Recommending/requiring calculators

[Belac]

Hello everyone, this is my first post here so I'll try to keep it concise.  I've been working on a particular game for four and a half years now and have struggled with a particular concept for a while.  The game uses a system I also designed.

(Most of thread deleted for not being concise)

After numerous attempts at making a skill system that works, I have found that the one that works the best, has the best win/loss ratios for my purposes, and is easiest for most people to learn works as follows:

1d20 * Skill vs 1d20 * Skill/Difficulty, highest wins, reroll ties

However, this could require a calculator as skills start a 1-4 for an untrained character, go up to 80 or so for the most skilled humans, and my game is a high-powered, high-fantasy, superpowers game where its conceivable that characters could have skill ranks exceeding 400.

If requiring a basic calculator that would probably be used about 5-15 times per four hour session (rough estimate) would greatly simplify my rules and make the game perfectly scalable (as it needs to be), would it be better than making a mechanic that's more complicated to learn, doesn't work nearly as well, but doesn't require a calculator?

Thanks in advance for any comments.

[Jack Aidley]

1d20 * Skill vs 1d20 * Skill/Difficulty, highest wins, reroll ties

I'm not sure what you mean by this. Who's skill(s)? What difficulty? Why is difficulty only on one side? Please elaborate.

Would it be better than making a mechanic that's more complicated to learn, doesn't work nearly as well, but doesn't require a calculator?

Using a calculator will (probably) be less intrusive than the table-lookup systems that rolemaster and MERP (for example) used, so I imagine you can get away with it. However I think you should view it as undesirable. I also think the assumption in your question above (calculator vs. more complicated, doesn't work as well) is not necessarily true. You may find that the clever folks round here can offer a low maths equivalent that is easy to understand and easy to work out.

[Belac]

I had it explained in a little more detail but my post was overly long, so I deleted much of it but then had to post the rest in a hurry.  My apologies.

If character A is making a contested skill roll against character B's skill, here's the procedure.  (Let's say character A is trying to Intimidate character B, and character B is using his Resist Intimidation skill to resist it.  Not that these are necessarily skills in my system, but they work for the example.)

Character A rolls 1d20 and multiplies his Intimidate rating by the result.  Character B rolls 1d20 and multiplies his Resist Intimidation rating by the result.
If Character A gets the highest result, he intimidates Character B; if Character B gets the highest result, he is not intimidated.  A tie is rerolled.

If Character A is trying to accomplish a particular task that's not resisted by a character, he instead rolls against a difficulty.

If Character A wanted to open a door, he'd roll his Door Opening Skill times 1d20 vs the door's Difficulty (to open) rating times 1d20.

(Alternatively, I could have just set a specific target number for the difficulty and not rolled, but that makes the contest overly random for my tastes.)

Make more sense?

As for calculators, I do view them as undesirable, but better than the alternatives.  However, if anyone can provide a simpler system the provides the following results, I'll be very happy.

SkillA 10 vs SkillB 10 means A wins 50% of the time and B wins 50% of the time.

SkillA 10 vs SkillB 10 means A wins X% of the time and B wins Y% of the time.

SkillA 10023 vs SkillB 20046 means A wins X% of the time (meaning, the same X% as in the above equation) and B wins Y% of the time.

In other words, if one skill is twice the rating of the other, the probabilities of either winning remain constant whether they're 2 vs 1, 6 vs 3, 160 vs 80, 8 million and 2 vs 4 million and 1, or whatever.

[Lxndr]

Doesn't the odds system in Sorcerer work like that?  What matters isn't so much how much dice you have, but how many multiples your dice are over the opponent's?

Let me go dig up some old threads...

[Shreyas Sampat]

The very easiest way to reduce calculation here is to use smaller numbers.  Since you don't note that you want to preserve granularity, this is what I would advise.  Use like a d6 and the same skill range; anyone worth their jambalaya can multiply double-digit numbers by 6 in his head.

Alternatively, you can do the math before the dice are rolled; find the ratio between skill ratings and multiply one of the die rolls by this.  This still requires math, but it's smaller math.

[Belac]

Thanks for the advice, but there are problems.

1) 1d6*rating is way too random, makes differences in ratings too extreme, and 1d6*two-digit-number is still too hard for most people to do in their heads.  (Oh, but that reminds me of something I forgot to specify; in situations where calculators are not used, I generally try to make sure numbers don't have more than two significant digits.)

2) Calculating the ratio between 6 and 7 and then multiply a dice by the result is probably harder for most people than 1d20*6 vs 1d20*7.

3) Thanks for pointing something out; I can make the numbers a little more "grainy", but don't want them extremely grainy.  ("Grainy" being understood to be like White Wolfs 1-5 rating system, as opposed to "Generic Example Systems" 1-100 rating system, etc.)

[Mike Holmes]

This thread might interest you, but beware, it's intense: http://www.indie-rpgs.com/viewtopic.php?t=5243

It references Walt's Symmetry system which you might want to get familiar with.

Sorcerer's method doesn't fit the bill in terms of odds shifts. However other dice pools do, I think. The problem with most dice pools is that you roll a number of dice equal to skill. That's not going to work here if skill can be arbitrarily high as the examples indicate.

There have been games like KABAL and Phoenix Command that have required the use of a calculator. They're played by very few people, but they do have a cult following.

Mike

[John Kim]

  In other words, if one skill is twice the rating of the other, the probabilities of either winning remain constant whether they're 2 vs 1, 6 vs 3, 160 vs 80, 8 million and 2 vs 4 million and 1, or whatever.  

OK, I started out on this with an explanation, then rapidly decided to calculate the whole thing as an example of showing the power of logarithmic systems.  

Your method can be reduced to a single universal table of skill vs skill, with the result being the number you need to roll under.  On the other hand, if skill really goes up to 80 or more, then this will be unwieldy -- because the table would be 80 rows by 80 columns.  

Personally, I'm in favor of logarithmic systems.  If you used a log of effective skill as your stat, you could get the right number to roll by just using the difference.  You could call the calculated number "Skill Factor" or something compared to linear skill.  Here's an example using log of 1.259.  (This scale mean +3 factor = x2 skill, and +10 factor = x10 skill.)

Skill    Skill Factor
  1           1
  2           3
  3           5
  4           6
  5           7
  6           8
 7-8         9
9-10       10
11-13     11
14-16     12
17-20     13
21-25     14
26-32     15
33-40     16
41-50     17
51-64     18
65-80     19
81-100   20

So now you need only a single-column universal table to get the roll needed.  Just take (Skill Factor A - Skill Factor B) and apply the table.  Here "SFA-SFB" is Skill Factor A minus Skill Factor B.  

SFA-SFB   Chance   

 -12     0% (  0.48%)
 -11     1% (  1.24%)
 -10     2% (  2.05%)
  -9     3% (  3.31%)
  -8     4% (  4.80%)
  -7     6% (  6.72%)
  -6     9% (  9.20%)
  -5    12% ( 12.65%)
  -4    16% ( 16.65%)
  -3    21% ( 21.79%)
  -2    30% ( 30.01%)
  -1    39% ( 39.19%)
   0    50% ( 50.00%)
   1    60% ( 60.81%)
   2    69% ( 69.99%)
   3    78% ( 78.21%)
   4    83% ( 83.35%)
   5    87% ( 87.35%)
   6    90% ( 90.80%)
   7    93% ( 93.28%)
   8    95% ( 95.20%)
   9    96% ( 96.69%)
  10    97% ( 97.95%)
  11    98% ( 98.76%)
  12    99% ( 99.52%)

The chances here very closely approximate the chances using your method of (Skill A * 1d20) vs (Skill B * 1d20).  For example, suppose Skill A is 10 and Skill B is 20.  By your exact method, we get 23.75% of A winning.  By my method, Skill Factor A is 10 and Skill Factor B is 13.  10-13 = -3, so the chance is 21%.  

If you want a closer approximation, you can use the log of a smaller number.

[M. J. Young]

To focus on your question, calculators scare people--if they even think there's that much math involved, they'll run.

I keep a calculator at the table when I run Multiverser; I often have one at the table when I run D&D, for spot adjusting encumbrance and experience during play. Multiverser's most difficult math problems are things like add a column of four or five two digit numbers and then subtract a couple of two digit numbers from the sum, or subtract a two digit number from one hundred and take ten percent, or divide the percentile roll by an easy number (2, 5, 10, 20, 50) and round up. Most people can do those things in their heads, if they try.

However, someone once saw a picture of me running a game at a convention, and noticed that next to the dice there was a calculator. They commented that the game must be terribly complicated if I needed a calculator at the table to run it. (Odd thing is that although I ran that game all day at that convention, I never used that calculator once--but the fact that it was there was enough to scare someone.)

Multiverser does recommend that having a calculator at the table can speed the game. We also put a couple of tables in an appendix that would provide the answers to commonly calculated problems, and encouraged referees to recognize that in most cases they didn't need to do the math because the probabilities are transparent enough that they'll know what the roll means four out of five times once they get the basics down.

I don't think there's anything wrong with suggesting that referees keep a calculator handy when they play; however, if you become known as "that game that requires a calculator to play", you're dead in the water. Find a way around it if you at all can. At least be offering something on the order of "do this or use a calculator".

I hope that helps.

--M. J. Young

[Belac]

Thanks for the replies.

After doing some testing and writing, I decided to change the rolls to 1d10 * Skill, and I think by doing so I can reduce the skill levels somewhat as well.

Also, an important point is that if Character A has Skill 40 and Character B has Skill 57 (although I wouldn't recommend using "57" as a skill rating; 60 would be a better choice), and Character A rolls a 1 and Character B rolls a 7, there's not much need to use the calculator. :)  (Also, hopefully most people could figure out that Skill 40 vs Skill 60 is really Skill 2 vs Skill 3.)

[Mike Holmes]

Hah, I think I have it. Actually, I haven't calculated the odds, but I think it works in general.

Basically, it combines a method that Andrew Martin uses in some of his systems, and something like the system from Wayfarer. The idea is, in general that you roll an arbitrary sized die to get under the stat for both sides, the first one to do it when the other does not wins. Now, how to get that arbitrarily large die, and make it not too cumbersome?

Well, look at the number of significant digits (it was the mention of that above that got me thinking about this) in the larger stat. Add zero digits to the left of the opposing stat until you have the same number for each. So, if I have 1004 and you have 67 your stat becomes 0067. Then take a d10 and roll it trying to get the first digit or less with zeros being zero not ten. The opponent does the same. Keep checking the first digit only unless you succeed in which case you move on to the second digit and so on. As soon as one player gets a success rolling under all digits, and the other does not, it's all over. If you get to the end with both players, start over again.

What's really happening here is that you're rolling a d10000 in this case. But to make it work more quickly and avoid problems with having to have loads of dice of different color, you're using the shortcut method of rolling only one die at a time, and comparing each digit pair-wise.

Howzat?

Mike

[Belac]

Hmm...thanks Mike, but I'll have to do some extensive testing before I can tell if your system would work.  It's a good idea, anyway.

I'd think that method would take longer than mine (even with the calculator), though; it would eliminate the calculator, however.

I've got a question.  I notice that most gamers (maybe not most here, but most overall) are willing to learn hundreds of pages of rules to play D&D, and roll things like 2d6+7 (multiplied by 2 if a roll of 19-20 is rerolled and hits) plus 1d6 fire damage (not multiplied by anything) plus 2d6 damage if the target is evil, except on a Tuesday.  On the other hand, a simple game that uses a calculator must be really complicated.  Any ideas why?

(My theory: D&D set a standard that most people still don't question even with the rise of more streamlined RPGs, but nobody has set a standard involving a calculator.)

[Mike Holmes]

Hmm...thanks Mike, but I'll have to do some extensive testing before I can tell if your system would work.  It's a good idea, anyway.

I'd think that method would take longer than mine (even with the calculator), though; it would eliminate the calculator, however.

Try it. It's actually not as long as it sounds. Many times you'll only have each side roll a d10 each, and it's all over. Failures are quickly read, and rerolls are easy comparisons. Give it a shot.

(My theory: D&D set a standard that most people still don't question even with the rise of more streamlined RPGs, but nobody has set a standard involving a calculator.)

Many of us consider that a truism around here. That is, somehow people think of D&D as an easy system when it's really not at all, it's just what people are used to playing.

Heck, I've personally developed systems that run on spreadsheets. It's not calculators or spreasheets that people object to, it's the lack of the rest of the system being compelling enough to justify these things. To be compelling you have to either already be invested in the system (D&D) or the rest of the game has to seem to merit the calculator.

What's the rest like?

Mike

[Belac]

To be vague, the rest is fairly good and popular, but many players say its too simple, so I'm giving up a little ease of play in exchange for a lot more detail (in theory; if it turns out not to be, I won't pursue this path any farther).

Essentially, my theory is that the additions will improve the game and will also be good enough to justify the occasional use of the calculator to most players.

Right now, one of the main "identity crises" of the game's design is exactly what theme/scenario to focus on most.  It's a high-powered, high-fantasy game set on modern Earth after an invasion by superhuman aliens which pretty much reveals to Humans that most of the other folks in this section of the universe are not amazingly nice, that apparently almost everyone else in the universe has supernatural powers, and that Earth at one time was a more magical place and magic may be returning.  Mostly, PCs are Humans that are either trying to defend Earth (if the campaign is just focusing on the invasion of Earth by one specific alien race, which can work well for short campaigns) or search for/establish a new Human identity in the universe and try to promote peace and prosperity on Earth and everywhere else.  Combat is a mix of console game (especially games like the latest Final Fantasy games) and comic book styles, and most of the characters have a wide range of superpowers that can help in combat.