the number of leaders wind up much lower than the Vol-3 bandit specifications (about 1/4 what's predicted there).<br /><br />See this PDF, esp. pages 3-5. Thanks for the suggestions!<br /><br /><a href="http://www.superdan.net/download/blog/deltasdnd/Arena-ManVsMonsterResults.pdf" rel="nofollow">http://www.superdan.net/download/blog/deltasdnd/Arena-ManVsMonsterResults.pdf</a>Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-76060159022008751822014-08-29T12:51:40.372-04:002014-08-29T12:51:40.372-04:00I'm pretty sure the answer to that is definite...I'm pretty sure the answer to that is definitely "yes". At some point in a long run someone runs into an 8 hit point giant and can kill it with one sword blow, for example.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-11693163306425725022014-08-29T12:38:37.132-04:002014-08-29T12:38:37.132-04:00... Which is not to say that if there's a grea...... Which is not to say that if there's a great interest I wouldn't add more details to the simulation.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-2170237526012357403.post-59006302738447910952014-08-28T21:48:50.116-04:002014-08-28T21:48:50.116-04:00Awesome, I love these tests.
It would be interest...Awesome, I love these tests.<br /><br />It would be interesting to track what the lowest level fighter was to kill each of the monsters. Does a 1st level guy ever kill what ever the toughest creature it can face?<br /><br />Thiles Targonhttps://www.blogger.com/profile/02928790313150694394noreply@blogger.com