D&D General Deck-based Ability Score Generation

clearstream

(He, Him)
Coming out of a few threads on generating ability scores, and in particular conversation with @EzekielRaiden I came up with an interesting tweak to the deck-based score generation that I'd like to share. @EzekielRaiden made an argument for surprise - i.e. for not knowing what your total scores would be, and for each score being unpredictable. Dice achieve that through the independence of each result. I came up with another solution, as follows...

Make a 20-card deck from which you will draw 3 cards for each score without replacement, leaving 2 cards in the deck. For example - 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2. This deck has interesting features -
  • The range for the sum of scores is 60 to 66
  • The range for an individual score is 6 to 15
  • A character can have no more than one 15, and no more than one 6
  • Scores will average to at least 10, and at most 11, i.e. 10.5
Here is another, a 14-card deck from which you will draw 2 cards for each score without replacement, leaving 2 cards in the deck. In this case - 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2. Some features are -
  • The range for sum of scores is 54 to 66
  • For an individual score is 4 to 16
  • A character can have no more than one 16, and no more than one 4
  • Scores will average to at least 9, and at most 11, i.e. 10 (for a 'harder' baseline difficulty)
Features of this deck-based method that I believe are desirable are -
  1. Mitigates overshadowing - you cannot get a character more than several points better than another (although precisely where points fall can feel more or less exciting)
  2. Unpredictable (suprising) - the distributions are 'hard' to analyse, and the draw is quite random seeing as you don't know which cards will be left in the deck
  3. System-friendly, tunable range - the deck can be tuned to place scores inside the range your group find right, for eample 6 to 15 for the 20-card deck above
  4. Fair - per another thread that makes a point I agree with, characters generated this way will feel fair compared with one another; a character with flaws more likely has strengths in compensation
Finally, a group can choose to allocate cards to scores as they are drawn - for 'organic' arrays - or assign them as desired - for concept-friendly arrays.
 

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Yaarel

Mind Mage
I like the approach. I have to think about the numbers.

I want a range that is mainly 10 to 14, tho a less likely 8 or 16 is ok.

So I would probably not have cards worth a 2.



Maybe draw two cards?

4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8
 

Stalker0

Legend
I like this idea a lot. Having just done something similar through a "alternate deck of many things" concept..... the players got to pick a stat and draw two cards, the sum replaced their stat (for good or ill). Was a lot of fun for the players, so I think doing that as a default concept could be fun.

For me, the main advantage of rolling is the chance to get a really high stat or one low stat that can be a fun weakness. I think the issue with rolling is when you get the character with two 18s or 3 stats below 10, that kind of thing. So a deck that automatically removes that I think has a lot of potential.

For the first deck, my issue is I can go down to 6 (which is fine) but I still can only get a 15 at best. That's basically point buy but worse. If I can get as low as a 6, I should be able to get as high as a 16 or maybe even 17. So perhaps swap two of the 5s with 6s in that deck. Gives you a shot at that high number, slightly increases your average, but provides I think a nice range of options.

I like that better than the 2 draw deck myself. I think 4s can be problematic. A 6 is a noticeable penalty, a 4 I think is very hard to roleplay in certain cases (what is a 4 int really mean? a 4 charism basically be someone who never talks or does anything but just follow what other people said)...I think that's a bit too much.
 

clearstream

(He, Him)
I like the approach. I have to think about the numbers.

I want a range that is mainly 10 to 14, tho a less likely 8 or 16 is ok.

So I would probably not have cards worth a 2.



Maybe draw two cards?

4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8
You could try this 20-card deck - 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6. Drawing three per score, and leaving the last two cards in deck.

Scores range from 8-16
Scores total from 69-75
Scores average 11.5 to 12.5

A high array might look like 16, 15, 13, 12, 10, 9
A low array might look like 15, 14, 12, 11, 9, 8

What do you think?
 
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clearstream

(He, Him)
I like this idea a lot. Having just done something similar through a "alternate deck of many things" concept..... the players got to pick a stat and draw two cards, the sum replaced their stat (for good or ill). Was a lot of fun for the players, so I think doing that as a default concept could be fun.
I didn't mention it, but fun is also part of why I like this method. It's very easy for players to use. They don't need to know the complicated part, which is working out a good deck composition!

For me, the main advantage of rolling is the chance to get a really high stat or one low stat that can be a fun weakness. I think the issue with rolling is when you get the character with two 18s or 3 stats below 10, that kind of thing. So a deck that automatically removes that I think has a lot of potential.

For the first deck, my issue is I can go down to 6 (which is fine) but I still can only get a 15 at best. That's basically point buy but worse. If I can get as low as a 6, I should be able to get as high as a 16 or maybe even 17. So perhaps swap two of the 5s with 6s in that deck. Gives you a shot at that high number, slightly increases your average, but provides I think a nice range of options.

I like that better than the 2 draw deck myself. I think 4s can be problematic. A 6 is a noticeable penalty, a 4 I think is very hard to roleplay in certain cases (what is a 4 int really mean? a 4 charism basically be someone who never talks or does anything but just follow what other people said)...I think that's a bit too much.
Taking the deck I posted in reply to @Yaarel and swap in a 2 for a 3, and a 6 for a 5 - so you have 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6.

Scores range from 7-17
Scores total from 68-76
Scores average 11.3 to 12.7

A high array might look like 17, 15, 13, 12, 10, 9
A low array might look like 15, 14, 12, 11, 9, 7

Is that about what you were thinking of? It'd take a bit of effort to figure out the average array. Generating one at random I get 9, 12, 13, 11, 12, 13. Another, 14, 11, 14, 11, 12, 13.
 

Stalker0

Legend
I didn't mention it, but fun is also part of why I like this method. It's very easy for players to use. They don't need to know the complicated part, which is working out a good deck composition!


Taking the deck I posted in reply to @Yaarel and swap in a 2 for a 3, and a 6 for a 5 - so you have 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6.

Scores range from 7-17
Scores total from 68-76
Scores average 11.3 to 12.7

A high array might look like 17, 15, 13, 12, 10, 9
A low array might look like 15, 14, 12, 11, 9, 7

Is that about what you were thinking of? It'd take a bit of effort to figure out the average array. Generating one at random I get 9, 12, 13, 11, 12, 13. Another, 14, 11, 14, 11, 12, 13.
I would probably leave the extra 2 in there (aka three total). I think getting a 6 is a rare but perfectly fine result, as is the high rariety in getting a 17.
 

GMMichael

Guide of Modos
Here is another, a 14-card deck from which you will draw 2 cards for each score without replacement, leaving 2 cards in the deck. In this case - 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2. Some features are -
  • The range for sum of scores is 54 to 66
  • For an individual score is 4 to 16
  • A character can have no more than one 16, and no more than one 4
  • Scores will average to at least 9, and at most 11, i.e. 10 (for a 'harder' baseline difficulty)
I like this one better than the first; it requires only one deck. But it's weighted towards low scores. You might fix (?) this by removing a 2 and adding a 3.

You might add some zany options to make it more interesting:
  • the jester allows you to steal a score from another player (in exchange for the next score you draw).
  • the jack gives you a 10 total, even if it's the second card you draw.
  • the queen is +1 and draw again.
  • the king lets you look at the deck and remove one card.
 

clearstream

(He, Him)
I like this one better than the first; it requires only one deck. But it's weighted towards low scores. You might fix (?) this by removing a 2 and adding a 3.
I prefer the shorter decks, too. They're more volatile i.e. produce spikier arrays. The one I am thinking of switching to is 13-card - 8, 7, 7, 6, 6, 5, 5, 5, 4, 4, 3, 3, 2 - of which you draw twelve (six pairs).

Scores in the range 5-15 suit my campaign. The average is 10 so it's yielding characters that are going to have a slightly harder time of it than average. 10.5 after the TCoE ASIs.

You might add some zany options to make it more interesting:
  • the jester allows you to steal a score from another player (in exchange for the next score you draw).
  • the jack gives you a 10 total, even if it's the second card you draw.
  • the queen is +1 and draw again.
  • the king lets you look at the deck and remove one card.
The method is begging for wild cards and such like!
 

Yaarel

Mind Mage
@clearstreams

Yeah, the tailoring the deck for specific ranges, looks good.




By the way, because high scores are worth way more than low scores, referring to "total scores" feels less helpful. If you convert this metric into a point-buy total, and compare the point-buy total of each deck, that would feel more helpful.
 

Yaarel

Mind Mage
I would probably leave the extra 2 in there (aka three total). I think getting a 6 is a rare but perfectly fine result, as is the high rariety in getting a 17.
It is a matter of taste. Each table will probably evolve its own preference, or multiple preferences depending on the setting concepts.

For me, I like numbers that are low but non-negative. So, +0 to +3 is ideal. But a +4 or even a −1 can add flavor.



It looks like the new format will have all player characters add a +2 and +1, or else three +1s, on top of whatever scores get generated.

But this deck method could tailor to numbers to already be equivalent to this improvement step, and not do it.
 

Yaarel

Mind Mage
Assuming six ability scores, consider the following point-buy numbers.



Score (Cost)

6 (−4 points)
7 (−3 points)
8 (−2 points)
9 (−1 point)

10 (0 points)
11 (1 point)

12 (2 points)
13 (3 points)

14 (6 points)
15 (9 points)

16 (18 points)
17 (27 points)

18 (54 points)
19 (81 points)

20 (162 points)
 

clearstream

(He, Him)
It is a matter of taste. Each table will probably evolve its own preference, or multiple preferences depending on the setting concepts.

For me, I like numbers that are low but non-negative. So, +0 to +3 is ideal. But a +4 or even a −1 can add flavor.
I like something in the range perhaps −2 to +3 at 1st level, leaving scope for ASIs as characters advance.

It looks like the new format will have all player characters add a +2 and +1, or else three +1s, on top of whatever scores get generated.

But this deck method could tailor to numbers to already be equivalent to this improvement step, and not do it.
I like giving players that bit of control, on top of the deck. That's why I tend to tune my decks slightly low - to make space for those three points.
 

Stalker0

Legend
Hehe I was trying to calculate the various number probabilities with just some brute force tactics (aka just generate a giant list of random number combinations and see what shakes out).

In my head I was like "Combination of 20,18 isn't that large"..... but then I realized because the timing of the numbers matters for what gets added into what number....its more like "Permutation of 20,18". And that is a VERY LARGE number!

Since cards are deterministic unlike dice, and the timing of the cards is important, calculating the probabilities is much more difficult. It actually would make for a very solid advanced probability question.

Best I could do was determine the chance of getting a 6 with this array:
[2,2,2,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,6,6]
was .5%
 
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clearstream

(He, Him)
Hehe I was trying to calculate the various number probabilities with just some brute force tactics (aka just generate a giant list of random number combinations and see what shakes out).

In my head I was like "Combination of 20,18 isn't that large"..... but then I realized because the timing of the numbers matters for what gets added into what number....its more like "Permutation of 20,18". And that is a VERY LARGE number!

Since cards are deterministic unlike dice, and the timing of the cards is important, calculating the probabilities is much more difficult. It actually would make for a very solid advanced probability question.

Best I could do was determine the chance of getting a 6 with this array:
[2,2,2,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,6,6]
was .5%
The distributions are indeed hard to analyse! One way I use is just to Monte Carlo them. A friend wrote a deck shuffling plugin for me, for Excel. So I can create a deck, clone it many times, and apply some basic statistical analysis to get a sense of how it performs.

Another approach is to focus on combinations rather than permutations, to get a sense of how many ways there will be to get each value. Say we are drawing pairs - we don't care about the order of the cards in the pair - so we don't need to worry about all possible permutations because (for example) 5+6 will be identical to 6+5 for our purposes. If you allow assign-as-desired, the ordering of the pairs in the deck is also irrelevant, further simplifying, because in that case (for example) 12, 17, 7 is the same as 7, 12, 17 etc.

I've found I like 12-card arrays with relatively low average values. Like this one - 8, 7, 7, 7, 6, 6, 5, 5, 4, 4, 4, 3 - which gives swingy scores from 7-15 summing to 66. Average 11.5 after TCoE ASIs. Final modifiers generally sum to +3 to +4. In my campaign, scores are allocated as drawn (and I am not concerned about 'surprise' - or rather I think of that as a feature of the whole array, and not of a given score or of total point value variance).
 

Stalker0

Legend
The distributions are indeed hard to analyse! One way I use is just to Monte Carlo them. A friend wrote a deck shuffling plugin for me, for Excel. So I can create a deck, clone it many times, and apply some basic statistical analysis to get a sense of how it performs.

Another approach is to focus on combinations rather than permutations, to get a sense of how many ways there will be to get each value. Say we are drawing pairs - we don't care about the order of the cards in the pair - so we don't need to worry about all possible permutations because (for example) 5+6 will be identical to 6+5 for our purposes. If you allow assign-as-desired, the ordering of the pairs in the deck is also irrelevant, further simplifying, because in that case (for example) 12, 17, 7 is the same as 7, 12, 17 etc.

I've found I like 12-card arrays with relatively low average values. Like this one - 8, 7, 7, 7, 6, 6, 5, 5, 4, 4, 4, 3 - which gives swingy scores from 7-15 summing to 66. Average 11.5 after TCoE ASIs. Final modifiers generally sum to +3 to +4. In my campaign, scores are allocated as drawn (and I am not concerned about 'surprise' - or rather I think of that as a feature of the whole array, and not of a given score or of total point value variance).
Except the pair model isn’t quite sufficient. For example, a classic problem is “draw 6 cards, what is the possibility of a pair?”

that doesn’t work for this example because the order of the cards is particularly important. A 2,2,3 in the first 3 cards generates a 7, but a 2,2,X,3 (two 2s, a different card, then the 4th card a 3) generates different numbers. Cards are spacially connected to each other, so I’m not sure how to calculate that, gnat probability math seems way over my head
 

jgsugden

Legend
I get the idea, but in general it seems like a loss of control over a point buy system. You get roughly the same range but give people less control.

In my experience, whether a PC has straight 18s or no score greater than 14, the PC works fine. The relative difference in power is noticeable, but not game breaking, and a DM that accounts for it with strategic introduction of magic items or storyline benefits can balance it out without difficulty. To that end, I settled on my system and have not looked back:

Each player rolls 3d6 6 times. For each trio of rolls, they replace the lowest number with a 4. This gives a range of 6 to 16 (with only one in 36 PCs getting that 16). If they accept them 'in order' I give them a minor boon. If they change the order, no boon. A minor boon is a weak feat, a minor magic item, an ally, etc... If they're unhappy, they can use point buy.

I've been very happy with it since implementing it.
 

clearstream

(He, Him)
I get the idea, but in general it seems like a loss of control over a point buy system. You get roughly the same range but give people less control.
That's right. It's not intended to replace point-buy, which is a good method for when a group wants 100% control. Rather it is intended to be an alternative to random methods like rolling dice.

In my experience, whether a PC has straight 18s or no score greater than 14, the PC works fine. The relative difference in power is noticeable, but not game breaking, and a DM that accounts for it with strategic introduction of magic items or storyline benefits can balance it out without difficulty. To that end, I settled on my system and have not looked back:

Each player rolls 3d6 6 times. For each trio of rolls, they replace the lowest number with a 4. This gives a range of 6 to 16 (with only one in 36 PCs getting that 16). If they accept them 'in order' I give them a minor boon. If they change the order, no boon. A minor boon is a weak feat, a minor magic item, an ally, etc... If they're unhappy, they can use point buy.

I've been very happy with it since implementing it.
Part of the problem-definition for the deck-generation solution, is overshadowing. The method is designed to put characters on a mechanically fair footing. It's also simple in application, so that it levels the playing field for system mastery.
 

payn

Legend
I like, but ultimately, it just seems like extra work to get to a stat array. This is where all my stat gen travels take me. I may try this next time I'm doing a Traveller game though.
 

clearstream

(He, Him)
Except the pair model isn’t quite sufficient. For example, a classic problem is “draw 6 cards, what is the possibility of a pair?”

that doesn’t work for this example because the order of the cards is particularly important. A 2,2,3 in the first 3 cards generates a 7, but a 2,2,X,3 (two 2s, a different card, then the 4th card a 3) generates different numbers. Cards are spacially connected to each other, so I’m not sure how to calculate that, gnat probability math seems way over my head
I mean more this situation. Picture a simplified deck of six cards - three 3s and three 4s - from which we'll draw and sum two cards for each score. (I referred to those two summed cards as a 'pair'.)

Say the deck look like this after shuffling - 3, 3, 4, 3, 4, 4 - so that our scores would be 6, 7, 8. For our purposes, that is identical to a deck that looks like this after shuffling - 3, 3, 3, 4, 4, 4 - because that will also make our scores 6, 7, 8. It doesn't matter what order the middle pair are drawn in. It also doesn't matter which 3 and which 4 because for our purposes 3s are all the same, and 4s are all the same.

So long as we're agnostic as to where each score is allocated - so 8, 6, 7 is as good as 6, 7, 8 - say because we are allocating-as-desired (or are happy with anything we get), then - 4, 3, 4, 4, 3, 3 - is also identical to the above shuffled decks (for our purposes).

If precise card order mattered, we'd have to worry about 720 permutations. Given that the ordering within pairs doesn't matter, we can worry about just 30 permutations. And given that the ordering of pairs doesn't matter, we can worry about just 15 combinations. At least, that is my understanding.

Does that sound right? Or have I gone wrong somewhere?
 

Stalker0

Legend
I mean more this situation. Picture a simplified deck of six cards - three 3s and three 4s - from which we'll draw and sum two cards for each score. (I referred to those two summed cards as a 'pair'.)

Say the deck look like this after shuffling - 3, 3, 4, 3, 4, 4 - so that our scores would be 6, 7, 8. For our purposes, that is identical to a deck that looks like this after shuffling - 3, 3, 3, 4, 4, 4 - because that will also make our scores 6, 7, 8. It doesn't matter what order the middle pair are drawn in. It also doesn't matter which 3 and which 4 because for our purposes 3s are all the same, and 4s are all the same.

So long as we're agnostic as to where each score is allocated - so 8, 6, 7 is as good as 6, 7, 8 - say because we are allocating-as-desired (or are happy with anything we get), then - 4, 3, 4, 4, 3, 3 - is also identical to the above shuffled decks (for our purposes).

If precise card order mattered, we'd have to worry about 720 permutations. Given that the ordering within pairs doesn't matter, we can worry about just 30 permutations. And given that the ordering of pairs doesn't matter, we can worry about just 15 combinations. At least, that is my understanding.

Does that sound right? Or have I gone wrong somewhere?
Unfortunately no that's not correct.

Here is another way we could arrange those same cards:

33 43 44 (6 7 8)
34 34 34 (7 7 7)

That's a permutation not a combination, as order does matter. Now you are correct that within our blocks order doesn't matter, so the theoretical number of permutation is smaller, but it still grows very very quickly. And we never really get back down to "combination level"

As another example, just take 3 and 4s but now its 12 draws (2 draws per stat x 6 stats)

33 33 33 44 44 44 (6 6 6 8 8 8)
34 34 33 33 44 44 (7 7 6 6 8 8)

Same exact cards just drawn in a slightly different order produces a different stat block. So yes unfortunately the position of the card draws is quite important to what numbers you get. And this problem gets progressively worse when you look at 3 draws per stat and more than 2 types of cards. But even just a 20 card deck where I draw 12 cards from (aka 2 cards x 6 stats), is a 10 to the power of 13 number in terms of permutations (aka 10 trillion)..... far more than most programs can easily calculate (for reference excel only has 17 billion cells, you would need to utilize 588 worksheets all completely filled to the brim to display all of the possibilities). Even if I can cut that by 4 or 6 or heck even 10 by noting certain permutations are "the same".....I still have a very complex problem to solve.
 
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