Re: Number Appearing? « Reply #15 on Jan 30, 2012, 11:23pm »
I have an inexpensive TI-30XIIS calculator. It has a function called RANDI, used to generate a random integer between two integers you specify: RANDI(a,b). Presumably, these random integers are drawn from the discrete uniform distribution: RANDI(a,b) ~ DU(b-a+1,a,1), where the notation DU(k,c,h) means a discrete uniform distribution with the probability range consisting of the k distinct values x_j = c + h*j for j = 0,1,...,k-1 with equal probabilities 1/k.
The keystrokes for RANDI(30,300) are PRB, left arrow, Enter, 30, 2nd, right parens, 300, right parens, Enter. To repeat the calculation (draw another random number from the same range), you can type up arrow, Enter. I suspect most calculators have similar random number generating capabilities.
The other dice methods suggested here all have the same endpoints (30 and 300) and the same mean (165). But they all have different probability ranges (i.e., possible outcomes) and different standard deviations. The mean value is not always part of their probability range. Let's look at some of the possibilities in detail:
RANDI(30,300) This is the discrete uniform distribution: DU(271,30,1). The probability range is 30 to 300 in steps of 1. There are 271 possible outcomes. Each outcome has the same probability 0.369%. The mean is 165 and this is a possible outcome. The standard deviation is 78.2304288624.
d10x30 This is the discrete uniform distribution DU(10,30,30). The probability range is 30 to 300 in steps of 30. There are 10 possible outcomes. The probability of each outcome is 10%. The mean is 165, but this outcome is not in the range. The standard deviation is 86.1684396981.
d30x10 reroll on a 1 or a 2 This is the discrete uniform distribution DU(28,30,10). The probability range is 30 to 300 in steps of 10. The probability of each possible outcome is 3.571%. The mean is 165, but this outcome is impossible. The standard deviation is 80.777472107. The chance of one or more rerolls is approximately 7.14%.
3d10x10 This is a bell-like distribution. The probability range is 30 to 300 in steps of 10. There are 28 possible outcomes. The mean value of 165 is not a possible outcome. Probabilities are symmetric about the mean. The mode is both 160 and 170, each with probability 7.5%. The probability of 30 (or 300) is 0.1%. The standard deviation is 49.7493718553.
5d10x6 Another bell-like distribution. Range is 30 to 300 in steps of 6. 46 possible outcomes. Mean value is not a possible outcome. Mode is 162 and 168 w/prob 6% ea. Probability of 30 (or 300) is 0.001% ea. Standard deviation is 38.535697736.
30d10 Bell-like. Range is all integers from 30 to 300, so the mean value of 165 is possible. P(X=165) = 2.523%. P(X=300) approx 0. Spread is 15.7321327226. So this distribution has the smallest standard deviation of all those considered.
Re: Number Appearing? « Reply #17 on Apr 11, 2012, 5:52pm »
I also simply used 1d10*30 to generate a number of orcs, additionally I would tend to put that many orcs in the 1st level of the dungeon and or around the surface or 2nd level.
Finarvyn Administrator Dungeon Master member is offline
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Re: Number Appearing? « Reply #18 on Apr 14, 2012, 5:46am »
1. Wow. That's cool. I don't do much with calculator programming anymore, but I remember old calculators that would generate a random three-digit decimal from 0.000 to 1.000 and then I could just multiply by whatever dice type I wanted. Seems similar, and often a pain. Nice post, though.
2. I always found it interesting that there was no "official" way to do this. It could be 1d10*30 (as per nizrad's suggestion) or 30d10 if a person was more into accuracy. Heck, with the funky dice out there I suppose it could be 1d30*10.
3. It is also interesting to me that there is a single number range given, apparently most approapriate for wilderness adventures rather than the dungeons. (I suppose there could be 30-300 orcs in a dungeon, but that really messes up low-level characters.) There really should be three number ranges: wilderness wandering, wilderness lair, dungeon encounter.
Marv / Finarvyn DCC playtester (2011) C&C playtester (2003) I'm partly responsible for the S&W WhiteBox Builder of the TrollBridge Master of Mutants; MA since 1976 OD&D Player since 1975
"Don't ask me what you need to hit. Just roll the die and I will let you know!" - Dave Arneson
2. I always found it interesting that there was no "official" way to do this.
The point is to give you a convenient range, not to specify how you generate a number within that range. Rolling dice is really only secondary; you're best off choosing the number you want.
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3. It is also interesting to me that there is a single number range given, apparently most approapriate for wilderness adventures rather than the dungeons. (I suppose there could be 30-300 orcs in a dungeon, but that really messes up low-level characters.) There really should be three number ranges: wilderness wandering, wilderness lair, dungeon encounter.
The Number Appearing is explicitly only for wilderness encounters, whether lair or not.
Starting with the '81 revision of the rules, the Number Appearing statistic changes. Goblins, for instance, have "28 (660)." The first range is the number appearing in a dungeon and not in a lair. The range in parentheses is both the number appearing in a dungeon lair and the number appearing in the wilderness but not in a lair. Multiply the second range by 5 to get the number appearing in a wilderness lair.
Number Appearing in a dungeon is modified by distance from the dungeon level corresponding to the monster's level. Monster level is determined by hit dice, not counting pluses or minuses, but adding one level for each special ability bonus (the latter not mentioned in the rules but generally applied in the wandering monster tables). Goblins have 1-1 HD, so they're level 1 monsters. You could therefore find them on levels 13 of the dungeon, roughly doubling or trebling (exact numbers are not mentioned) them on levels 2 or 3, respectively. Monsters are usually not encountered more than two levels away from the dungeon level corresponding to their monster level.
Goblins have Treasure Type "R (C)" (individuals R; C in lair or wilderness). The amount of lair treasure rolled (if determined randomly) assumes the maximum number of monsters in the lair. If there are fewer monsters, adjust the treasure by the ratio of monsters present to the maximum number. Wilderness lairs therefore have more guardians of the same amount of treasure than dungeon lairs.
2. I always found it interesting that there was no "official" way to do this.
The point is to give you a convenient range, not to specify how you generate a number within that range. Rolling dice is really only secondary; you're best off choosing the number you want.
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3. It is also interesting to me that there is a single number range given, apparently most approapriate for wilderness adventures rather than the dungeons. (I suppose there could be 30-300 orcs in a dungeon, but that really messes up low-level characters.) There really should be three number ranges: wilderness wandering, wilderness lair, dungeon encounter.
The Number Appearing is explicitly only for wilderness encounters, whether lair or not.
Starting with the '81 revision of the rules, the Number Appearing statistic changes. Goblins, for instance, have "28 (660)." The first range is the number appearing in a dungeon and not in a lair. The range in parentheses is both the number appearing in a dungeon lair and the number appearing in the wilderness but not in a lair. Multiply the second range by 5 to get the number appearing in a wilderness lair.
Number Appearing in a dungeon is modified by distance from the dungeon level corresponding to the monster's level. Monster level is determined by hit dice, not counting pluses or minuses, but adding one level for each special ability bonus (the latter not mentioned in the rules but generally applied in the wandering monster tables). Goblins have 1-1 HD, so they're level 1 monsters. You could therefore find them on levels 13 of the dungeon, roughly doubling or trebling (exact numbers are not mentioned) them on levels 2 or 3, respectively. Monsters are usually not encountered more than two levels away from the dungeon level corresponding to their monster level.
With the above paragraph I assume we are back to OD&D?: especialy the quote from pg 11 of UW&A "If the level beneath the surface roughly corresponds with the level of the monster then the number of monsters will be based on a single creature, modified by type (that is Orcs and the like will be in groups) and the number of adventurers in the party. A party of from 1-3 would draw the basic number of monsters, 4-6 would bring about twice as many, and so on."
So, assuming I'm reading you right, an adventuring pary of 3 would encounter 3-9 goblins on level 1, 6-18 on level 2 and 12-36 on level 3. Is that consistent with your reading?
Goblins have Treasure Type "R (C)" (individuals R; C in lair or wilderness). The amount of lair treasure rolled (if determined randomly) assumes the maximum number of monsters in the lair. If there are fewer monsters, adjust the treasure by the ratio of monsters present to the maximum number. Wilderness lairs therefore have more guardians of the same amount of treasure than dungeon lairs.
That makes sense, but I'm wondering what you are drawing on here. I've seen a lot of commentary that assumes the the treasure tables amount is independant of the actual number of monsters present.
I hadn't realized that the B/X multiply by 5 rule would get you the OD&D numbers. That's cool.
Only kinda-sorta. They obviously weren't trying to reproduce them exactly, just generally, as convenient.
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With the above paragraph I assume we are back to OD&D?
No, still in the '81 rules.
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So, assuming I'm reading you right, an adventuring pary of 3 would encounter 3-9 goblins on level 1, 6-18 on level 2 and 12-36 on level 3. Is that consistent with your reading?
Not according to the '81 rules. In those rules, monster numbers are not adjusted according to party size. Strictly speaking, a dungeon encounter with goblins (No. Appearing 28 (660)) on level 1 will have 28 goblins, no matter the size of your party. You will encounter more goblins on levels 2 or 3. Exact numbers are not defined for deeper (or less deep) levels, but I believe that in general double the number one level deeper or triple the number two levels deeper are good values.
Let's take a more interesting example. Ogres have 4+1 HD and No. Appearing 16 (212). On dungeon level 4, a party will encounter 16 of them outside of lairs, or 212 of them in a lair. On dungeon level 5, a party will encounter 212 of them, or 424 in a lair. On dungeon level 6, a party will encounter 318 of them, or 636 of them in a lair. On dungeon level 3, a party will encounter 14 (16); on dungeon level 2, there will be 12 (14). Ogres are very rare on dungeon level 1, and if they appear there there will only be 1 of them at a time. Ogres on dungeon levels deeper than 6 will rare, but if they are found there will be many of them, and they will probably be in the employ of a greater power (to explain their presence). There will be no lairs outside of levels 26.
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That makes sense, but I'm wondering what you are drawing on here. I've seen a lot of commentary that assumes the the treasure tables amount is independant of the actual number of monsters present.
Basic Set p. B45: "An encounter with less than a full lair should yield less treasure." An example of this is illustrated on p. B56, where the fraction of monsters out of a full lair yields an equal fraction of rolled treasure.
Note that in AD&D the treasure types assume an average lair, not a full lair. The difference is probably due to the fact that the original rules don't specify clearly how the adjustment should be made.
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Re: Number Appearing? « Reply #23 on Jul 3, 2012, 10:45am »
If you are using a computer during prep (or use on during play) go to www.random.org and type in the range of 30-300, or whatever else you want. It generates a true random number based on any parameters you choose.
Re: Number Appearing? « Reply #25 on Aug 9, 2012, 8:57am »
As an aside - one interesting take on the number appearing I've seen suggested is to use the wilderness number and apply it to the whole HD-appropriate dungeon level.
So if you encounter hobgoblins on wandering, you'll encounter a 'party and level appropriate' quantity, but then the DM can also create a lair on the HD equivalent level that has the wilderness amount of hobgoblins scattered about the level in groups of varying sizes to be encountered. Of course they will coordinate to defend their lair.
I use this on levels I haven't fleshed out yet to help me populate them - once the PCs encounter something on the wandering monster table, I build out the lair on the right level.
Joined: May 2009 Posts: 2 Location: Argentina Karma: 0
Re: Number Appearing? « Reply #26 on May 2, 2013, 4:36pm »
If you have python installed (maybe running some sort of *nix), then you could use the random library to generate numbers.
bsd52$ python2.7 Python 2.7.3 (default, Aug 3 2012, 05:33:56) [GCC 4.2.1 20070719 ] on openbsd5 Type "help", "copyright", "credits" or "license" for more information. >>> import random >>> random.randint(30,300) 162 >>> ^D
Joined: Jun 2007 Gender: Male Posts: 216 Location: Greenlawn, NY Karma: 4
Re: Number Appearing? « Reply #28 on May 11, 2013, 11:01am »
The monster tables were designed at a time when Chainmail was still large in the players' minds. Since Chainmail primarily uses a 1:10 figure ratio, and since the Number Appearing column refers only to wilderness adventuring, it might make sense if those numbers were designed to make scaling for Chainmail easy.
Thus, for non-fantastic figures, you'd need No. App. in multiples of 10which is exactly what we have! Hence when goblins are encountered, there aren't just 40400 of them; there are 440 figures. This means a random determination of goblins would have to be 4d10 figures, or 4d10Χ10 goblins, not 40d10 goblins.
Naturally, monsters that don't come in multiples of 10 are not "fantastic" types, and use a figure ratio of 1:1.
Michael Mornard -------------------------- Played in the original Blackmoor, Greyhawk, and EPT Campaigns "Gronan of Simmerya" aka "Old Geezer" aka "LORD Grumpy"
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