Saturday, May 28, 2016

Tabletop Library: Now You Can Keep Your Shirtless Heroes Where Your Husband Can't See Them

The post title is my unsolicited attempt to create fake banner ad text for the new Tabletop Library. It was inspired by this real banner ad:
Tabletop Library: Digital games that won't stack up where your wife can see them.
This ad ran on what I assume is a gaming discussion board or at least was grabbed by someone from somewhere and put up on the board. The screenshot is from RPG Pundit:

The Pundit also captured Christopher Helton's silly attempt to show off his feminist, or anti-genderist or anti-whateverist cred.

I'm sure this is an extremely minor tempest and that Tabletop Library wasn't trying to be ideological or political or anything else. I'm not saying that Tabletop Library has any particular agenda or would even necessarily agree with what I'm saying here.

But that's sort of the point. It's just an ad.

On RPG Pundit's post, Tenkar* commented that it's simply a fact that 85% of all RPG gamers are men--a proportion that's probably even higher in the OSR.

That of course is absolutely true, even though it's a general fact and not true in every particular case (as most general facts are not true in every particular case).

But even to the extent (15%) that it's not always true, the ad is still, well, funny. To lift my own comment from the Pundit's post:
You should be able to joke in a friendly way about silly differences between the sexes even when they're only general differences. And the joke is partly self-deprecating. It's just as much about men being silly hoarders of stupid stuff. It's also a silly joke about the minor "strains" (which of course aren't really strains) of marriage. That anyone would have a problem with this sort of thing is insane.
That 14 people (or whatever) would "like" Helton's dumb comment--"yeah, you tell those sexist bastards what's what, Chris!" is just another example of how busybodies with nothing else to do love spoiling things.

On a brighter note, it looks like the new Tabletop Library is doing quite well. Now I just have to figure out how to hide all those $3.99 digital gaming purchases from my wife when she looks at the credit card bill.

*At Tenkar's Tavern, there is also a funny self-referential riff on this.

Wednesday, May 18, 2016

That Chesterton Misquote: a Detective Story

Old School Renaissance

In a post a few days ago, I made a quasi-defense of allowing our four-year-old son to read the 1981 Advanced Dungeons & Dragons Fiend Folio. In my Google+ and Facebook intro blurbs for the link, I paraphrased an alleged G.K. Chesterton quote. The paraphrase went like this:
Fairy tales do not tell children that monsters exist. Children already know that monsters exist. Fairy tales tell children that monsters can be killed.
Now my "paraphrase" was actually a direct word for word copy of an actually existing rectangular Chesterton quote thingy--the sort of picture people post and repost on Facebook and other social media (though note the wonky punctuation):

But I thought (though I honestly don't remember why I thought) that that itself was probably a paraphrase of something where Chesterton was actually referring to dragons not monstersI used "monsters" (while acknowledging that it was probably a paraphrase) because it squared better with my post--I was talking about monsters in general, such as the monsters in the Fiend Folio, not dragons specifically. Here's one of the rectangular quote thingies on the Chesterton dragon version:

And here's another:

And here are three more:

I've posted five of these because they all differ. The major differences are the substitution of "Fairy tales are more than true-" for "Fairy tales do not tell children dragons exist," and "beaten" for "killed." But minor differences include "don't" for "do not," "that dragons" for "the dragons," "the children" for "children" and the insertion of "that" in-between "us" and "dragons."

This is, of course, annoying. If Chesterton really said it, you would think someone would simply look at exactly what he said in Collected Essays Volume XXVII or whatever and just quote it. Is it "don't" or "do not"? Well, what did he actually say?

Okay. Now it gets even more annoying. Hold onto your hats and wait for it . . .

The quote has also been ascribed to Neil Gaiman:

And now, instead of "killed" versus "beaten," we have "beaten" versus "defeated."


What was the original quote and who actually said it?

In fact it was Neil Gaiman quoting Chesterton in the epigraph to his 2002 Coraline, p. 7:

Fairy tales are more than true: not because they tell us that dragons exist, but because they tell us dragons can be beaten. 
- G.K. Chesterton
But the story is not over. As Gaiman later admitted, he misquoted Chesterton--and this was in the epigraph!

How did he misquote Chesterton? Why did he misquote Chesterton?

Well, Gaiman may have had his memory filtered through an earlier misquotation from a third source. Hold onto your hats again. That source is . . . 

Terry Pratchett.

In When the Children Read Fantasy, published in SF2 Concatenation (1994), which obviously preceded Coraline, Pratchett wrote:
One of the great popular novelists of the early part of this century was G.K. Chesterton. Writing at a time when fairy tales were under attack for pretty much the same reason as books can now be covertly banned in some schools because they have the word ‘witch’ in the title, he said: “The objection to fairy stories is that they tell children there are dragons. But children have always known there are dragons. Fairy stories tell children that dragons can be killed.” 
Now, do not misunderstand what I'm doing here. I'm not being critical of Gaiman. Indeed, we have Gaiman to thank for admitting his mistake.

Gaiman himself realized that he had misquoted Chesterton and attempted to unravel what had happened:
It’s my fault. When I started writing Coraline, I wrote my version of the quote [from Chesterton's] Tremendous Trifles, meaning to go back later and find the actual quote, as I didn’t own the book, and this was before the Internet. And then ten years went by before I finished the book, and in the meantime I had completely forgotten that the Chesterton quote was mine and not his.
(See this Tumblr post by "MJS.")

So what was the original quote? it's from "The Red Angel," Chapter XVII of Chesterton's Tremendous Trifles (1909):
The timidity of the child or the savage is entirely reasonable; they are alarmed at this world, because this world is a very alarming place. They dislike being alone because it is verily and indeed an awful idea to be alone. Barbarians fear the unknown for the same reason that Agnostics worship it--because it is a fact. Fairy tales, then, are not responsible for producing in children fear, or any of the shapes of fear; fairy tales do not give the child the idea of the evil or the ugly; that is in the child already, because it is in the world already. Fairy tales do not give the child his first idea of bogey. What fairy tales give the child is his first clear idea of the possible defeat of bogey. The baby has known the dragon intimately ever since he had an imagination. What the fairy tale provides for him is a St. George to kill the dragon.
Of course, in classic Chestertonian fashion, Chesterton restates essentially the same idea at least three more times in the chapter. Here's another version in the very next paragraph (warning: one of the terms used is now considered politically incorrect):
Exactly what the fairy tale does is this: it accustoms him for a series of clear pictures to the idea that these limitless terrors had a limit, that these shapeless enemies have enemies in the knights of God, that there is something in the universe more mystical than darkness, and stronger than strong fear. When I was a child I have stared at the darkness until the whole black bulk of it turned into one negro giant taller than heaven. If there was one star in the sky it only made him a Cyclops. But fairy tales restored my mental health, for next day I read an authentic account of how a negro giant with one eye, of quite equal dimensions, had been baffled by a little boy like myself (of similar inexperience and even lower social status) by means of a sword, some bad riddles, and a brave heart. Sometimes the sea at night seemed as dreadful as any dragon. But then I was acquainted with many youngest sons and little sailors to whom a dragon or two was as simple as the sea.
So, what does this all mean? Well, obviously, quotes on the internet are often very unreliable, at least if one is a stickler for accuracy. Then again, I do not think anyone can deny that the basic spirit of what Chesterton originally said was preserved through the various permutations, even though technically he was misquoted again and again. And while I obviously like reading actual Chesterton, I think the best version of the quote is that first "monsters" one. It's simple, stark and clear. But I would have preferred that its origins hadn't been misdescribed.

[Crossposted at Mahound's Paradise]

Tuesday, May 17, 2016

My Son's Favorite Book is the Fiend Folio

Okay, he's four years old.

Before anyone calls Child Protective Services, at least let me explain.

First of all, I didn't exactly start it or encourage it. The proximate cause was that my kids get into everything. And at some point my son dragged my old AD&D books out from a partially concealed shelf. I don't think he understands that the books constitute a game. Nor do I think he's necessarily aware that they are linked to "my game" or "the game" that I spend time writing on the computer. And oddly, it's my four-year-old daughter who likes the Dungeons & Dragons cartoon series. My son is scared to watch it.

He first discovered the 1977 Monster Manual. He actually wanted me to read it to him as a bedtime book. My daughter was also interested and followed along. Within a few days she could give a comprehensive discourse on how to best kill a vampire (and which methods were too gross). She thinks waiting for sunlight is the best idea.

My son was simply fascinated by all the different monsters and wanted to learn all about them. He has some speech pronunciation problems and so in a sort of rebellious style, enjoys pronouncing back weird monster names.

Then he discovered the Players Handbook.

Then he found the Fiend Folio.

As I implied, he is a somewhat sensitive child. Most live-action (as opposed to cartoon) science-fiction television shows frighten him. He'll want to watch Classic Star Trek but then run into the other room at the sight of the first monster. But for some reason he is not scared by the Fiend Folio. Or at least, he is not scared away. I think the fact that as horrifying as some of the monsters are, that they are not moving and thus are not real, is reassuring. 

"What's that, Daddy?"
"A Necrophidius."
"A Mekrabeelious!"
"What's that, Daddy?"
"A Needleman."
"A Deebledan!"
"Yes, it's pretty bad."

My daughter has a more clear-eyed attitude. During bedtime stories, I'll ask whether she wants to read a monster description or turn the page.

"No. No. No. No and No, Dad (that was for a page that contained five monsters). Turn the page."
"What about these?"
"No. No. And definitely No. Next page."

Last night my son lovingly placed the Monster Manual, Fiend Folio and Players Handbook in a sort of display on his bed.

I am actually not concerned by this. To me, it's the equivalent of fairy tales. But all three of those books have more extensive (and better) illustrations than their fairy tale books.

We are a traditionalist Catholic family. One of our primary goals as parents is to protect our children from what we see as certain dangerous secular or modern influences. And I wrote "my game" as something that would be potentially children friendly and Christian friendly (though it is certainly not a "Christian game" by any means).

But I do not think exposing my children (or letting them expose themselves) to "monsters" is bad, or at least bad per se, at least if it's not going to give them nightmares. I imagine some parents, including Catholic parents, will be disturbed by this. And I do want to reassure everyone. I take the general issue very seriously. I just think that being interested in monsters is actually healthy. My children don't want to be monsters (though they may sometimes act like them). Rather, they want to fight them.

That's okay. Perhaps more than okay.

Sorry, pacifist parents.

By the way, I don't believe my children ever dream about monsters, or at least they don't tell me that they do.

When I ask my son what he's going to dream about (a prelude to getting him to settle down in bed), he says, "Hot Wheels!"

When I ask my daughter what she's going to dream about, she says, "What a good day I'm going to have tomorrow. And how I love Mommy."

And again, hey, I didn't do it. They dragged the books down from a shelf . . .

Monday, May 16, 2016

"Imagine the Hell Out of It!"

"No. Giant Ants are diurnal."

I hope I don't embarrass Matt Finch by calling him one of the "fathers" of the old school gaming movement. He created Swords & Wizardry and I called Swords & Wizardry White Box (co-authored by Marvin Breig) the "gold standard" of OD&D clones. But if he's only remembered in the community for one thing, I propose it should be a slogan:
Imagine the hell out of it!
What could better express the OSR, and thus the original promise of paper and pencil adventure games, in a sentence?

The idea is that minimalism in rules presentation and design has a purpose (beyond just saving the author and reader time). If paper and pencil fantasy adventure games are about anything, they're about imagination. But too much descriptive prose, or even too many fussy mechanics can often kill imagination or at least suppress it. Here is a great passage from White Box that makes this point:
There’s not a lot of detail given about the monsters, because the more detail given, the more your own mental image of the fantasy world is going to be locked into a single track. We’re not going to say that giant ants are red, nocturnal, three feet long, and fond of eating Elves. Because in your mind, they might be blue, diurnal, five feet long, and eat only plants unless they’re attacked. Details about monsters toss roadblocks in front of your imagination. Yes, details can also inspire the imagination, but we’re making the assumption that if you’re interested in fantasy gaming in the first place, you’ve got a good imagination that doesn’t need details about the size of a giant ant.
In my view, this is the key to the brilliance of the first edition of Dungeons & Dragons, the "three little brown books," published in 1974. For example, for each of the monsters in Monsters & Treasure, their actual appearance is rarely described, and when they are described they are never described in much detail beyond the general. Goblins are merely "small monsters," Wights are "nasty critters" and so on. There are a few exceptions, whose rarity, as Finch might agree, in and of itself stimulates the imagination--"Thin and rubbery, loathsome Trolls" being one of the best examples.

Interestingly, much of the implicit description comes in the form of rules mechanics. For example, Goblins, "when they are subjected to full daylight they subtract -1 from their attack and morale dice." In play, this penalty is negligible, costing Goblins a mere 5% on their to-hit probabilities. But what the mechanic is in fact doing is telling you that Goblins don't like sunlight.

Each edition of Dungeons & Dragons introduced progressively more description, which is one of the reasons for the progressively expanding rules bloat. So, for example, the Monster Manual (1977) not only greatly increased the number of monsters, but also expanded each of their descriptions by (I would guess) a factor of ten. And of course most of them also had illustrations.

Now this is not a criticism per se. I like the minimalism of the three little brown books, but there's no question that the original Monster Manual was a brilliant and now iconic product. My point is that a perfectly reasonable sounding desire--why shouldn't we know a bit more about these monsters and have pictures of them?--can in the end, especially by the time you get to even later editions, have unintended consequences. Consequences that are bad.

But there were other, not so innocent reasons why imagination was gradually leeched out of things. One of them was the tendency to increasingly treat the reader as if she were a stupid child. Consider these two explanations of Fighters from 0e and 2e D&D:
0e (1974):
Fighting-Men: All magical weaponry is usable by fighters, and this in itself is a big advantage. In addition, they gain the advantage of more "hit dice" (the score of which determines how many points of damage can be taken before a character is killed). They can use only a very limited number of magical items of the non weaponry variety, however, and they can use no spells. Top-level fighters (Lords and above) who build castles are considered "Barons", and as such they may invest in their holdings in order to increase their income (see the INVESTMENTS section of Volume III). Base income for a Baron is a tax rate of 10 Gold Pieces/ inhabitant of the barony/game year. 
2e AD&D (1989): 
There are many famous fighters from legend: Hercules, Perseus, Hiawatha, Beowulf, Siegfried, Cuchulain, Little John, Tristan, and Sinbad. History is crowded with great generals and warriors: El Cid, Hannibal, Alexander the Great, Charlemagne, Spartacus, Richard the Lionheart, and Belisarius. Your fighter could be modeled after any of these, or he could be unique. A visit to your local library can uncover many heroic fighters.
(By the way, the 1989 segment on Fighters is eight times longer than the 1974 segment. The above is just a partial excerpt.)

The 1974 version has no description at all, though the thing about baronies sets a certain tone.

The 1989 version, while on its face encourages a sort of imaginative diversity, almost implies that the person reading the rules has little familiarity with the standard archetypes, or at least needs to be reminded of them.

But if that were the case, why would they be reading the rules or playing the game in the first place?

As should be obvious, I find the whole trend annoying. And it's one of the reasons I wrote the quasi-minimalist clone, Seven Voyages of Zylarthen. It's a game intended in part for children, but I like to think it treats them as adults.

And yes, Zylarthen does itself have a kind of tone, just as OD&D has a kind of tone. And yes, there are pictures--pretty good ones, if I may say. But I would like to think that the tone is not oppressive. The goal is to spark your imagination but also to give it room, so to speak.

From a design point of view, the goal is to be minimalist without being bland--partly because bland is boring, but also because blandness itself can be a kind of imaginative straightjacket.

Finding the right "balance" (if that is even the right word) is not easy. But who ever said it would be?


Follow Save Versus All Wands on Twitter at the Twitter home of its author: @OakesSpalding

Sunday, May 15, 2016

An Oddity in the Gamma World Artifact Use Charts

Yesterday, I discussed how to estimate the odds for the Gamma World technology charts using the RandBetween function on an Excel spreadsheet. 

But today, I want to look at an oddity in the charts themselves--or specifically at an oddity in Chart A. I have no idea if anyone else has remarked on this oddity. It may be quasi-common knowledge among some in the community or not. The only thing I can say is that I haven't seen it discussed, and I have been jumping around the blog posts on this issue a fair amount recently. 

Here's the oddity:
Without explicitly computing the probabilities or doing random simulations, it would seem obvious that the longer you spend in sustained concentration trying to figure out an item, the greater your chance of success. The rules also state that while you can fiddle for as long as you want, any interruption means you must begin again at the start. It would seem, therefore, that you don't want to stop or be interrupted. However, while it may seem that way, it's actually not the case. For Chart A, at least, it's actually better to stop or be interrupted after just a few rolls (and thus begin again at the start) than it is to try to continue rolling.
Now, it might be objected that this is a trivial observation, at least in certain cases. If you keep on getting high rolls, then you're probably moving closer to that skull and crossbones (again, henceforth A) and so in that kind of a case it's better to start over than to keep going. While this might be true, it's not precisely what I'm getting at. The falsity of the claim does not depend on the player knowing what his rolls are. The claim would be false even if the referee were rolling behind a screen.

Here's the basic point: while each roll gets you potentially closer to F, it also gets you potentially closer to A. However, it takes fewer rolls to get to F than to A. That implies that after a certain number of rolls (whatever they are) it might be better to start again at the beginning than to continue.

Remember the results of our first sample of 1000 attempts at rolling ten times:

F (success): 503
A (accident): 32
No Result: 465 

Now let's look at what happens when we roll only five times:

F (success): 324
A (accident): 5
No Result: 671

The 5 accidents make sense, since we saw yesterday that we know for certain that after only five rolls there is only a 0.63% chance of getting to A.

So, while taking ten rolls as opposed to five increases the odds of success by 50% or so (503 as opposed to 324) , it also increases the chance of catastrophic failure by perhaps 600% (32 to 5). The chances are still small, but when it comes to, say, dying, I'd rather have a really small chance--0.63%--than a small chance--3.0%.

But by stopping at five rolls, don't you also sacrifice your chance of success? So, isn't there a trade-off between risk and reward?

No, actually, there isn't.

How about this strategy: Make five rolls. If you don't get to F (or A), stop, go back and try again from scratch.
The results of this strategy will roughly approximate those below:

F (success): 543
A (accident): 8
No Result: 449

(We get 543 by using this formula: 324 + (.324 * 671). We get 8 by using this formula: 5 + (.005 * 671).)

So, it's better to start again after five rolls, than to continue on to ten. It's better to be interrupted.

In choosing two sets of five rolls (if we need them), rather than ten, we have roughly the same chance of success (or even more of a chance according to one simulated set of 1000 iterations) but a much lower chance of catastrophic failure.

But, of course if we had been thinking clearly, we should have already had a hint of this phenomenon. To see this, consider the results of only four rolls:

F (success): 227
A (accident): 0
No Result: 773

We had 0 occurrences of A. Should we roll 1000 more times to see if this was a fluke? No. As we saw yesterday, it takes a minimum of 5 rolls to get to A. It is impossible to get to A in only four rolls. We should have known that. We could have known that by simply looking at the chart.

So, how about a strategy of choosing three sets of four rolls (if we need them)? Here are the results:

F (success): 539
A (accident): 0
No Result: 461

So, again, the chances of success are about the same, but now we have completely eliminated the chance for catastrophic failure.

Hurrah, we've just come up with a foolproof scheme for sussing out simple artifacts without risk of breakage, injury or death!

We've also shown how Chart A is slightly broken.

Does this sort of thing also apply to Charts B and C? I'll leave that for another time. For now, though, how can Chart A be fixed?

Three possibilities come to mind. One is to make the minimum path to A shorter than the minimum path to F. Another (though this is potentially far more lethal) is to give some chance of getting to A from any position or at least from more of them. Finally, we could simply decree that being interrupted or voluntarily stopping does not mean that you go back to S. Rather, you always start where you left off from.

We'll discuss these in another post.


Follow Save Versus All Wands on Twitter at the Twitter home of its author: @OakesSpalding

Saturday, May 14, 2016

Gamma World: How to Determine Probabilities for Chart A

I've been doing work on a post-apocalyptic or far-future supplement to Seven Voyages of Zylarthen. The idea is sort of to do for Zylarthen what Mutant Future did for Labyrinth Lord--not a clone of Mutant Future (since that would be pointless) nor a precise clone of Gamma World (since that would be pointless and probably a violation of copyright) but a variation on Zylarthen, incorporating much of the Gamma World vibe.

Among other things, I've been looking at the 1st edition Gamma World technology charts--the mechanism by which the game simulates the process by which player-characters figure out the function and use of ancient technological artifacts.

There are three sorts of increasingly complex flow charts representing different sorts of artifacts--from laser pistols (Chart A, the simplest chart) to, say, permanent cybernetic installations (Chart C, the most complicated chart). The idea is that you roll a ten-sided die to negotiate through, with possible bonuses or penalties based on intelligence and how many others are available to help. The longer you take (the more die rolls you make) the greater the chance you'll figure out the artifact out but also the greater the chance you'll end up breaking it or even harming yourself or your party. Chart A looks like this:

So, after discovering an artifact--"a sort of jumble of sticks or tubes containing many grooves and colored knobs"--you start at S and want to get to F. In the process, you want to avoid getting to the skull and crossbones (henceforth A for accident). Depending on the artifact and the kindness or lack thereof of the referee, an "A" result could mean anything from "you break the trigger rendering it permanently inoperable" to "you shoot yourself in the face with a laser at point-blank range--roll 10d6 damage."

Now, I think the consensus is that the "chart system" is original and in theory very cool but it is usually a disappointment in practice. At worst it takes something that should be quite exciting--learning the purpose of some wondrous and powerful device--and turns it into something boring--rolling a die over and over again to track an abstract mechanic with no opportunity for player choice or referee creativity.

What can be done about that is a question for another time. And of course since Gamma World was published, all sorts of tweaks have been offered, in places ranging from the early issues of Dragon Magazine to the latest blog posts.

What I want to do first, however, is to look at the charts (or rather Chart A) from the point of view of probabilities. Given x number of rolls, what is the probability that you will get to F, or get to A or simply get nowhere at all?

For low numbers of rolls, the probabilities are easily calculated. Then it gets tougher:

From S to F (the number of rolls is the number on the left):

1: 0%
2: 0%
3: 10.5%
4: Complicated

Why 10.5%? Because there is only one path that will get you there in three rolls. Using a d10, you need to roll a 1-7, then a 1-5, then a 1-3. The chance of doing that is 70% * 50% * 30% or 10.5%.

From S to A:

1: 0%
2: 0%
3: 0%
4: 0%
5: 0.63%
6: Complicated

Why 0.63%? Because there is only one path that will get you there in five rolls. Using a d10, you need to roll a 1-7, then a 1-5, then a 8-10, then a 9-10 and then finally an 8-10. The chance of doing that is 70% * 50% * 30% * 20% * 30%, or 0.63%.

Though it might be complicated to precisely compute the odds at higher number of dice rolls for getting to F or A, we can roughly calculate them by performing simulations in Microsoft Excel. I imagine some of you mathematics wonks have done this or something like it in the past, or even have a better way of doing it using Excel or some other program. But I thought a few of you might be interested to see how I did it.

First you assign a number to each of the nine squares, circles and diamonds. I assigned them numbers from 101 to 109 so as not to get them confused with the pips 1 to 10 on a d10. I started at the top, going row by row down, and then left to right in each row where there was more than one shape. Thus, the top circle is 101, S is 102, F is 105, the diamond is 108 and A is 109.

We can then render the flow chart into this nested IF/THEN formula, where A1 is where you are and B1 is a random number from 1 to 10:  
Once you get to 105 or 109, you stop, or rather, you "move" nowhere.

So, to simulate one set of rolls, you would create these cells from left to right:
  • A1: "102" (that's because you always start at S)
  • B1: "=Randbetween(1,10)" (that gives you a random integer from 1 to 10)
  • C1:"=IF(A1=102,IF(B1<=7,103,102),IF(A1=103,IF(B1<=5,104,IF(B1<=7,103,101)),IF(A1=101,IF(B1<=2,104,101),IF(A1=104,IF(B1<=3,105,IF(B1<=7,104,107)),IF(A1=106,IF(B1<=2,103,IF(B1<=4,102,106)),IF(A1=108,IF(B1<=3,106,IF(B1<=7,102,109)),IF(A1=107,IF(B1<=1,105,IF(B1<=5,106,IF(B1<=8,107,108))),IF(A1=105,105,IF(A1=109,109,0)))))))))"
That gives you one roll. To simulate the next roll, add two more cells:
  • D1: "Randbetween (1,10)" (or take B1 and copy it to D1)
  • E1: Take C1 and copy it to E1.
And so on, for how many rolls you want.

After simulating the desired number of rolls, add three cells to record whether you ended up at F, ended up at A or failed to arrive anywhere. After, say, ten rolls, your ending point will be in U1. You will thus put a 1 in V1 if U1 is 105 (you ended up at F), a 1 in W1 if U1 is 109 (you ended up at A) and a 1 in X1 if U1 is anything else (you failed to arrive at F or A). You can do this automatically with more IF/THEN formulas:
  • V1: "=If(U1=105,1,0)"
  • W1: "=If(U1=109,1,0)"
  • X1: "=if(V1+W1=0,1,0)"
You now have one row in Excel simulating ten (or how ever many) rolls through Chart A. This of course doesn't give you the odds of anything. It simply tells you what happened one time.

Now, pull that row down, say 1000 times. You may have to pull A1 down separately to get 102 in each cell. Otherwise B1 may become 103, C1 may become 104 and so on. Obviously, you don't want that.

Now you have 1000 rolls. And it only took you a few seconds.

Finally, add three SUM formulas at the top or the bottom (or anywhere else, really). It's probably better to add them at the top, thus instead of your sets of rolls going from rows 1 to 1000, you can make them go from rows 5 to 1004 or whatever. You want the sum of F's, the sum of A's and the sum of no results. Assuming you've pulled the whole set down so as to start at row 5, you then have:
  • V1: "=SUM(V5:V1004)"
  • W1: "=SUM(W5:W1004)"
  • X1: "=SUM(X5:X1004)"
Let's try it for the first set of 1000 rolls. I get:

F (success): 503
A (accident): 32
No Result: 465

What about a second set of 1000 rolls? As you probably know, just by changing what is contained in one cell--say a dummy cell somewhere--every random result (all 10,000 of them) is automatically re-rolled by Excel.  So, now I get:

F (success): 558
A (accident): 33
No Result: 409

Here's a third set:

F (success): 528
A (accident): 28
No Result: 444

We have discovered a few things:
  1. After ten rolls, while we do not know precisely what the chance of success is, it looks like it's 50% to 55%.
  2. The chance of an accident is much much lower--only around 3%.
  3. Roughly 40% to 45% of the time, you get nowhere.
I find that interesting. It's certainly not obvious from the chart. Among other things I would have thought the chance of an accident would be higher.

Of course it presumably would be higher if the character had a low intelligence. On the other hand it would probably drop do almost negligible if the character had a high intelligence.

I hope some of you find this useful and helpful. Though again, I imagine a few of you have already done this on your own. Despite its seeming complexity, it actually doesn't take very long to set up, at least if you're familiar with some of the simpler Excel formulas. Of course, writing the formula for Charts B or C would take somewhat longer.

If you can believe it, I did write the formula for Chart C and then I lost it (or maybe it's some anonymous "Workbook1" in my documents). But I did save the results. After ten rolls on Chart C the numbers are:

F (success): 90
A (accident): 78
No Result: 832

Yeah, there's an almost 10% chance you'll figure out how to operate that permanent cybernetic installation after only a few hours. On the other hand, there's also a close to 10% chance you'll blow yourself up (or whatever) in the same amount of time. 

Is that how you thought it would turn out?

Please let me know if you have any questions or if I made any mistakes on the above. I think it's all correct, but it's not very difficult to make mistakes with so many formulas. 

NEXT POST: An oddity that these results reveal about Chart A...