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Author Topic: How good are you at mental arithmetic?  (Read 7994 times)
Jack Aidley
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« on: June 06, 2003, 04:58:33 AM »

I am exceptionally good at mental arithmetic. Not as good as I used to be, mind, but still exceptionally good. I have never played a roleplaying system in which the mathematics of the conflict resolution was a problem. Throw four dice, drop the lowest, add up the rest. *Bang* - I can give you the answer. Throw two dice subtract the second from the first and add your skill *Bang* - I can give you the answer.

Braging over, I'll come to my point.

This leads me to a problem. I have great difficulty working out whether or not a mechanic is hard for players to cope with. My most recent system uses this method. The players throw one green and one red ten-sided dice, they count 0 as 0, not as ten, and subtract the red from the green. Additionally if they throw a 9 on either dice they throw it again and add the result to the total. This gives a number between -18 and 18 with a rather nice probability curve. To this they add their skill, and the result is compared to a target number.

I think this is easy. Throw the dice *bang* give an answer. But my players, while not exactly struggling with it, don't exactly rattle off the answers.

So, does anyone have any guidelines for how difficult the arithmetic can be without causing difficulties to the typical (whatever that means) player? Or examples of the most complex arithmetic they've seen function?
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W. Don
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« Reply #1 on: June 06, 2003, 07:36:43 AM »

It sounds easy enough to do, and I'm nowhere close to being a numbers person. Maybe they just need time to get used to it. Especially where the 0 is concerned since I assume a lot of folks automatically read them as 10s from years and years of training.

Makes me remember something I was discussing with my players after a game I had last week. We were all having fun with a very rules light system/game, the action was flowing and the story had everyone's creative engines cranked up. When it came to actually rolling the dice, however, we'd look at the pile of numbers and somehow had difficulty adding them up. While the narration of events was quick and snappy, adding dice was very slow by comparison.

I know this might sound a bit hokey but:

Thinking about it all afterwards led me to consider that maybe this has something to do with which side of the brain was being used. In general, the right side is the creative side, more suited to viewing things as complete wholes, quickly catching differences in patterns, and so on. The left side handles logical step-by-step problem solving, deduction, breaking down wholes into parts.

Maybe what happens when you're collaborating on a story is largely a right-brained process. But adding the dice up is largely a left-brained process, so there's a shift from right to left brain processing when you stop and add the dice up. Thus, you get players who pause for a bit as they shift modes -- and so they don't end up rattling the answers off as fast as you'd expect them.

Sorry for diverting a bit. Just trying to find ways to explain what you're observing, drawing from my own background.

Incidentally, it also occurs to me that it's generally the right brain that handles quick comparisons. So comparing results from a pool of dice, instead of adding up totals and then comparing might be a better way to roll for games that require more "creative" thinking.
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Mike Holmes
Acts of Evil Playtesters
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« Reply #2 on: June 06, 2003, 07:50:26 AM »

The problem is, as you note, that there is no "Typical Player".

Don't think in terms of absolutes. Instead, try to minimize the difficulty of the process while still retaining all the benefits that you wish to keep. That is, if the method produces something important, then keep that important thing. Just try to come up with an easier way to get that thing. This is the principle of elegance in it's commonly used (computer programming, for instance) meaning.

If it can't be made any more elegant without sacrificing something, then it's at the point it needs to be at.

So, for instance. If your system is all-opposed, you can just have each side add 4d10 to their score and then compare. Same curve, no subtraction (assuming that's the percieved problem). If you have a target system, simply do the same and raise all targets by 22 (the average of 4d10). Also, if you don't mind a larger grained game, you could reduce the number of dice on each side to only 1 up and 1 down die.

But if you want, for aesthetic reasons or for other system requirements to have that zero center, and you need the finer granularity of the extra dice, then you'll either have to find a more radical solution, or you are already at maximum elegance for this mechanic.

Mike
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Ron Edwards
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« Reply #3 on: June 06, 2003, 08:25:49 AM »

Hi there,

One of the issues at work here is not whether a person can or cannot perform the calculations quickly, it's whether he or she wants to, and most importantly, wants to do it repeatedly, in the context of role-playing.

I've tried to work this out for myself in terms of game design, observing tons and tons of play with just this issue in mind, and here are my terribly non-scientific conclusions.

1. No one minds matching. Reading Fudge dice in terms of matching (as the text recommends) is wonderfully fast and easy.

2. Over or under a particular number is also pretty accessible, per die. The more dice, of course, the more annoying it gets.

3. Adding and subtracting are, comparatively, a pain in the ass. This probably sounds odd to those of us who can read a 3d6 total in under a second (due to tons of Champions and GURPS play), but I tend to think of us as pathological - after all, we could have been honing very different skills and probably should have, during the course of learning that ability.

4. Comparing to target numbers and taking a difference of some kind represents a quantum of extra effort.

I think all of this relates back to my Infamous Five threads, one of the points of which was to say, "The gaming we are used to is neither socially nor procedurally functional, given our goals." We, as gamers, are used to going around the mulberry bush to get what we want, and we've mistaken that route in many cases for what we want.

So my recommendation is much like Mike's: examine every step of the procedures in question in terms of value added regarding the goals of play - if you can't find it, then remove that procedure.

Quote
The players throw one green and one red ten-sided dice, they count 0 as 0, not as ten, and subtract the red from the green. Additionally if they throw a 9 on either dice they throw it again and add the result to the total. This gives a number between -18 and 18 with a rather nice probability curve. To this they add their skill, and the result is compared to a target number.

I think this is easy.


Arithmetically, so do I. Procedurally? Gotta tell you, man, I'm gone. It strikes me as waaaay mulberry-bush, specifically because I'm far less invested in "-18 to 18 with a rather nice probability curve" than I am in my skill vs. the target number ... and if we want a normal distribution above and below that to be affecting my skill-performance, it seems to me that Fudge provides that without the bush to go around. If I want a different curve from the standard 4dF, that's easy too: use 2dF, 3dF, 5dF, whatever, as seems best.

Best,
Ron
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Emily Care
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« Reply #4 on: June 06, 2003, 08:58:57 AM »

Hi WD,

Welcome to the Forge! If that hasn't been said already. :)
Quote from: WDFlores
Maybe what happens when you're collaborating on a story is largely a right-brained process. But adding the dice up is largely a left-brained process, so there's a shift from right to left brain processing when you stop and add the dice up. Thus, you get players who pause for a bit as they shift modes -- and so they don't end up rattling the answers off as fast as you'd expect them....
Incidentally, it also occurs to me that it's generally the right brain that handles quick comparisons. So comparing results from a pool of dice, instead of adding up totals and then comparing might be a better way to roll for games that require more "creative" thinking.


This is a good insight, and reflects why even minor number-crunching can be disrupting .  As you and Ron suggested, comparisons can make the transition from narration and general role-play to mechanical procedure easier, reducing handling time and increasing enjoyment (at least for folks like me!).  This shows how the kind of points of contact can be as important as how many there are for system.

--Emily
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Koti ei ole koti ilman saunaa.

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damion
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« Reply #5 on: June 06, 2003, 09:06:37 AM »

Here is my take on this:

I know for me, the problem with these things one of memory. How many serial steps are there?

Most games have two:

1)Add up dice
2)Add modifiers.

Now for yours:
Quote

The players throw one green and one red ten-sided dice, they count 0 as 0, not as ten, and subtract the red from the green. Additionally if they throw a 9 on either dice they throw it again and add the result to the total. This gives a number between -18 and 18 with a rather nice probability curve. To this they add their skill, and the result is compared to a target number.


This has a few serial steps:
1)roll dice
2)See if you need to reroll the green die
2.5)Reroll and total green
3)See if you need to reroll the red die
3.5)Reroll and total red
4)Subtract

5)Possibly add any modifiers to the roll.

Total of 5-7 steps.

Unlike some people I don't think subtraction is inherently bad, I've never seen anyone have
 problem with 3d6-X vs 3d6 + X.   For some reason subtracting dice is harder, I think because you have to visually search for the dice on the table and find them in the correct order (order is irelevent when adding).

It might help your players if you explain it like this.

Roll two D10:Subtract the red from the green. If either is a 9, reroll it and add or subtract the result, depending on the color.

Personally, I find that easier as your previous explanation caused me to mentally check for 9's before doing the additions, but that's not necessary.  It depends on your players.
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James
Jack Aidley
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« Reply #6 on: June 06, 2003, 10:40:21 AM »

Damion: Yeah, that's a much better way of putting it.

Mike: I'm a big, big fan of average 0 systems, both aesthetically and mechanically. For example, I have all roles unopposed. By using an average 0 system, I can just use the opponents skill as the target number, and have it symetrical.

Ron: I'd not come across the Fudge dice system before. It is nice, I like. I think you're right, I have got myself too caught up in the mechanics of the system. Which is why people with Masters of Mathematics shouldn't right systems, I guess. I think a rethink is in order.

We didn't roll any dice at all during the last session I ran. The one before there were about two rolls. You don't roll unless the target number is higher than your skill, or you're under pressure. Most of the time I fudge stuff anyway, or ignore the dice to get the result that comes out best. The only really good reason for the dice at all is that it lets me do bad stuff to the players without it being my fault.
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Ron Edwards
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« Reply #7 on: June 06, 2003, 11:26:56 AM »

Boink!

That was a very useful self-expressive insight you've provided. Lemme show ya now ...

Here's my thoughts for a fun experiment for you.

Run games as usual, most Drama-driven or free-form as you've described it. Also, have a handful of Bad Dice. Make a chart, as specific or abstract as you see fit, about the Bad Stuff that happens.

Players have Good Dice. For now, let's just say that all the dice are 1-6.

In any given situation, when you as GM say so, you're going to roll the Bad Dice, and check your chart. The player(s) get to roll their Good Dice, and whatever individual numbers match your Bad ones, those dice are removed. Use the remaining Bad Dice to reference the chart and add that Bad Stuff to the resolution during the situation.

If I'm not mistaken, this system or one very much like it will meet the goals you've stated, without running into things like skill levels and "can my character do this" and modifiers and all that stuff.

What do you think?

Best,
Ron
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Mike Holmes
Acts of Evil Playtesters
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« Reply #8 on: June 06, 2003, 12:13:17 PM »

Or just try freeform. Sorry if I ruined your cognative shifting technique, Ron. :-)

Mike
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jdagna
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« Reply #9 on: June 06, 2003, 01:54:55 PM »

I think the key thing with any dice mechanic is: what does is add to the game?  Many very complicated dice mechanics still boil down to comparing a die to a target number; the complications just add lots of extra steps and muddle the probabilities.

This is one reason I'm almost entirely opposed to the concept of exploding dice.  For a tiny little twitch in the statistical model, players are constantly adding, re-rolling and and sorting.  Most exploding models could use a White Wolf-style dice pool for what they want.

Likewise, I think a 0-centered die mechanic requires a lot of math for a minor aesthetic point that doesn't really affect game play.

Some games have managed to make gimmicky dice mechanics work.  Paladin is a great example.  Basically, you roll a poll of d6's, count 5's as 1 success and 6's as 2 successes.  If that were the whole mechanic, I wouldn't have liked it.  But the game lets you re-roll some of the dice based on your abilities, and at the cost of points.  Furthermore, as you're re-rolling, you're also fleshing out a scene with increasing amounts of detail, with the dice providing continuous feedback on how things are going.  So it works well here - and not because of the mechanic, really, but because of what the game does with it.

PS: I don't have a problem with math-heavy mechanis or games.  But instead of counting sheep, I calculate (in my head) how long it takes light to reach Pluto, so I'm not exactly normal.
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Justin Dagna
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John Kim
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« Reply #10 on: June 06, 2003, 02:47:06 PM »

Quote from: Mr Jack
  So, does anyone have any guidelines for how difficult the arithmetic can be without causing difficulties to the typical (whatever that means) player? Or examples of the most complex arithmetic they've seen function?  

Well, in Champions we would constantly go with the fairly laborious operation of rolling 15 or more d6 and counting it up two different ways: once for total, once for BODY damage (+1 for each 2-5, and +2 for each 6).  This always took a while, and yet players nearly always loved it.  So I think any amount of arithmetic is fine -- as long as it is fun for the players, and consistent with the game.  

Conversely, no amount of arithmetic is fine if it detracts from the game.  Personally, I tend to prefer an absolute minimum of physical die operations and math during play.  I certainly see a visible difference in play between number plus single die (like Unisystem, say) and anything more complicated.
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M. J. Young
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« Reply #11 on: June 06, 2003, 05:04:47 PM »

I've got two things to share about math complexity in game mechanics. Understand that although I'm not a math wiz, I am a 710 GRE in the area (93rd %ile, I think), do addition of columns of two-digit numbers in my head, and don't balk at two and three digit multiplication. So I, too, have a bit of trouble determining whether a particular mechanic is too complex. Still, here's a rule of thumb:
    [*]Read the dice and compare to the number is always easiest.[*]Count/consider the number of dice having a particular value or value range is a bit tougher.[*]Addition not greater than two-digit addenda is more difficult, but nearly all current gamers accept it.[*]Subtraction is tougher, and a lot of gamers balk at it as too complex during play.[*]Multiplication will cut another batch out of your group, as being even tougher than subtraction.[*]Once you get to division, most people are gone, and beyond that you're quibbling about whether you want to reach two percent or one percent of gamers, I expect.[*]Any applications of algebra beyond this, of powers and roots, equations with multiple variables, obviously is going to appeal to only a very few math heads (although might be useful in designing the core engines of a computer game). I only mention this because--[*]Some few games have used trig functions. The one that comes to mind was a spaceship combat game in which targeting was based on calculating angular size of the target at range. It's extremely realistic, and absolutely useless in play, because the majority of players can't do it and larger chunk of those who can think it entirely unnecessary.[/list:u]
    So that should give you some idea of how "difficult" things are.

    Now, there's another aspect: who does the math?

    Multiverser sticks to addition and a bit of subtraction. Once in a great while you have to add two or three dice together; more often you have to sum values from the character sheet with some known only to the referee. There may be subtractions here and there. However, all of this is done by the referee. Players rarely know their chance of success accurately--they only know approximately, and based on assumptions they make of the situation (just how hard is this). The referee takes the numbers, determines the target, and lets the players roll against that target.

    As a second point to this, it is not always necessary to do the math. I emphasize this because people overlook it. Consider a simple pre-D&DIIIE game. On a combat attack, the player rolls D20 to compare to a chart. Do you look at the chart? I find that I rarely do. I know that this character missed with a five, hit with a seventeen--really, I only have to check if it's close. The same is true with Multiverser--only about one in five rolls is going to be "close" in the sense that I have to do the math to find out whether it's success or failure. The rest are going to be patent.

    So it's important to answer the questions, who has to do the math? and how often does he have to do it? If players never have to calculate anything at all, they feel like the game is running smoothly, even if the referee needs a programmable calculator behind the screen to work out the results (provided he can do so reasonably quickly).  Then the question isn't who thinks the game too hard to play, but who thinks it too hard to run?

    I hope this helps.

    --M. J. Young
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    talysman
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    « Reply #12 on: June 06, 2003, 08:48:40 PM »

    here's an idea:

    instead of subtracting a red d10 from a green d10, with the appropriate expansions, and comparing to a target number, why not add a red d10 to the target number and add a green d10 to your skill? which ever is higher wins.

    strangely, it was M. J. Young's reference to algebra and "who does the math?" that made me think of this. why shouldn't the game designer do the math in advance?
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    John Laviolette
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    Shreyas Sampat
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    « Reply #13 on: June 06, 2003, 09:19:28 PM »

    Now, personally, I don't like doing mental arithmetic.  I can do it no sweat, but I'd rather be sailing.

    So, why does there need to be math at all?  My game Refreshing Rain doesn't have math during any of the high points of play, beyond mathching (this was a typo, but an amusing one) and comparison; it does have math between scenes, but of a limited nature.  It's the closest I've gotten to the 'mathless game' ideal that Legends of Alyria exemplifies (deliberately?).  The Nighttime Animals Save The World does this too, though in a dramatically different way.

    This doesn't answer your question, though.  If you ask me, it comes down to player preference.  Comparison is definitely the easiest operation.  I start to look away when dice pools and subtraction collide.  The best thing I can tell you is to have a consistent 'concentration'.  If your game is very mathy, then you can have a lot of complex, different math things, but you can't tell anyone to even take the sum of Warfare and Psyche in Amber.
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    Jack Aidley
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    « Reply #14 on: June 07, 2003, 02:30:11 AM »

    Not quite sure what freeform is taken to mean here, Mike, but by my reckoning (no dice, players describe their actions, GM probably does, but may not, allow the described action to happen) I have tried. I recently took a two week break from my main game and ran a diceless Secret Agent game. I found it interesting, and it certainly worked for the genre, and for a short bash. However my experiences from running a longer game with a 'near-freeform' system led to me to desire a more defined and 'crunchy' system.

    Ron, that is an interesting experiment. I don't think I'll use it though. It is, in result, if not in procedure, pretty similar to a method I have used before and that method left me wanting rules to define 'can the character do this' and 'can the character do this better than this other character'.

    That's the thing I really like about this place - there's a whole new way (to me) of thinking about roleplaying games here.
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