Here’s a quick example of putting the ideas in Game design musing: Pricing breadth in skills to work:

GURPS’ Wildcard skills (BS 175) allow purchase of multiple skills for the price of three; Talents (BS 89) allow a bonus to many skills (plus other minor benefits) for a fraction of the eventual cost of full levels in those skills. Both share fuzziness in common: There’s no stated limit on on how many skills a Wildcard skill covers (so why stop at 10 if the GM will allow 20?), and you can freely choose the number of skills a Talent covers, within the limits of its group size (gee, should I take one skill or six for the same 5-point cost of a small group?). 

There’s no big problem in all that, but what if you wanted more varied costs to reflect the number of skills covered? The “Zeno’s method” suggestion in those breadth rules offer a solution:

Smooth pricing for Talents

A Talent costs 5 points (per +1) for 1 to 6 skills, jumps to 10 points for 7 to 12, and maxes out at 15 points for 13 or more. Obviously, the lower numbers of each range (like 7 skills) aren’t nearly as cost-effective as the higher numbers (like 12 skills). How could we set a cost that rises gradually from 6 skills to 7 skills to 8 skills and so on? 

Assume you want to set 15 points as the maximum point cost for any number of skills included in the Talent. The question becomes: For any number of skills n, what is the multiple of the base cost (which is 1 point; we’re asking how many individual points the combination will cost) for that n, when the maximum cost is 15?

Input “15” into cell A2 of the spreadsheet, “1” into C3 (see article for the workings behind that). The results, rounding costs up:

 

cost	# skills
1	1
2	2
3	3
4	4
5	5
6	6-7
7	8-9
8	10-11
9	12-13
10	14-15
11	16-19
12	20-23
13	24-29
14	30-39
15	40-infinite

 

So. A Talent covering 6 or 7 skills costs 6 points; 8 or 9 skills costs 7 points; 24 to 29 skills costs 13 points; 30 to 39 skills costs 14 points; and 40 or more skills costs 15 points.

A couple of things stand out. One: We’re handing out more skills for 10 points than GURPS does. Two: For 15 points, you get 40 to infinite skills! Actually, GURPS allows that too – it places no max number on skills other than GM fiat, and gives you 13 to infinite skills for those points. Still, one wishes for at least the suggestion of a logical limit.

Try this: Set costs to max out at 20, not 15. Bear with me a moment and look at the results:

cost	# skills
1	1
2	2
3	3
4	4
5	5
6	6
7	7-8
8	9
9	10-11
10	12-13
11	14-15
12	16-17
13	18-20
14	21-23
15	24-27
16	28-31
17	32-36
18	37-44
19	45-58
20	59-infinite

 

Let’s see what we have here. A Medium-sized talent in GURPS allows up to 12 skills for 10 points. Here, too, those 12 skills cost 10 points. The cost keeps rising with more skills, reaching 14 points for up to 23 skills, and 15 points for up to 27.

What about the oddity of even bigger numbers, up to infinite skills? No problem: though the table was built on a max cost of 20 points, you don’t have to allow that expenditure. Just set maximum expenditure to 15 points, and you’ve created a new limit of 27 skills in a Talent.

Want to reduce that skill cap even more? Redo the table using a max cost of 25, and (as you’ll see if you change cell A2 on the spreadsheet) you limit the max expenditure of 15 points to buying 22 skills. Use a max cost of 40, and 15 points will buy only 18 skills. Experiment as you like; results are quite flexible.

Finally, what about numbers on the low end? Either of the above two tables says you get 5 skills for 5 points. That’s right in line with GURPS – but what’s up with 4 skills for 4 points, or 2 skills for 2 points? Isn’t that a point crock?

No – no more than Talents themselves are. Using our calculated method, it’s unavoidable – and sensible – that if 5 skills costs 5 points, 2 skills will cost 2 points. (Or thereabout; remember, we’re rounding.) But if that seems “wrong” for Talents, the solution couldn’t be simpler: Just as we set 15 points as the maximum Talent expenditure above, we can set 5 points as the minimum.

The end result: GURPS-like costs of between 5 and 15 points per level of Talent, but with costs in between those bookends that rise smoothly with number of skills covered. There you go, should you want it.  

Smooth pricing for Wildcard skills

Wildcard skills don’t actually offer room for smooth pricing. What are the choices? If the price of one skill (logically) buys you one skill, and three times that single price buys you a big bunch of skills (per the rules), all that’s left to ask is how many skills you could buy for two times the single price. (Kind of a “Wildcard junior” option.) 

Well, it’s not much of a question, but let’s ask. 

First, what are we working with? Our base cost will be one again – though in this case, it’s not 1 point, it’s 1 multiple of the cost of a Very Hard skill. Different unit, but workable.

The maximum multiple, set by GURPS, is 3. Putting those numbers into the spreadsheet, we get…

1 skill for the cost of 1, 2 skills for the cost of 2, and 3 or more skills for the cost of 3. Bleah. Not too interesting.

The problem is poor use of the tool; there’s no space for cost to gradually expand over a large number of terms. Let’s try again, multiplying that max multiple in order to spread things out, and then divide final costs by the same amount. I’ll use a multiple of 4, meaning “12” goes into cell A2: 

cost	# skills
1	1
2	2
3	3
4	4
5	5-6
6	7
7	8-10
8	9-12
9	13-15
10	16-20
11	21-28
12	29-infinite

 

Very well. Now divide those costs by 4 and round them up. The result:

cost	# skills
1	1-4
2	5-12
3	13-infinite

 

There you go: If your Wildcard skill covers 13 or more skills (and many do, when optional specializations, per-weapon skills, and so on are considered), it’ll cost 3x the cost of one Very Hard skill. But if it covers only 5 to 12 clearly-countable skills, it’ll cost you only 2x the cost of one Very Hard skill.

But what of the result that you can get up to 4 skills for the price of one Very Hard skill? You could of course disallow such a narrow Wildcard skill. Or, you could allow it – perhaps stipulating that all covered skills must be originally Average or Easy. GURPS also suggests Unusual Background, and of course such skills are restricted by the GM in number and content. With those limitations in place, such “Wildcard mini” skills could be interesting. 

Wrapping up

None of the above is the least bit necessary. It’s just an exercise in putting the breadth-pricing tool to work on real examples. (Not an exciting example in the Wildcard skill case, true, as just making up something works as well.)

Mostly, the article was an excuse to play with a random thought and avoid actual work today. : / But the exercise is helpful to me as I set about putting the tool to work on some plans of my own; anyone else see interesting uses for it?