Feb 21, 2011

GURPS Optimizing: DX and Skills

This post is a continuation of the previous post on IQ and skills. When playing GURPS (Steve Jackson's Generic Universal Role-Playing System), what is the best DX score to buy to make the most efficient use of your character creation points?

DX has the same point costs and levels as IQ, but the related skills are priced differently.  Skills are only easy, average, or hard.  An easy skill costs 1 point to buy at the same level as the character's DX, an average skill costs 2, and a hard skill costs 4.  Lower levels can be bought for half the price as the next higher level, down to .5 points (so .5 points will buy a hard skill at the DX-3 level).  Higher levels cost twice as much as the previous level until the cost is 16 points (e.g.: average skill at the DX+3 level), then each level costs 8 more points than the previous level did.  Buying hard skills above one's DX score is very expensive indeed.

Here is a graph showing the probabilities of success with average DX skills by cost and DX score:

I also created a table that you can use to easily see what DX to buy after you decide how many average DX skills (or equivalent) you want and how often you want to be successful using them (success probabilities below 25% are not shown):

*Though an DX of 3 is technically optimal in these cells, a score up to 9 may be a better choice because the point cost difference is very small and DX will have impacts on game play beyond the cost of skills.

You can see that this table is much easier to use than the IQ table.  The multipliers to convert easy and hard skills to average skill equivalents do not change (they change for some inefficient arrangements, but not for any optimal arrangements).  For all white cells: easy skills count as .5 average skills, and hard skills count as 2 average skills.  For the grey cells, the multipliers vary, but are irrelevant.  

Similarly to the IQ table, we see that a score of 13 is great if you want your character to be pretty consistently successful at a good handful of skills.  A below average (10) DX score is only appropriate if you want your character to never be effective at more than a single DX skill.  Min-maxers may be tempted to trash a stat to get points to spend on the other, but I would be hard-pressed to think up a character (okay, besides a Professor Xavier type) that would be better off with a low DX.  In fact, it seems that most characters should have both a DX and an IQ of at least 13, and would not be significantly sacrificing uniqueness or wasting points.  

A nit-picker may point out that many skills have default values (e.g.: DX-6), so characters technically have lots of skills for free.  The default values are such that even with a DX of 15, the character may have a 50% chance of success with an average skill.  A DX of 17 only gives about a 75% chance of success.  High enough DX or IQ scores to make default skill levels reliable are so expensive that a character will have significant opportunity costs for other features that were passed up.  The term "Jack of all trades, master of none" comes to mind.  It is generally more effective and efficient to be a specialist, and spend the points on actually having the skills you think will be useful for you.

Feb 16, 2011

GURPS Optimizing: IQ and Skills

When playing GURPS (3rd ed.), what IQ should your character have in order to optimize your use of character creation points?

GURPS lets players buy skills for their characters at different costs depending on the levels of the characters' attributes and the difficulty of each skill.  I will focus on the IQ attribute and its related skills for now.  IQ is purchased with points, ranges from 1 to infinity (practically 20), and defaults to an average score of 10.  Increasing IQ costs 10 points for each of the first three increases above 10, then 15 points for each of the next two steps, 20 points for each of the next two steps, and 25 points for each subsequent step.  So, having an IQ of 18 costs 125 points.  A character can get points back by having a below average IQ, earning 10 points for each level below 10 (except, inexplicably, the only 5 points for level 8).

Skills are either easy, average, hard, or very hard.  There are very many mental skills.  For 1 point, you can get an easy skill at the same level as your IQ, an average skill at IQ-1, a hard skill at IQ-2, or a very hard skill at IQ-3.  Spending half a point instead of 1 reduces the skill level by one (this is the lowest you can go), or you can increase your skill level by 1 for an additional 1 point (additional increases cost more per point: 2 each for the next three increases, then 4 each above that).

To succeed at a task, you roll 3d6 (3 six-sided dice) and sum the results.  If the sum is less than or equal to your skill level, you succeed, but a sum of 17 or 18 always fails (critical successes and failures are not important for this analysis).  Given our knowledge of the distribution of results on 3d6, we can figure out the best way to spend our points on IQ and skills for our characters.

Step 1) Figure out what mental skills you want your character to have, and what percent of attempts you want your character to be successful using them.

Step 2) Consult the table:
This shows the optimal IQ to have for a given number of average difficulty level skills (or their equivalents, see notes below) at a given average success rate (I did not bother showing success rates below 25%).

*Though an IQ of 3 is technically optimal in these cells, a 9 may be a better choice because the point cost difference is very small and IQ will have impacts on game play beyond the cost of skills.

How to convert non-average difficulty skills into average skill equivalents:

  • White cells:  Easy skills count as .5, Hard skills count as 2, Very Hard skills count as 3.
  • Black cells:  Easy skills count as .5, Hard skills count as 1.5, Very Hard skills count as 2.
  • Medium grey cells with white text: Easy count as .67; Hard count as 1.33, Very Hard count as 2.
  • Light grey cells: Easy count as .75, Hard count as 1.25, Very Hard count as 2.
  • Medium grey cells with black text: conversion is variable and not worth including

Derp is a big tough guy who lets his sword do most of the thinking for him.  He doesn't need many mental skills at all.  He takes four, but he wants to be really good at them because failure makes him mad.  An IQ of 3 would let him be regularly successful with his four mental skills while freeing up the most points to spend elsewhere, like on ST, DX, and HT.  An IQ of 9 may be a small but worthwhile expense, though, depending on role-playing goals.

Brainiac McGee knows how to do everything.  He got his first doctorate at the age of 7, and went back for more.  He is never (hardly ever) wrong, so the desire success rate for everything is 98.1%.  Since he'll have more than 9 mental skills, he'll definitely be in the white cell area, so very hard skills count as 3 average skills, and hard skills count as 2.  Somewhere between 40 and 50 average skill equivalents is where an IQ of 18 is a better buy than an IQ of 17.

Bob is a suave dude.  He's got a good mix of social and professional skills.  He's not the best, but he gets by pretty well.  With a success rate target in the mid 80%s, an IQ of 13 is best for 5-14 average skills.  If he wants to be better at what he does, and has more than 7 skills, he should increase his IQ.  If he has 7 or fewer skills and wants to be better, he should just spend points on the skills.  An IQ of 13 is great for someone who wants to excel at a few core mental skills, especially if they are hard.

If you want to have a bunch of skills at different success rates, you're on your own.  This table was a beast, and I'm not making one for each of the thousands of likely combinations of skill success rates that people might want.  I recommend just planning to be really good at whatever skills you want, and working from there.  Or just have an IQ of 13 and don't think about it too much.