Using the chart below, one rolls d% to calculate a random character level. If a result of 01-90 is achieved the character is level 1-4 as shown on the chart. If a 91-00 is acquired then the character level increases to 5-8 and a second d% roll is made to determine the level. If that result is also 91-00 another roll is made moving on to levels 9-12, and so on. Note the levels end at level 20 and that if you get a final result of "Re-roll on this chart" you simply re-roll again on the level 17th-20th level chart.
My question is this mathematically speaking, what are the odds of rolling a character of 5th, 6th, 7th, 8th, 9th, 10th, 11th, 12th, 13th, 14th, 15th, 16th, 17th, 18th,19th and 20th level?
01-30 1st
31-55 2nd
56-75 3rd
75-90 4th
91-00 Roll Below
01-30 5th
31-55 6th
56-75 7th
75-90 8th
91-00 Roll Below
01-30 9th
31-55 10th
56-75 11th
75-90 12th
91-00 Roll Below
01-30 13th
31-55 14th
56-75 15th
75-90 16th
91-00 Roll Below
01-30 17th
31-55 18th
56-75 19th
75-90 20th
91-00 Re-roll on this chart
Up through 16th, this very easy.
5th: .1x.3=.03 = 1 in 33.33333
6th: .1x.25=.025 = 1 in 40
7th: .1x.2=.02 = 1 in 50
8th: .1x.15=.015 = 1 in 66.66667
9th: .1x.1x.3= .003 = 1 in 333.3333
10th: .1x.1x.25=.0025 = 1 in 400
etc.
The only wrinkle comes in that last chart, because each of the first four possibilities comes with an extra chance of occurring. It appears to become more difficult as it is possible to re-roll 91-100 multiple times. The trick is to realize that doesn't make any of the first four possibilities any more likely. Thus, the final 91-100 can be ignored in calculating the odds.
Thus:
17th: .1x.1x.1x.1x.3=.00003 = 1 in 33,333.3333
18th: .1x.1x.1x.1x..25=.000025 = 1 in 40,000
19th: .1x.1x.1x.1x.2=.00002 = 1 in 50,000
20th: .1x.1x.1x.1x..15=.000015 = 1 in 66,666.6667
Thank you, Overall I like the odds.
How come such a jump between levels 8th and 9th?
I assume we would see a huge jump again from levels 12th to 13th and again from levels 16th to 17th?
Anything I can do to reduce this gap?
How come such a jump between levels 8th and 9th?
I assume we would see a huge jump again from levels 12th to 13th and again from levels 16th to 17th?
Anything I can do to reduce this gap?
Only 1 in 10 goes above 4th level, and then you subdivide the levels a second time after that, with only 1 in 10 of those going above 8th. And so on. So 1 in 100 goes above 8th, 1 in 1000 goes above 12th, and 1 in 10000 goes about 16th.
Hence the big jumps.
To reduce the gaps, you need the odds of rolling on the next chart to be larger. Or, just decide what you want the odds to be for each level and make it a single d% roll (or use 3d10 to do d000 or 4d10 to make d0000).
Adding multiple rolls doesn't make it more random. It just gives you stepping functions in the probabilities.
What about this chart? What are my odds of rolling level 6, 7, 8, etc. all the way up to level 20?
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01-30 1st
31-55 2nd
56-75 3rd
76-88 4th
89-94 5th
95-97 Roll below for Levels 6-10
98-99 Roll below for Levels 11-15
00 Roll below for Levels 16-20
01-30 6th 11th 16th
31-55 7th 12th 17th
56-75 8th 13th 18th
76-90 9th 14th 19th
91-00 10th 15th 20th
What about this chart? What are my odds of rolling level 6, 7, 8, etc. all the way up to level 20?
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.01-30 1st
31-55 2nd
56-75 3rd
76-88 4th
89-94 5th
95-97 Roll below for Levels 6-10
98-99 Roll below for Levels 11-15
00 Roll below for Levels 16-2001-30 6th 11th 16th
31-55 7th 12th 17th
56-75 8th 13th 18th
76-90 9th 14th 19th
91-00 10th 15th 20th
1 is 30%, 2 is 25%, etc. Read it directly off the chart. 5, in particular, is 6%
The way to get 6-10 is to first roll 95-97 (3%) and then roll the corresponding number, so 6 is 3%x30% or 9%. 7 is 3%x25% or 7.5%, etc.
For 11-15, the multiplier is 2% (98-99), so 11 is 2%x9% or 1.8%
For 16-20, the multiplier is 1%, so 16 is 0.9%
There's still a discontinuity there. Level 15 is 2%x10% or 0.2% Level 16 is 1%x30% or 0.3%. There will be slightly more level 16 than level 15 characters. I concur with John; just decide what you want the probabilities to be and write them down.
I concur with John; just decide what you want the probabilities to be and write them down.
Ok thank you, I really hate the 3d10 (1-1000) roll or 4d10 (1-10,000) rolls because they feels so awkward. I'm assuming that this is what you two meant by "just decide what you want the probabilities to be and write them down."?
I concur with John; just decide what you want the probabilities to be and write them down.Ok thank you, I really hate the 3d10 (1-1000) roll or 4d10 (1-10,000) rolls because they feels so awkward. I'm assuming that this is what you two meant by "just decide what you want the probabilities to be and write them down."?
More or less, yes.
I don't see that "roll 3d10" is that much more awkward from "roll 2d10 and then maybe roll 2d10 several more times," but to each their own. But there's also no reason that you need to have that kind of fine grained detail. You could simply use a table like this, for example.
01-13 : first level
14-25: second level
25-37: third level
38-49: fourth level
50-60: fifth level
61-70: sixth level
71-79: seventh level
80-87: eighth level
88-95: ninth level
96: tenth level
97: eleventh level
98: twelfth level
99: thirteenth level
00: really really high (GM's choice)
I concur with John; just decide what you want the probabilities to be and write them down.Ok thank you, I really hate the 3d10 (1-1000) roll or 4d10 (1-10,000) rolls because they feels so awkward. I'm assuming that this is what you two meant by "just decide what you want the probabilities to be and write them down."?More or less, yes.
I don't see that "roll 3d10" is that much more awkward from "roll 2d10 and then maybe roll 2d10 several more times," but to each their own. But there's also no reason that you need to have that kind of fine grained detail. You could simply use a table like this, for example.
01-13 : first level
14-25: second level
25-37: third level
38-49: fourth level
50-60: fifth level
61-70: sixth level
71-79: seventh level
80-87: eighth level
88-95: ninth level
96: tenth level
97: eleventh level
98: twelfth level
99: thirteenth level
00: really really high (GM's choice)
I'll pass, this chart shows exactly what I'm trying to avoid and that is too many mid to high of a level NPCs for my campaign.
Of all the adventurers out there, only 13% are 1st level and 25% of adventurers are between 7th-9th level. There are almost twice as many mid-level adventurers than their are first level. This seems very unlikely in my opinion.
Way to many mid to high level NPCs running around for my taste. Just my opinion, glad it works for other people. Everyone's campaign is different.
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I'll pass, this chart shows exactly what I'm trying to avoid and that is too many mid to high of a level NPCs for my campaign.
Thank you. That's exactly the question I was asking. It's easy enough to fix; how many adventurers of each level do you want?
Basically, you're approaching the problem backwards. Instead of writing down a generation function and seeing if what it generates looks like what you want, figure out the distribution that you want, and write a generation function that produces it.
Is something like this what your asking me to do?
1st level: 1 out of 3
2nd level: 1 out of 5
3rd level: 1 out of 10
4th level: 1 out of 15
5th level: 1 out of 25
6th level: 1 out of 40
7th level: 1 out of 70
8th level: 1 out of 120
9th level: 1 out of 200
10th level: 1 out of 350
11th level: 1 out of 500
12th level: 1 out of 800
13th level: 1 out of 1200
14th level: 1 out of 2000
15th level: 1 out of 4000
16th level: 1 out of 8000
17th level: 1 out of 15,000
18th level: 1 out of 25,000
19th level: 1 out of 40,000
20th level: 1 out of 60,000
Do you care if you get unlikely distributions? I suspect you actually have in mind a specific number of NPCs for each level. Or at least a rough approximation of how many would be "too many".
Just write out the range of numbers you'd accept for each level, not the odds. Because if you write a function that randomly generates characters, sometimes that function is going to go all "100 heads in a row" on you.
If that happens will you accept the random results? Is it ok to have 500 9th level characters? Or did you really have more in mind "150-250 9th level characters for every 20th level character"
Do you care if you get unlikely distributions? I suspect you actually have in mind a specific number of NPCs for each level. Or at least a rough approximation of how many would be "too many".
Just write out the range of numbers you'd accept for each level, not the odds. Because if you write a function that randomly generates characters, sometimes that function is going to go all "100 heads in a row" on you. If that happens will you accept the random results? Or did you really have more in mind "3-5 5th level characters"
Not totally certain what you mean, can you show me an example?
I'll pass, this chart shows exactly what I'm trying to avoid and that is too many mid to high of a level NPCs for my campaign.Thank you. That's exactly the question I was asking. It's easy enough to fix; how many adventurers of each level do you want?
Basically, you're approaching the problem backwards. Instead of writing down a generation function and seeing if what it generates looks like what you want, figure out the distribution that you want, and write a generation function that produces it.
Not totally certain what you mean, can you show me an example?
With the table you set up, it looks like you want about 300 9th level characters for every 20th level character that gets rolled.
But if you're rolling randomly, you may end up with 500 9th level characters and no characters above level 15.
Is that acceptable?
What my intentions are is to reflect that 1 out of 200 NPCs would survive or adventure long enough to attain 9th level. Thus when PCs randomly encounter character class NPCs 1 out of 200 would be 9th level.
95% of NPCs should be level 1-5.
4% of NPCs should be levels 6-10.
1% of NPCs should be levels 11+.
Ok, you've got your distribution set up.
Now you just need to do some multiplication and division
You want a .3333 (1/3=.3333) probability of a 1st level NPC. That means that numbers 1-33 on your d100 will give you a first level character.
You want a .20 (1/5=.2) probability of a 2nd level NPC. So sides 34-64 will be a second level character.
you want a .10 probability of a 3rd level character. That's now sides 65-75 for a third level character.
Keep going until you get to level 7. At that point, you will have used 99 of the sides "100" on the dice will be Levels 8-20. If you roll 100, then you move to the next table and start rolling again.
Eventually you'll need to be rolling the equivalent of a 60000 sided die, since you have one event occurring one time out of 600000. That's about 5 d10 if you color code them and decide ahead of time which value each color will be. Your Level 20 NPC would be "all zeros on everything except the red die and a 1 on that die" or some such thing
Ok, you've got your distribution set up.
Now you just need to do some multiplication and division
You want a .3333 (1/3=.3333) probability of a 1st level NPC. That means that numbers 1-33 on your d100 will give you a first level character.
You want a .20 (1/5=.2) probability of a 2nd level NPC. So sides 34-64 will be a second level character.
you want a .10 probability of a 3rd level character. That's now sides 65-75 for a third level character.
Keep going until you get to level 7. At that point, you will have used 99 of the sides "100" on the dice will be Levels 8-20. If you roll 100, then you move to the next table and start rolling again.
Eventually you'll need to be rolling the equivalent of a 60000 sided die, since you have one event occurring one time out of 600000. That's about 60 d100.
Do you mean something like my original post? Or something like this?
This requires a d% roll on the left column giving a result of 01-95, 96-99,or 00. A second d% roll is made going across to determine actual character level. Then color code it so its easier to read.01-95.....01-30.....31-55.....56-75.....76-90.....91-00
................1st..........2nd.........3rd.......4th........5th
96-99.......6th.........7th..........8th........9th.......10th
.00.........01-35.....36-60.....61-72.....73-79.....80-85...etc.
..............11th.......12th.......13th.......14th.......15th.....etc.
I edited my post a bit after you grabbed the quote.
Yes, something like that, but you're going to need about 5 d10s for a slightly easier way to do it.
Suppose you say
Red d10 = 1s column
Yellow d10 = 10s column
Blue d10 = 100s column
Black d10 = 1,000s column
and then you have
White d10 = 10,000s column
If all the dice are 0 and the white shows a 6, then you've got your 1/60000 probability of rolling a Level 20 NPC. (You'll need to ignore any rolls that have a 7, 8, or 9 on the white d10).
Just work out the splits for the lower levels.
Level 1: you need all the numbers between 0 and 19,999 to give a 1 in 3 chance of rolling a Level 1 character. So that would be
White = 0 or 1
Black = all numbers
Blue = all numbers
Yellow = all numbers
Red = all numbers
You'd just work your way through the probabilities for each Level, assigning the numbers to give you the correct probability for the number of NPCs you want at that level.
From your table, you want about 20,000 numbers for Lvl 1; about 12,000 numbers for level 2; about 6,000 numbers for level 3; about 30 numbers for Level 14, etc.
Just keep adding the numbers until you get to Level 20, which will be that 1 in 60,000 chance.
But there may be a faster way to do the calculations. How are you planning on using these NPCs? Why do you need dice rolls to create them?
But there may be a faster way to do the calculations. How are you planning on using these NPCs? Why do you need dice rolls to create them?
It's part of a random encounter table I'm putting together. The monsters and different types of people encounters, including adventurers and random character class encounters are placed on the encounter table. That part is completed. I make one encounter table for each major region of the world, such as a kingdom or forest.
Once the encounter is determined (and if it is a people encounter) I like to roll for race and character class. This part is also complete.
What is left is level determination. I want a harsh world where few individuals (save but PCs rise past 10th level.) Those that do are very significant people and the tables we are working on should reflect that they are not a dime a dozen.
Using the traditional type of d% table where you stagger the levels and assign a number 1-100 to each level I feel gives me way to high of a chance of acquiring medium to high level characters.
Ok, here's your table. You will need 5 different colored d10s. For convenience, I'll use the scheme I posted above
Red d10 = 1s column
Yellow d10 = 10s column
Blue d10 = 100s column
Black d10 = 1,000s column
White d10 = 10,000s column
Reroll all the dice for any roll where the white die is higher than 4. (No, you cannot substitute a white d6. Use a d10)
Also reroll all the dice for any roll above 48035.
If you roll the numbers
0-19999 then the character is Level 1
20000 - 31999 Level 2
32000 - 37999 Level 3
38000 - 41999 Level 4
42000 - 44399 Level 5
44400 - 45899 Level 6
45900 - 46756 Level 7
46757 - 47256 Level 8
47257 - 47556 Level 9
47557 - 47727 Level 10
47728 - 47847 Level 11
47848 - 47922 Level 12
47923 - 47972 Level 13
47973 - 48002 Level 14
48003 - 48017 Level 15
48018 - 48025 Level 16
48026 - 48029 Level 17
48030 - 48031 Level 18
48032 - 48034 Level 19
48035 - 48035 Level 20
That leaves you with the following probable distribution of NPCs, which exactly matches the probability you gave above.
Level 1 20000
Level 2 12000
Level 3 6000
Level 4 4000
Level 5 2400
Level 6 1500
Level 7 857
Level 8 500
Level 9 300
Level 10 171
Level 11 120
Level 12 75
Level 13 50
Level 14 30
Level 15 15
Level 16 8
Level 17 4
Level 18 2
Level 19 2
Level 20 1
Remember that this is just the most likely distribution. There is no guarantee than your rolls will exactly match these (in fact, it's not very likely at all that you will exactly match these numbers).
Reroll all the dice for any roll where the white die is higher than 4. (No, you cannot substitute a white d6. Use a d10)
Nice work*. But why not? (1d6-1 and reroll 6s) is identical to rolling a d10 and keeping eveything from 0-4.
Nice work*. But why not? (1d6-1 and reroll 6s) is identical to rolling a d10 and keeping eveything from 0-4.
It may be true. I'd have to dig so deeply into old statistics books to verify that the probabilities are identical that I took the safe way out.
My thinking is that if you change the probability of a 4 showing up, you've overweighted the likelihood of the higher level NPCs.
Cheers.
I'm pretty sure they would - they're independent from the other digits and just a uniform distribution from 0-4 (20% chance of each). The advantage of 1d6-1 just being you only have to reroll 16andabit% of the time vs half the time.
Of course that distribution is just what you would get if you happen to randomly draw a single adventurer from a ballot box.
If your players are attending the "high level adventurers annual epic games" or for that matter happen to be in a ludicrously dangerous area that pretty much pulverises anyone below level 10ish stupid enough to enter, the distribution will be different.
Cheers.
I'm pretty sure they would - they're independent from the other digits and just a uniform distribution from 0-4 (20% chance of each). The advantage of 1d6-1 just being you only have to reroll 16andabit% of the time vs half the time.
Yes, that was my first thought too.
Those probabilities aren't independent. This is a permutation, not a combination like most dice rolls are. Which is why I'm not sure that you can just change the probability and get away with it
Cheers.
I'm pretty sure they would - they're independent from the other digits and just a uniform distribution from 0-4 (20% chance of each). The advantage of 1d6-1 just being you only have to reroll 16andabit% of the time vs half the time.
Yes, that was my first thought too.
Those probabilities aren't independent. This is a permutation, not a combination like most dice rolls are.
I don't think it matters though - the spread of each digit is still uniform. The order isn't being messed with no matter what size dice you use to generate the 'white digit' - provided white is 20/20/20/20/20 and the others are 10/10/10/10/10/10/10/10/10/10.
Apologies for the derail though - it isn't very important. :)
Apologies for the derail though - it isn't very important. :)
The levels of geek are getting pretty deep, aren't they?
Apologies for the derail though - it isn't very important. :)The levels of geek are getting pretty deep, aren't they?
:)
Ok, here's your table. You will need 5 different colored d10s. For convenience, I'll use the scheme I posted above
Red d10 = 1s column
Yellow d10 = 10s column
Blue d10 = 100s column
Black d10 = 1,000s column
White d10 = 10,000s column
Reroll all the dice for any roll where the white die is higher than 4. (No, you cannot substitute a white d6. Use a d10)
Also reroll all the dice for any roll above 48035.If you roll the numbers
0-19999 then the character is Level 1
[...]
48035 - 48035 Level 20That leaves you with the following probable distribution of NPCs, which exactly matches the probability you gave above.
Level 1 20000
[...]
Level 20 1
There's a little problem here. Eileen specified one character in 60,000 should be level 20, and your table gives one out of 48,035. Similarly, she suggested that one in three should be first level, and your table gives 20,000 out of 48,035, or roughly 2/5 (40%).
Of course, there's a reason for this. The probability mass she specified only accounts for 80% of the possible people (if you add up the 1/3 who are level 1 and the 1/5 who are level 2 and ... and the 1/60,000 who are level 20, it adds up to just over 80/100.) I assume she'd rather have more low level people than high level people, so that probability probably should be distributed at the low end rather than the high end. But, that table is certainly a better start, if only because now everyone knows what she's aiming at.
I've thought about this and here's the logic for sticking with a d10 instead of a d6
It's simply that there isn't a zero on the d6, so you have to do some arithmetic in order to convert the d6 roll into usable numbers. Using a d10 does not require anyone to remember to convert anything, nor to do the conversion accurately.
And it scales quite easily
And, of course, if she really wants 60,000 outcomes, then a d6 is useless and you need to switch to a d8.
Far more complex than I like to make instructions in an internet post for people who aren't very mathematically sophisticated
There's a little problem here. Eileen specified one character in 60,000 should be level 20, and your table gives one out of 48,035. Similarly, she suggested that one in three should be first level, and your table gives 20,000 out of 48,035, or roughly 2/5 (40%).
Of course, there's a reason for this.
Yeah, I noticed that discrepancy last night, but I'll leave the tweaks to someone else. I simply worked with what she gave me. Someone else can make her statements internally consistent
It's a pretty easy calculation once you get her distribution table set up correctly,
Thank you for your efforts though much of this conversation has gone beyond my mathematical understanding.
Yes, I favor low level results over mid and high level results. I'm just over my head on this conversation. Math is not my strong point. I put together a chart that I feel worked relatively for my purposes even if it isn't as mathematically sound or provide the "odds" I indicated I favored earlier in the conversation.
Yes, I favor low level results over mid and high level results. I'm just over my head on this conversation. Math is not my strong point.
That's not a problem. If you go to an architect and ask her to design a four-bedroom house for you, you're not expected to know the local building codes or which walls should be load-bearing. But it's helpful, to the point of necessary, if you say you want a four-bedroom house instead of a fourteen-bedroom one.