What is INT, and (in practical terms), what can it be used for?

I was strolling down the street the other day and noticed a logo consisting of a name and a number of dots, and for some reason, it sparked a new way of looking at INT scores, one that emphasized a practical application of the stat which would make a measurable and definitive difference of a single point of stat gain (on the 1-25 scale used by most game systems – adjust as necessary for systems like Traveler which runs on 2-12, from memory).

Champions / Hero Games represents a particularly thorny conversion problem that I’ll tackle separately a little later in the post.

Apprehension Of Number

Let’s start simple. If you look at the image below,

then you can see at a glance that there is one spot or counter. That’s just too easy.

Second Test

So let’s make it a bit harder, and see how people do. Can you count the spots below with a glance lasting 3 seconds or less?

Who got something other than 5? No-one? That’s what I expected. Anyone who can read a d6 would have no trouble.

Third Test

Let’s get harder again. Remember, 3 seconds or less.

Most people will still have succeeded. The answer, of course, is 12. But a few people will have to have counted four across and three down – each possible with a second or so of observation – and then put those numbers together to deduce 12. That’s still doable in 3 seconds, but it’s cutting it close.

Applied INT

This method of interpreting INT posits that the number of counters, coins, or whatever – when arranged in a simple pattern – that a character can count at a glance is equal to their INT score.

If the average person is defined as INT 10, then a character with that 10 can’t count this many at a single glance – but they can grasp 4 with one, and 3 with another, and multiply those to get 12 in the rest of the three-second window.

A character with INT 12 or better has no need for that – one glance is enough.

Fourth Test

It’s my experience that most RPG GMs and players rate fairly high in the INT stakes. They might not be in the genius bracket, but they are well above average – let’s suggest that their INT scores, on the D&D/Pathfinder scale, are between 12 and 18.

How many counters are depicted in the next image?

A few people could answer with a glance, but most people will have to break this down into 5 and 4 and then multiply to get 20.

Second and Third principles

The few will have INT scores equivalent of 20 or better. The majority won’t have that, and will have to have applied a process of simplifying the problem into three steps – and those steps each take as long as a single glance. That’s the Second Principle.

Furthermore, because there are two separate perception events to be performed, characters with INTs less than 10 taking this test would not be able to get the ‘5’ with a glance, they would have to actually count them. That’s the Third Principle but it’s not complete yet.

Fifth Test

So let’s look at something a bit more challenging. Same rules – let’s see how you do with this one:

What’s going on? Well, most people won’t be able to get the number of columns or rows without counting them – and it’s complicated because there are some missing counters on two rows of the pattern. I think you’ll agree that subtracting 1 from a count, or 2, is a trivial exercise – but it adds a process. So now we have five processes – count the number of token columns across, count the number of token rows, do the multiplication, count the number of missing tokens, and subtract that count from the previous total.

For the record, there are 9 columns, 6 rows, and 2 missing tokens, giving a total of 52 tokens.

• There are too many tokens for anyone to count at a glance – unless they have INT 104 (the INT score is halved because counting at a glance requires two operations – putting the missing tokens back in, then taking them away once you have a total).
• Characters with INT 18 or more might be able to tell at a glance that there are 9 columns, but I wouldn’t bet on it. Once you have more than 5 or 6 in a row, almost everyone has to count them – which means that the ‘extras’ count for more. Maybe 2 each, maybe 3 each. Simply putting them in a long row without a gap separating them into smaller groups makes a difference – instead of 9 (requiring INT 18), it’s 13 (requiring INT 26) or 17 (requiring INT 34) to count them with a glance. So we have to allow for this in our Third Principle.
• Counting: everyone starts at 1 unless they have trained themselves not to. If you can get 5 tokens at a glance – and anyone with average INT can do so – then it’s a lot faster to start counting at 5. I probably would accept an argument that characters with INT 20+ employ this trick instinctively. So that’s a Fourth Principle.
• Most people will count the number of rows correctly, but the lack of alignment makes it harder to do so with a glance. 6-at-a-glance usually requires INT 12, but those gaps would boost this by +1 or +2 token-equivalents each – so INT 14 or 16. That’s a Fifth Principle.
• Centering the columns that are missing tokens will also have thrown a lot of people off. Under time pressure, many will count two half-counters missing from each side as two counters missing on each of the affected rows, and so will get the wrong answer. Adding a couple of seconds to the time available – 5 seconds instead of 3 – is enough to relieve that pressure and overcome the problem for most people. For those with INT of 6-10, you might have to add this extra twice, and for those with INT 1-5, you might have to add it four times (exponential relationship). So that’s a Sixth Principle.
• The observant may have noticed that I’ve added a bit of shadow to the image to make the counters look more three-dimensional. That was in preparation for another image in the series that would examine how much difficulty was added by vertical stacking, but it quickly became apparent that a single glance was only enough to count a small stack, one small stack at a time. That means that a character with INT 1-5 can count or estimate one stack at a time; a character with INT 6-10 can do two (using relative heights to short-cut the second, if there’s a difference); a character with INT 15 can’t do any better; a character with INT 20 can do three stacks at once; and it would take INT 40 to do four stacks at once. But it’s not all doom and gloom – square counters placed side-by-side halve these INT increases above INT 10, so 3 columns INT 15, 4 columns INT 20, and 5 columns INT 30. 7th Principle.

It should also be pretty clear that I’ve thought very carefully about the examples that I need to demonstrate the principles!

Sixth Test

Having taken simple numbering about as far as I can – going any further wouldn’t really show anything you haven’t seen already – it’s time to move in a different direction.

In the tests so far, you will have gotten a big advantage from the structured arrangement. But Test 5 showed that this advantage is easily negated. So let’s look at that.

The image below has a number of tokens positioned randomly. At a single glance, can you tell how many of them there are?

My testing (on myself, naturally) has shown that this is right on the cusp of being too much. My single-second glances either moved up and right (missing the counter bottom right) or moved down and right (missing the counter at top right). A second glance usually filled in the missing piece of the puzzle. So Nine counters, arranged randomly, are just as hard to get right as 15 counters arranged in a pattern.

15/9 = 1 2/3.

In other words, random placement increased the INT requirement 66%, or multiplies the number of tokens that can be counted in a 3-second glance by 0.6.

But that’s a fairly inconvenient number – so let’s make it +50% INT requirement or 2/3 the number of counters at a glance.

That specific impact is my Ninth Principle,, while the general statement that ‘complications multiply the INT requirement by ‘a factor’ is the Eighth Principle.

This should come as no surprise – the 52-counter Test as good as demonstrated the general principle – but this makes it explicit.

As a confirmation, I simplified the problem:

Seventh Test

Taking one or more counters away should make it a lot easier to count them at a glance, despite the random placement (which I re-randomized for this test):

I still found myself getting “six +1” from a glance, but a single glance was enough to get the correct total. The correct answer is 7 tokens, of course.

7 = INT requirement of 14 × 1.5 = 21. That’s a little high, but I wasn’t quite getting them at a glance. 6 = INT requirement of 12 × 1.5 = 18, which is about right.

So I consider this validation of both the general principle and the specific +50% requirement.

Eighth test

The job is also made easier by the counters all being the same size. So let’s see what happens if that is no longer the case.

How many did you get at a glance? My results were “4+1 = 5”. That +1, as demonstrated in Test 7, is significant, but even more important is that this is the wrong answer. The correct answer is 6, not 5, and this time, a second glance wasn’t enough – the problem was that my brain wasn’t associating the big one as being the same as the smaller ones, I had to consciously remember to count it.

Adding it in is trivial, as noted earlier – you just have to remember to do it. That’s an extra process, so the +2 second rule comes into play with a second ‘complicating factor’, and suggests that a third complicating factor would add twice that, or another 4 seconds, to the time requirement.

Okay, so that takes care of the ‘error correction”, and means that I can turn my attention to analyzing the “4+1” part. The impact of the diversity of sizes was to make what was a “6+1” into a “4+1”.

6 / 4 = 1.5, or +50%.

There it is again. So two complications = two +50% INT requirement increases, compounding – or 4/9 the capacity to count at a glance. Again, let’s simplify the latter to 1/2.

Ninth Test (Virtual)

This test demonstrates a moving window, so that you can’t see the whole image at once – presuming the movement takes 1 second to show the whole image, you would only have the equivalent of a single glance to get a result. If it takes 3 seconds, you would have enough time for two, and putting them together, which is the minimum requirement. The slower the movement, the more time you have to deal with the situation and get an answer.

I wasn’t able to generate the series of animations that would be required to actually demonstrate this – I made do with a piece of scrap paper into which I cut a window, which I then moved at various speeds to get a sense of the impact. The image shown is illustrative only.

My estimate is that it would NOT take +4 seconds, but WOULD take +2 seconds – a total of 7 seconds, not 9. So that separates additional difficulties (Sixth principle) into two compounding effects – one based on INT and one on the number of difficulties, and inserts an additional clause to the principle: additional difficulties multiply by whatever the indicated INT-based time adjustment is to get the net increase.

Putting it all together

The principles, as they are currently arranged, are clunky and ill-defined. With a little effort, it should be possible to compact and compress them down into something more useful – so let’s do that before progressing. To start with, i divided them into General Principles and Specific Counting Principles, the latter only applying to this specific task.

General Principles

1. Characters can apply their INT score to tasks, which are measured in ‘Operations’ or ‘Ops’.
2. Tasks use a defined number of Ops per Task.
3. If a character’s Ops count is not sufficient to complete the task in two or less glances, it must be broken down into sub-tasks that are within the character’s capabilities.
4. The number of sub-tasks dictates how long the Task takes:
   1. An at-a-glance task takes 1 second.
   2. A two-sub-task task takes 3 seconds – one for each sub-task and 1 to integrate the results.
   3. If two sub-tasks are not enough, a time penalty applies. This time penalty is equal to the product of an INT-based time multiplied by the number of additional sub-tasks.
      • INT time penalty for INT 11+ = 1 second.
      • INT time penalty for INT 6-10 = 2 seconds.
      • INT time penalty for INT 1-5 = 4 seconds.

Perception / Counting of objects

1. Characters can count objects at a glance in an ordered pattern for 1 Ops per item.
2. If they have insufficient Ops to complete the task in a single glance, they have to grasp the number of columns and rows and combine the results for a 3-second glance. Each of these sub-tasks has an Ops cost of 2 pts.
3. Characters with INT 20+ get an advantage in that they can start counting at INT/2 entries in the row/column.
4. It takes 3 seconds to count INT/2 entries in a column or row. This is referred to as the Base Count.
5. Gaps are considered 2 or 3 ‘entries’ in a column or row count.
6. If items are stacked in a third dimension, characters with INT 1-5 can count / estimate 1 stack at a time; characters with INT 6-20 can count / estimate 2, characters with INT 21-40, 3, and characters with INT 40, 4.
7. If the stacks can be placed next to each other and are of a shape suitable for comparisons of stacking to be made visually, these change to INT 1-5, 1 stack; INT 6-14, 2 stacks, INT 15-19 3 stacks, INT 20-29 4 stacks, and INT 30+, 5 stacks.
8. Every complication to the count increases the Ops required for a task by +50%, compounding.
9. Complications include: Random / disordered arrangement, significant size variations, windows blocking perception or other animated phenomena, three-dimensional stacking, and a column or row count that is more than the Base Count in line.
10. An incorrect answer can be identified by spending an additional time unit (refer general principles) on verification. This also counts as a complication for the purposes outlined above.

So far, so good. But I promised practical application, and while being able to instantly count the number of steps in front of a building a-la Sherlock Holmes, or the number of poker chips in a stack, is a neat party trick, I doubt that it will be of practical value very often.

So, let’s talk about Mathematics.

Maths

Depending on the game system, it may or may not require a specific skill to utilize INT this way. If it does, the processes outlined below still apply but the character will have extra Ops to use – see “Applied Skills” later in the article.

Let’s start with a calculation that is pretty much at-a-glance for most people of gamer caliber – in fact, anyone over INT 10:



A Fourth Addition Element

Adding a fourth element to the addition and for most people, it becomes a two-step operation – usually the first three at a glance and the fourth then has to get ‘read’ separately and integrated.



That means that each element to be added in a column of numbers normally consumes 4 Ops to do at a glance. As before, if you have to break the task up into two or more separate sub-tasks, it takes additional time.

Thus, INT determines how many single-digit numbers you can add up at a glance:

• INT 1-4 = 1, and presumably the arithmetic is done on fingers and toes.
• INT 5-8 = 2.
• INT 9-12=3.
• INT 13-16=4.
• INT 17-20=5.
• INT 21-24=6.
• INT 25-28=7.

Each additional number beyond this maximum adds 1 to the time-count, plus one for the integration of results.

But there are complicating factors to consider.

Totals more than 10

If the total comes to more than 10, it takes more mental capacity to do the calculation. We’re just not as good at instinctively grasping the total.

There are multiple ways that this can be broken up. My instinctive method is to add the two largest numbers together (7+6=13) and then add the 1 and the 4 together (1+4=5), and then put the totals together (13+5=18) – but some people will do the 1+7 first. while others will instinctively notice that 6+4=10 with their first glance.

Whatever the method you use, the mechanics so far as Applied INT are concerned are the same: Each element in a total greater than 10 has an Ops requirement of +1, and each element greater than the resulting ‘at a glance’ total adds +50% to the total:

• INT 1-5 = 1, the arithmetic is done on fingers and toes.
• INT 6-10 = 2.
• INT 11-15=3.
• INT 16-20=4.
• INT 21-25=5.
• INT 26-30=6.

… and so on.

So, four numbers, total more than 10:

• INT 1-5 = 1, plus 3 more = 5 × 1.5 × 1.5 × 1.5 = 16.875 = 17 Ops for at a glance; so +3 time units of 4 × 1.5 × 1.5 × 1.5 sec each = 13.5 sec each = (3+40.5 = 3+41) = 44 sec.
• INT 6-10 = 2, plus 2 more = 5 × 1.5 × 1.5 = 11.25 = 11 Ops for at a glance, but 2 +1 sub=processes is enough to solve the calculation, so 2 × 1.5 × 1.5 = +9 sec each additional sub-process, giving a total of 3+18=21 seconds to solve the calculation.
• INT 11-15=3, plus 1 more = 5 × 1.5 = 7.5 = 8 Ops for at a glance. Total time = 3 seconds.
• INT 16-20=4, so a single glance of 1 second is still enough.
• INT 21-25=5, so a single glance of 1 second is still enough.
• INT 26-30=6, so a single glance of 1 second is still enough.

Upping The Ante: numbers greater than 10

In the calculation below, I’ve added a 5th element, and three of them are double digits. Obviously, the result is going to be two digits, maybe even three (depending on how big the numbers are). Each element that’s more than 1 digit counts as two elements.

So the base number of Ops per element is 5 × 1.5 × 1.5 × 1.5 (for three double-digits) × 1.5 (for a total greater than 10) = 25.3125 =25 Ops for at a glance. Only characters with INT 25 could do so, everyone else will have to break the task up.

And it now matters what sequence you do the math in. My mental process instinctively does the easiest part first (3+8=11), then the next easiest part (11+12=23), then the next easiest part (23+23=46), and then the hardest part (46+34=80). But my mental capacity is enough that the first two of those (three numbers) can get done at a glance, so it only takes me 2 additional sub-tasks at 2 seconds each, or a total of 7 seconds, to do the mental arithmetic – and most of it (the four additional seconds) is devoted to that last calculation.

• INT 1-5 = 1, plus 4 more = +3 time units of 4 × 1.5 × 1.5 × 1.5 × 1.5 sec each = 20.25 sec each = (3+81) = 84 sec.
• INT 6-10 = 2, plus 3 more, so 3 additional sub-tasks at 2 × 1.5 × 1.5 × 1.5 = +6.75 sec, giving a total of 3+20.25 = 23 sec.
• INT 11-15: but adding two numbers both >10 at a glance is now possible – Ops count of 5 × 1.5 × 1.5 = 11, and the initial 3+8 is an at-a-glance 1 second calculation. Three sub-tasks thus gets this and the next two calculations done in the initial 3 second burst, leaving 2 more at 2 × 1.5 × 1.5 = 4.5 sec each, or a total of 3+9=12 seconds.
• INT 16-20=4 so the first 4 numbers get totaled in the initial 3 seconds, +1 sub-task at 4.5 seconds as above, for a total of 7.5 seconds.
• INT 21-25=5, so a single glance of 1 second is still enough.
• INT 26-30=6, so a single glance of 1 second is still enough.

A more serious calculation: Subtraction

Here, every number has at least two digits, two of them have three, and there’s a negative number i.e a subtraction, buried in the middle. Unsurprisingly, the triple digits are an extra complication, and the double digit subtraction is another. What’s more, any non-trivial subtraction takes twice as long as an addition, so the subtraction counts not as a 5th element, but as a 6th element as well.

At a glance: 5 × 1.5 ^ 6 elements × 1.5 × 1.5 (triple digits) × 1.5 (result greater than 10) × 1.5 (result greater than 100) = 288.3251953125 Ops. NO-ONE is solving this at a glance unless they have some freakish ability (Lightning Calculator exists in the Hero System and GURPS, but not in several other game systems).

Fortunately, our powers-of-ten maths permits us to deal with each column separately – so this is 3 calculations:

1+3+5-4+5 = 10, keep the zero and carry the 1;
1 (carried)+3+2+8-3+3 = 14; keep the 4 and carry the 1;
1 (carried)+1+2 = 4; integrate the total to get 440.

Trying to do the math any other way is a LOT slower, as the trends from previous calculations clearly showed, and the at-a-glance made clear.

First calculation: 6 elements, all single digits, but we can save one since 1+3=4 and there’s a -4 in there – so (1+3), then (-3), then (5+5) to a result. That’s 4 sub-tasks. Some characters will be able to do this at a glance.

Second calculation: 6 elements, all single digits – but the last element is a 3 and there’s a -3 right above it, so (3-3), then (2+8=10), (10+1 carried=11), (11+3=14). Again, four sub-tasks. Same.

Third calculation: 3 elements, all single digits. Many characters will be able to do this at-a-glance.

Fourth calculation (integration of results) – include in third calculation for an additional sub-task.

• INT 1-5 = 1. Calculation 1 is plus 3 more sub-tasks= +3 time units of 4 × 1.5 sec each = +18 sec total = (3+18) = 21 seconds. Calculation 2, same as calculation 1, = 21 seconds. Calculation 3 is 1 + 1 more at 6 seconds = 9 seconds. Total: 51 seconds.
• INT 6-10 = 2. Calculation 1 is plus 2 more sub-tasks at 2 × 1.5 = +6 seconds for both, so 3+9 = 12 sec. Calculation 2: same as calculation 1, 12 sec. Calculation 3 is covered under the 3-seconds / 2 sub-tasks rule. Total = 27 seconds.
• INT 11-15 = 3. Calculation 1 is +1 sub-tasks at +6 seconds = 9 seconds. Calculation 2, same as calculation 1. Calculation 3 is 3 seconds. Total = 21 seconds.
• INT 16-20=4. Calculations 1 & 2 & 3 all take 3 seconds each, for a total of 9 seconds.
• INT 21-25=5. All three calculations are at-a-glance, so 3 seconds total.

On Paper

Let’s calculate the time required for totaling 40 two-digit numbers.

The total might be less than four digits, but it probably isn’t – (40 × 100 =4000, -20 (max is 99, not 100) =3980; average = 1990; 999/1990 = 50.2% chance enough numbers are low enough that the total is 999 or less). However, an average of 1990, divided into 4 columns, means that each column is likely to be only 3 digits in length.

This would be a lot easier to do it on paper, and that’s not something we’ve looked at – how much faster is it?

For a comparison, we need to work the problem both ways. Fortunately, this is already broken into 4 calculations of 10.

Doing it the hard way: 4 × 9 = 36 sub-processes, plus 3 more integration steps, plus trying to remember each total. Okay, I’ll let you write those down. Or, one at a time, 39 sub-processes, no integration, but there are massive penalties for complications – all 2 digits, probably 4 digit answers. No, that’s not viable, there’s too much overhead. 36+9 it is.

I’ll bunch the calculations together even though that’s harder to read.

At a glance: 5 Ops (base) × 1.5 ^ 10 (all double-digit numbers) × 1.5 × 1.5 (triple-digit results) = 648.73 Ops. Not going to happen unless the character has a freak talent.

• INT 1-5 = 1. Calculation 1 is plus 8 more sub-tasks= +8 time units of 4 × 1.5 × 1.5 × 1.5 sec each = +13.5 sec each = (3+108) = 111 seconds. Calculations 2, 3, and 4 are the same. Calculation 5, the integration, is 3 sub-tasks at 4 × 1.5 × 1.5 × 1.5 × 1.5 = +20.25 seconds. Total:444+20=464 seconds = 7 minutes 44 seconds. And an incredibly high chance of making a mistake. And that time is probably being generous; if I assume that there’s an additional penalty because we have ten numbers in a row, it inflates to 686 seconds, or 11 minutes 26 seconds. Working flat-out. Most people can’t concentrate that hard for that long, and a low INT character would find this especially challenging. So that’s probably another 2 complication levels, elevating the total to 1519 seconds, or 25 minutes, 19 seconds. Finally, remember that this represents 39 INT rolls – maybe at +2 because the character can take his time, but INT is not his strong suit – the odds of multiple mistakes along the way are pretty enormous. In conclusion, then this is probably beyond the abilities of such a character.
• INT 6-10 = 2. Calculation 1 is plus 8 more sub-tasks at 2 × 1.5 × 1.5 × 1.5 sec each, × 1.5 (ten numbers in a row) × 1.5 (concentration) = +15.1875 seconds each = 121.5 seconds, +3 seconds = 124.5. Calculations 2, 3, and 4 are the same. Integration is 3 sub-tasks at 15.1875 × 1.5 × 1.5 = 34.17 seconds each. In total, 601 seconds, or 10 minutes 1 second, and again with virtually zero confidence in the answer.
• INT 11-15 = 3. Calculation 1 is +7 more sub-tasks at +15.1875 seconds each = 106.3125 seconds, +3 = 109.3125. 2, 3, 4, are the same, so 437.25 seconds total, Integration is 3 sub-tasks at 34.17 seconds = +102.51 seconds. Grand total = 540 seconds – which is 9 minutes. If you did it enough times to get three totals that agrees, you’d be reasonably confident that it was error-free – but that could take hours.
• INT 16-20=4. Calculation 1 is +6 sub-tasks at +15.1875 seconds each = 91.125 seconds, +3 = 94.125. Calculations 2, 3, and 4 are the same, so 376.5 seconds. Integration is still 3 sub-tasks at 34.17 seconds = 102.51 seconds. Grand Total = 479 seconds, or 7 minutes, 59 seconds – call it 8 minutes. But, for the first time, there’s a fair likelihood of getting the right answer at the end of that 8 minutes. You would probably do it again to check your work, though.
• INT 21-25=5. Calculation 1 is +5 sub-tasks at +15.1875 seconds each = 75.9375 seconds, +3 = 78.9375. Calculations 2, 3, and 4 are the same, so 315.75 seconds. Integration is still 3 sub-tasks at 34.17 seconds = 102.51 seconds. Grand Total = 418 seconds, or 6 minutes, 58 seconds – use 7 minutes. And, for the first time, you would be confident in your answer first time around.

Now, the easier way: 4 calculations of 10 single digits, a 2-digit carry, so 4 more calculations of 10 single digits and the carry. But there’s a trick that makes it even easier, since we’re doing this on paper.

Cross out all the zeros in the column you’re adding up. Do all the digits that add up to 10, and cross those off as you go as well. These multiple single-digit 2-item sums are all going to be at-a-glance, pretty much, and they vastly reduce the complexity of the rest of the calculation by eliminating elements.

A 7, but there are no 3s – skip.
8 & 2 make 10.
4 and 4 and 2 make another 10.

And here’s what’s left:

That’s a single addition of 7 and 5. Column total = 20+12=32, determined with just 4 sub-processes.

Repeat the trick with the tens column:

7 and 3 (carried) = 10. 8 & 2 = another 10. 5 and 5 = third ten. 6 and 4 = a fourth ten. 7 and another 3 = fifth 10 There’s even less left over.

And there’s no doubt about the accuracy because these small calculations are so simple. So the first string of 10 double digits total 572.

For characters of INT 1-5, these small calculations will take 3 seconds each, plus 14 seconds for the final integration – a total of 44 seconds.

For everyone else, 10+14=24 seconds. But take an extra 20 seconds, no need to rush.

No need to continue – the results are blindingly obvious at this point. Instead I’ll leave the other three columns for readers to practice on. (BTW: When I’m adding time – minutes or seconds – I look for total of 10s and 6’s).

5. Doing maths on paper or a blackboard or whiteboard or whatever – doing it written down – divides the Ops requirements by 2, round down, minimum 1 – unless there is some identifiable trick that makes the math easier, in which case it’s divide by 4, round up, minimum 1. This divisor gets applied to the Ops cost per process.

Troubles Multiplied

Multiplication is all about technique. If you know how, it’s not hard at all, especially if you can do it on paper.

It doesn’t take much longer than addition, really – on paper. Multiplication has a cost of 6 ops for the first one, doubling for each additional multiplication (if you’re doing them mentally).

There are shortcuts that I use all the time. Doubling is easy, tripling is a little less so, quadrupling is doubling twice, five-fold is add multiply by ten and halve, times six is x2 x3, times seven is times 10 – the original number three times (but still the hardest calculation on this list), times eight is x2 x2 x2, times 9 is times ten minus the original number, and times ten is trivially easy.

But the calculation offered above is a little more complicated than that, because it is multiplying three numbers together.

You could go 3 × 8 = 24, and you’re left with 23 × 24 – which is 4 at-a-glance calculations, plus the first one. On paper, you can solve that as fast as you can write – 3 × 4=12, 2×4+1 carried=9, write a 0, 2×3=6, 2×2 = 4, add 490+92=582.

If I were doing it mentally, I’d employ the shortcuts and look for the most efficient route: 3 × 23 = 69, double, double, double again. It takes about twice as long as doing it on paper – for this particular calculation.

Division

Mental division can be hard. Even very hard. Making life easier is the fact that errors also shrink in proportion to the divisor, so you can approximate and generally get away with it.

There are also some shortcuts, but they are a bit trickier.

• /2 is easy.
• /3 can be slightly easier – add up all the digits, keep going until you have a single digit. If that’s 0, 3, 6, or 9, the original number is evenly divisible by 3; if there’s a remainder, that’s also the remainder of the original. Then see below for the ‘perfect divisibility’ technique – it’s so simple, you won’t believe it!
• /4 is /2 /2.
• /5 is x2 / 10.
• /6 is /2 /3.
• /7 is a royal pain. It’s usually faster to do /6 and /8, add, and /2. This isn’t quite accurate – it gives 49/48 of the correct answer – but I can usually live with that margin of error. You can even minimize it a bit more by always rounding down.
• /8 is /2 /2 /2.
• /9 is /3 /3 but that’s also a bit of a palaver. Sometimes it’s easier to average /8 and /10 and live with the error – 81/80ths of the correct answer. You can estimate the error by dividing the original number by 80 – you’re only really interested in the integer results. You can also check your results by dividing by 3 and repeating the sum-the-digits trick, but that’s usually not worth the effort, either.
• Divide by 10 is easy.
• Divide by 11 is messy, but you can get within 1% of the correct answer by dividing by 10 and subtracting 1/10th of the result. You will be 1% low, but rounding up will usually more than compensate.
• Divide by 12 is /4, /3.
• Divide by 15 is x2, /3, /10.
• Divide by 16 is /2, /2, /2, /2.
• Divide by 17 – I can’t remember ever having to do so. I don’t have a shortcut for this. It’s going to be about 6% less than the division by 16, for whatever that’s worth.
• Divide by 18 is /3, /3, /2.
• Divide by 19 – another painful calculation. No satisfactory shortcut
• Divide by 20 is /10 / 2.

So let’s look at the problem stated above. 532 / 3, to start with: 5+3+2=10, 1+0=1, so there will be a remainder of 1, and 531 is what we should be dividing. That’s 300/3 + 231/3.

The perfect divisibility trick

Here’s a peculiarity: run through the multiples of 3 and note the final digit each time: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. Strip out those tens digits and you get 3, 6, 9, 2, 5, 8, 1, 4, 7, 0. Let’s arrange those: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. So the final digit of a number is diagnostic of the division by 3 – there are No repeated digits in that list!

300 / 3 = 100; 231 / 3 = 21 / 3 + 210 / 3. so 532/3 = 177 1/3.

177 / 3?

1+7+7 = 15; 1+5 = 6 – so perfect divisibility by 3.
177 – 27 = 150. So 177 / 3 = 50+9 = 59.

59 / 2 = 29.5. But there would be a small fraction left over from the previous calculations – enough to tip the rounding to round up. Call it 30. Or 29 and a remainder – whatever’s most convenient.

Higher Maths

The same principles can reveal a character’s facility with higher maths, simply increasing

There is a progression to the higher math elements. Each step of the progression adds 1 to the cost of that operation, plus a base value of 6 Ops.

• Algebra = +1
  • Exponent 2: Squares = -2 – this is just multiplication
  • Exponent 2: Square Roots = +1
  • Exponent n, greater than 2 = +2 per, or per part thereof.
  • Areas, simple shapes = -1
  • Areas, complex 2-dimensional shapes = +0
  • Areas, three-dimensional shapes = +2
  • Volumes: simple shapes = +1
  • Volumes, complex 3-dimensional shapes = +3
  • Each additional dimension = +1 to the above
• Basic Calculus
  • Simple Differentiation = +2
  • Simple Integration = +3
  • Complex Differentiation (involves math below this point in the list) = +4
  • Complex Integration (same definition) = +6
  • With discontinuities: +1 to the above
• Trigonometry
  • Basic (2-dimensional) with right-angle triangles= +2
  • Basic (2-dimensional) with non-right-angle triangles = +3
  • Complex (3-Dimensional) = +4
  • Additional dimensions over three = +5, base, plus 1 per extra dimension
• Logarithms = +3
• Three dimensional vector sums = +3
• Exponentials = +4
• Probability
  • Simple = +4
  • Factorials = +4
  • Complex, 2 independent variables = +5
  • Complex, 2 dependent variables = +6
  • Additional variables = +1
• Harmonic Motion & Elasticity problems = +5
• Partial Differentiation, Partial integration = +5
• Fibonacci Numbers, Primes, etc = +6
• Multi-variable Analysis & Simulation = +7
• Higher Applied Math = +8, +1 per additional difficulty
• Higher Theoretical Math = +10, +1 per additional difficulty
• Unsolved Mathematical Problems = +12, +1 per additional difficulty

The reader will appreciate that I didn’t want to bog down in specifying a lot of exotic math types that they will never have heard of, so the last three are fairly generic and the GM gets to assign whatever he thinks appropriate, starting at the base value.

Everything prior to those I’ve had occasion to use or study. For example, at one point I became really interested in studying that rate of change of probability with increasing numbers of dice – there’s a lot of this sort of math buried in the Sixes System.

Rate of Change is differentiation, in this case of probability, with each additional dice after the first being an additional variable. So Rate of change of probability = 6+1 (algebra) +2 (simple differentiation +4 (simple probability) [+1 per additional dice] = 13; 2-dice=14; 3-dice=15; 4-dice=16, and so on. Which seems really impractical to do when you’re getting up to 10 or 15 dice!

But each step up that chain is a partial solution to the next problem up, and don’t forget the ‘doing it on paper’ modifier, and it becomes a lot more practical. Once you’ve identified a pattern of change from one number of dice to that number +1, the whole world opens up before you, and solving the individual problems become much simpler, because you don’t have to ‘reinvent the wheel’ each time..

Quite honestly, the housing price calculator (see: The Price of Bricks and Soil (and more)) with it’s multi-variable analysis – some of them dependent, some independent, and some partially both – was a little more difficult.

Mysteries & Puzzles

Okay, so now things begin to get a bit more interesting. I mean, who really cares how long it will take a character to solve a maths problem? On the rare occasions when it’s necessary, most GMs (including me) will simply pluck a number out of the air that seems reasonable, and move on.

Hopefully, the math tricks and shortcuts will be worth reader’s time.

But now, we’re looking at a question that’s not so easily answered, and one in which the difference between what the player is capable of, and what the character can do, matters massively – with the GM expected to make up the difference, without messing with player agency, and while keeping the game-play interesting and role-playing, not roll-playing.

Let’s say that the adventure revolves around an Agatha-Christie style murder-mystery, the PCs gather clues and have to then use those clues to eliminate the suspects who are innocent in order to apprehend the guilty party.

If we knew the INT score of the player of the smartest character when it comes to solving this sort of puzzle,, we could simply let the player work at his own pace while applying a conversion factor to go from ‘real time’ to ‘game time’. We could then use that conversion factor to schedule plot developments in ‘game time’.

We have the basic tools – more than enough of them to actually test a player’s applied intelligence. ‘Total a column of ten 2-digit numbers’ would work fairly well, for example. We then calculate how long it would take their character, and we have an instant conversion rate from one to the other. Or perhaps some of the simpler mental arithmetic challenges.

It would probably be better to run a number of small tests and average the results, that’s up to you.

Solving mysteries – Ops and Sub-tasks

Analyzing each clue to determine its significance relative to the bigger picture is a sub-task requiring 1 Ops points. Integrating that clue with the state of the investigation to this point is a sub-task requiring 2 Ops points. So that’s a total of 3 Ops points and two sub-tasks per clue.

Because clues tend to be more abstract than numbers and numeric operations, the time penalties are increased × 2.5 to 5 seconds and 10 seconds, respectively, rising by 1 second for each clue after the first.

Number Of Clues

As a general rule of thumb, it takes 1 clue to eliminate 1 suspect. At least, it would if no-one lies or tries to fabricate an alibi (which is a specific kind of lie, in my book).

It takes an additional clue to prove that someone is lying and another additional clue to determine the motive for the lie, and it may well take a third additional clue to establish the truth – sometimes, that 3rd extra isn’t necessary.

On top of that, the GM is likely to throw red herrings across the party’s path, each of which needs still another clue to identify. Another way to phrase this is that some of the clues may be misleading and need another piece of information to clarify their significance. That adds another clue and another sub-task to the total, per red herring.

And, just to make matters worse, each clue is probably buried amongst a mass of other information, with the rest being irrelevant – so you often need to analyze three or more pieces of information just to determine what’s an actual clue and what isn’t. That adds one more sub-task per clue.

Furthermore, not all the clues may be available – someone (either the criminal or someone protecting someone else for whatever reason) may have actually destroyed key evidence.

Finally, mysteries that would be easy to solve if the information was arranged and delivered in logical sequence become a lot harder when the clues are delivered in a more random and realistic sequence.

I’m reminded of the episode of MASH in which BJ Hunnicutt is sent a mystery novel, The Rooster Crows At Midnight with the last page missing, and the whole camp tries to figure out whodunit.

Put all this together and you might be forgiven for thinking that no mystery can ever solved! But that’s no fun.

The Process Of Solving A Mystery

1. Crime Scene. What would be required to actually carry out the crime?

2. Initial Suspects. Rule out – provisionally – anyone who doesn’t possess the attributes necessary.

3. Interview Suspects. Analyze their statements to determine which information is relevant and which is chaff.

4. Analyze clues for verifiability. Verify everything that you can. Anything that can’t be verified is a possible lie.

5. Investigate possible lies and deceptions. Now that you have better questions, re-interview suspects.

6. Look for pieces of the puzzle that don’t fit. If all the evidence except one indicates that a person is guilty, focus on verifying that one; if you can do so, then some of the evidence against that person is a red herring. Theorize that each, in turn, is a red herring and look for a way to use the evidence, or additional evidence, to test that theory.

7. No Red Herring exists without someone attempting to construct a false narrative to cast blame on that person, and that means a lie or misdirection. Look for evidence of falsification and motives for doing so. If you find it, you can eliminate that red herring.

8. Means, Motive, Opportunity. Focus on these one at a time (and not necessarily in that order). If you get stalled on one front, turn to one of the others.

9. If evidence is missing / destroyed, treat that as a separate crime committed in furtherance of escaping justice. This is often a simpler puzzle to solve, and successfully doing so will often tell you what the missing evidence was.

10. Construct a set of theories of the crime in which each of your remaining prime suspects is the guilty party. Look for ways of testing those theories. For a theory to pass, it has to satisfy all three evidentiary legs listed in 8. Failure to pass doesn’t mean that the theory is necessarily wrong – but it does make it possible wrong. Determining the case in respect of a theory is the purpose of testing that theory.

11. One or more theories may pass, becoming your leading theories – test those looking for ways to disprove them.

12. Continue to narrow your field of prime suspects and eliminating theories. Each theory you bust may eliminate a prime suspect, each suspect that you eliminate also busts all theories based around them.

13. If you run out of theories or prime suspects, it usually means that you have eliminated someone you shouldn’t, often as a result of a flawed assumption. Double-check everything looking for both.

14. Ultimately, there will (hopefully) be one single theory (and only one) that satisfies the Means, Motive, Opportunity triangle and explains away any apparent reason why they could not have been the culprit. That is the solution.

As a Function Of Intelligence

Each of these 14 logical stages is a separate task in its own right. They do not have to be conducted concurrently, but neither do they need to be conducted in isolation. Breaking things down into their stages of investigation in this way is the equivalent of the simplification into fewer and/or simpler sub-tasks that was demonstrated in some of the math examples.

The higher the INT of the character, the more they can do simultaniously, and the faster the character can reach a conclusion. The total number of sub-tasks remains the same, but the number of them that can be processed at once makes the smarter character more efficient.

A critical quantity is the number of suspects. A high-INT character might be able to consider them all concurrently, whereas someone less-gifted might have to do so one or two at a time. Everything else is proportionate to the number of suspects, which is why heavy emphasis is placed on reducing that number as quickly as possible in the process.

There’s more that could be said – I could do a breakdown by INT, for example – but time is beginning to press, so I’ll leave it at that and move on.

Plans

Characters make plans all the time. Each step in a plan is a sub-task to achieving the overall objective. Planning a sub-task requires 4 Ops, plus 1 for each sub-task after the first in the unified whole.

The higher the INT, the more sub-tasks can be planned in advance; when you run out of available Ops points, the remaining sub-tasks become vague and non-specific.

The Unpacking Example

Unpacking after my forced relocation back in March was troublesome. Quite often, things could not be stored where they were eventually supposed to go, because I needed the empty space to unpack something else. In the meantime, the things to be unpacked had to be kept in storage. A lot of my planning for the task involved creating the space needed to accomplish the next step.

Each step in the process therefore became dependent on the successful completion of the previous step. To unpack the fiction library, I needed to have unpacked the non-fiction library. To unpack the magazines, I needed to have unpacked the fiction library. To unpack the non-fiction library, I needed to have unpacked the “to read” library. To unpack and set up my office space, I needed to have finished assembly of all the bookcases. And so on.

It was not dissimilar to solving one of those sliding-panel puzzles. There was only so much operational space to employ at a time, which limited the size of the process that could be carried out, breaking the overall task into sub-steps that would fit within the space available. Right now, the end is finally in sight.

Viewed from another perspective, to unpack something you need (1) to be able to get to where it is stored; (2) a location in which the contents will be stored when they are unpacked; (3) space to unpack and organize the contents of one or more boxes; and (4) a place to store the empty box. Put all four steps together and the contents in question go from ‘packed’ to ‘unpacked’. And the space used to store the previously ‘unpacked’ becomes empty and available for some other purpose – temporary storage space or working space or whatever.

You can get some impression of the scale of the problem by the fact that there were more than 500 boxes to be unpacked. Most of them were relatively small in size because of limitations of physical capacity. And a big complication was needing the space to assemble the furniture that would eventually be filled with the contents of those boxes. Which in turn was a function of the planned layout of the new residence.

Characters Planning

It’s exactly the same when a PC makes a plan. Or rather, when the character’s Player makes a plan. The question is, how much assistance does the GM need to provide? How much will ‘go right’ simply because the GM is able to presume that a character of that level of INT would get that planning right – and how much is he justified in having things go awry because the character’s INT could not anticipate every contingency?

To answer these questions, you need to break the main plan down into its necessary sub-steps, at least in general and vague terms. The number of Ops points available gives the maximum number of sub-steps that can be employed, but most tasks won’t need anywhere near that number.

Zenith-3 Mission Example

Team Zenith-3 were handed the problem of intervening to stop a bunch of domestic-US terrorists from utilizing a black market nuclear weapon that they have purchased from a Russian General. At it’s simplest, this is a fairly basic operation:

1. Contact Agent
2. Get Specifics of the mission
3. Plan the mission
4. Carry out the plan.

In-game politics had to be taken into consideration. The PCs are not welcome in the country where all of the above had to take place.

So they had to adopt new identities. And enter through Central America. And travel through post-Ragnarok Central America and post-Ragnarok Mexico to get to that country.

But to enter Central America, they needed the support of Brazil, which is under the control of an enemy. So they had to go to Brazil and obtain that assistance.

So now, the plan looks like this:

1. Adopt new identities.
2. Brazil.
3. Get Local Assistance (i.e. navigate Brazilian Politics)..
4. Central America. Insertion.
5. Meet Guide arranged by the Brazilians.
6. Travel through Central America.
7. Travel through Mexico.
8. Leave the Guide.
9. Enter the target country.
10. Contact Agent
11. Get Specifics of the mission
12. Plan the mission
13. Carry out the plan.

Steps 1 through 9 were a lot of work to carry out for a one-off mission, and it seemed more prudent to take advantage of that effort to establish a longer-term operation that could not only deal with the immediate, known, problem, but could also handle other problems as they arose.

So the plan was modified to incorporate this as part of the mission.

10. Select a region to contain ‘home base’.
11. Search the region for a suitable dwelling to use as a ‘home base’.
12. Purchase said dwelling.
13. Adapt and install facilities to make it an actual home base.
14. Contact Agent.
15. Get Specifics of the mission
16. Plan the mission
17. Carry out the plan.

Additional mission requirements were identified and inserted. Establishing the new identities and forging a working relationship with the local police forces, for example. Arranging the finances need to purchase the property and refurbish the resulting base. Settling on the parameters of the search. Obtaining vehicles to carry out the search. Establishing some operational procedures for performing missions in the target country.

A big one was that there would not be enough time in the schedule to achieve everything. So that added a time-travel item to the list. Deciding how far back to time-travel. Avoiding paradoxes as much as possible and working around the ones that were inevitable, like being in two places at the same time.

And so on. Few of these could be planned in advance; each one had to be planned out as it became imminent. And there were unexpected developments – in each region that they traveled through, they would have to earn the right of passage from the local ruler. Their guide would initially be, officially, an enemy – they had to keep him or her in the dark as to their true purpose (by the time they parted ways, they had cemented a loose alliance with him and come clean about their primary mission).

Here’s the key point: most of these steps weren’t aimed at the primary mission (the terrorist plot) or even at the secondary mission (establishing a base of operations); they were necessary simply to get the PCs into a position to execute the next step.

You can read a lot more about what actually happened and why in the series A Long Road (be warned, it’s very long – about the length of a typical paperback novel).

Analyzing The Process

This is a great example of the planning process because it demonstrates the principles of Step-wise Refinement and Iteration, explained in more detail in Top-Down Design, Domino Theory, and Iteration: The Magic Bullets of Creation.

In essence, start with a simple overall plan, factor in the complications one at a time even if you don’t know what the specifics are going to be, yet, and repeat this simple process until you’ve covered everything you can think of.

This takes a hugely-complicated plan and breaks it down while not pushing anyone’s INT capabilities too far. As each step gets encountered, it then gets broken down further into specifics.

Flawed Plans

Very few plans can be made without an error creeping in, somewhere. There will always be unexpected plot twists and surprises. It doesn’t matter if it’s a PC plan or an NPC plan.

The more of your INT that you aren’t using for a broad plan, the more you can anticipate things going wrong and preparing contingency plans.

That was the whole thesis of Making a Great Villain Part 1 of 3 – The Mastermind, in which I looked at ways that the GM could run NPCs who were far smarter than the GM himself.

Early In A Plan

When a plan is just getting underway, it’s far easier to roll with the punches and find an alternate route to achieving a goal, no matter what surprises get thrown at you. Some characters will develop resources and capabilities with no idea of what they will eventually do with them – they are simply accumulating resources that might be beneficial in achieving their overall ambitions.

The Midpoint

At some point, though, they will recognize a pathway to their goals that derives from these capacities, and the specific additional needs that they have in order for that plan to succeed. This marks a transition from Early Planning to Late Planning.

Late In A Plan

Once a pathway is seen, activities become more purposeful. Flexibility gets traded for greater certainty, and the closer the character gets to achieving their goals, the more flexibility will have been traded in this way.

Complicating factors that the Intelligent character will take into account will be misdirection and security. Most plans fail because not enough attention has been paid to one or both of these – and GMs are usually careful to preserve these blind spots to give the PCs a reasonable chance at successfully stopping the plot.

The more Intelligent the villain, the better they should be able to respond to the exposure of such flaws in their plans. There can be exceptions, when obsessions and blind spots come into play, but as a general rule of thumb, unused Ops points should permit the formulation of alternatives and contingencies at the rate of 1 per 2 available Ops points.

The simpler the plan, the more routes to victory. The more detailed the plan, the more restrictive it is.

That means that a character with INT 18 has markedly different capabilities than one with INT 16, for example.

But beyond Masterminds, who can often be characterized as simply having “enough INT”, the more important application here is for determining the capabilities of a lower-INT villain – one with INT 8 vs one with INT 9, for example.

INT 8: A 4-step plan with 2 contingencies.
INT 9: A 5-step plan with 2 contingencies – or a 3-step plan with 3 contingencies.

Applied Skills

Mathematics as a skill simply adds one Ops point capacity per skill level, and – at the GM’s discretion – reduces the Ops cost of specific tasks by 1 for every 5 skill levels. It is also entirely reasonable to restrict characters from even understanding certain mathematical tasks unless they have a total skill (INT bonus plus skill points) sufficient to that task.

The same can be applied to every other INT-based skill – in fact, to every skill, period.

Carpentry, for example, is more commonly DEX based than INT based. But why should we let that stop us?

Estimate By Eye

The golden rule of carpentry is measure twice, cut once. It’s therefore incredibly impressive when someone eyeballs a job and cuts a piece of timber accordingly – and it fits perfectly.

But let’s be honest – any fool can cut more-or-less to length, in fact, to within 3 inches or so. Furthermore, if the cut is too long, that’s easily corrected – it’s just a little wasteful of wood. It’s coming up short that’s the real problem.

So let’s assign the basic task – sawing the piece of timber – and appropriate number of Ops points. It’s fairly basic, so maybe 2, maybe 3. For every Ops point unused, the character can use them to improve his ‘by eye’ measurement for 2 Ops points each step. These are in 1/2 inch increments until the error is 1 inch, then 1/4 inch until the error is 1/2 inch, then tenths of an inch.

So,
3 Ops points = 3 inches plus or minus.
5 Ops points = 2.5 inches short or over.
7 Ops points = 2 inches short or over.
9 Ops points = 1.5 inches short or over.
11 Ops points = 1 inch short or over.
13 Ops points = 0.75 inches short or over.
15 Ops points = 0.5 inches short or over.
17 Ops points = 0.4 inches short or over.
19 Ops points = 0.3 inches short or over.
21 Ops points = 0.2 inches short or over.
23 Ops points = 0.1 inches short or over.
25 Ops points = perfect fit.

Planning ahead

Being able to visualize blueprints in your head and execute them is another impressive trick. Initially, this is only enough to create the parts list in their general shapes (5 Ops). Being able to shape them exactly as you need is the next step – either 10 Ops points and +1 per component after the first four. Knowing how they are to fit together and designing them to so is 15 Ops points +1 per component more than the first four.

An example: A drawer to fit a certain-sized cavity. First four components gets a box the right size (measured) with no top and no bottom. 5th component adds a bottom. Sixth and Seventh are a pair of rails for it to slide along, or a groove to fit an existing one if the cabinet was designed in advance. Eighth is a face-plate, with holes pre-drilled for a handle. Ninth is the handle itself, and Tenth would be the assembly.

So, 21 Ops = do it all without blueprints.
20 Ops = do all but 1 component without blueprints.
18 Ops = do all but 2 components without blueprints.
…
16 Ops = do 5 components without blueprints OR do all ten without blueprints but needing to add intricate details as you go.
15 Ops = 4 components without blueprints OR do nine without blueprints but needing to add intricate details as you go. One piece will have to be measured.
14 Ops = do eight without blueprints but needing to add intricate detail. Two pieces have to be measured.
…
10 Ops = do four pieces without blueprints (the open box) but everything else needs to be measured.
… and so on.

Hero System Conversions

The hero games system defines 10 in a stat as normal human, but permits scores less than zero, there is no minimum. So a score of 1 won’t mean the same thing. Each +5 doubles capability, which is often undefined. Each -5 halves it. The rate of change in capacity is not defined in the d20 system.

All of which makes conversion difficult, and why there are dozens of conversion regimen to choose from.

The simplest is simply to read the stats from one into the other. STR 18 in Hero = STR 18 in D&D. The most complicated, and potentially the most accurate, uses character Lifting capabilities to map conversion rates for every possible d20 stat value, then arbitrarily equates the results to all the other stats (except body, which does the same thing using hit points).

There are no right answers. So let’s use a wrong one.

HERO -> D&D	HERO -> D&D	HERO -> D&D	HERO -> D&D
0 = 0 5 = 5 10 = 10 15 = 12.5 20 = 15 25 = 17.5 30 = 20 35 = 22.5 40 = 25 45 = 27	50= 29 55 = 31 60 = 32 65 = 33 70 = 34 75 = 35 80 = 36 85 = 37 90 = 38 95 = 39 100 = 40	110 = 41 120 = 42 130 = 43 140 = 44 150 = 45 160 = 46 170 = 47 180 = 48 190 = 49 200 = 50	thereafter, +20 = +1 so 400 = 60 600 = 70 800 = 80 1000 = 90 1200 = 100 and so on.

I have chosen these values because the flavor that I expect this system to generate (based on the D&D scale) matches the in-game flavor that I would expect of the Hero scale equivalent indicated.

In other words, the look-and-feel is about right, and the mathematical niceties are not so important as that.

Wrap-up

And that, fortunately (because I’m out of time) is where my notes for this subject come to an end. Can the system be tweaked / refined? Yes, endlessly. But down that road, eventually, comes the hard reality of a different scale for every stat and skill, and that’s not an end worth achieving. This is a close-enough system that yields results useful in the real world from a generic basis.

And that should be good enough.