Common Usage and problems with fractions.

[cooper]

I'm at an impasse wether to using lowest common denominators or not. I'm not sure if the math works out correctly. As some of you may have noticed, I used lowest common denominators in my examples in the other thread (thanks for letting me high-jack it by the way). 5th level strider vs. 12 goblins.

It's light vs. heavy armor (2:1) in which it takes two 6's by the goblins to equal one "hit" against the hero. I wrote it as: 6d6/6 with 5 hits needed to take strider out. Simple enough yes? Instead of rolling 12d6 and counting every two 6's as one hit.

but what happens when you have an armored hero vs. 4 horse dragon? it's 3:1, but there are 4 horses! Without reducing the fractions its:

4d6/6 by the hero with every three 6's counting as 1 hit means it takes a cumulation of twelve 6's to kill the 4-heavy horse dragon, yes? Would it be acceptable to list it as 1d6/6 with 3 hits to kill the dragon? But what happens when I give the hero a magic sword? Sure I can roll 8d6/5-6 for the dragon instead of 4d6/5-6 and count each hit as two, but I can't reduce 5d6/6 and 12 hits to lower fraction! Since there is no way to reduce this, I think it is dangerous i.e. confusing--as a general rule, to use lowest common denominators in the strider vs. 12 goblin battle, or for the dragon, but not for the hero. Am I wrong? I'm quite worried about clarity. Lowest common denominators in chainmail just might be the devils work. What would be a good short hand instead when showing an armored hero vs. 4 heavy horse dragon?

Is the standard usage: 4d6/6(3:1) vs. 4d6/5-6(1:2) Roll four dice counting every third 6 as a hit vs. 4d6/5-6 roll four dice counting every 5 and 6 as two hits. or this: 4d6/6(AF) vs. 4d6/5-6(HH)

Which do you find easier to read? The ratio (4:1) or the initialism (AF)?


edit: 4d6/6AF(3:1) vs. 4d6/6HH(1:2) not 4:1 as I had mistakenly written.

[tombowings]

Personally, I like the ration, but I think it works better with both the ratio and the italics. It's a little more work, I know, but it's a lot easier for me to understand the prose than the mechanical jargon.

[thegreyelf]

There's something too many people overlook about game design.

Whether the math works out correctly is a complete non-issue. Break down the d20 system, for example, and you'll see that. Mutants and Masterminds (an offshoot of d20) is another great example.

Why is this? Because--and this is important--dice are not perfect random number generators. Far from it, in fact. They have quirks, minute differences in weight per side, non-perfect shaping, etc. Even the way you flick your wrist when rolling can have an effect on outcome. I have a d6 (which I never use for gaming because of this) that ALWAYS comes up 4 or 6 when I roll it properly. I'd say 8 out of 10 rolls I can get it to produce a 4 or 6 result. And it's not a gimmick die, either--just a normal die that happens to have a quirk that causes it to roll as though it were deliberately weighted.

This is why some dice seem to roll better than others.

This doesn't even take into account the fact that statistics assume a perfectly neutral environs and never work out in practice the way they do on paper.

Often, a game can look 100% perfect statistically on paper...and just play like crap. Numbers have to be tweaked by gut feeling and through playtest.

Thus, the common usage is almost always better than statistical analysis when dealing with game design. A lot of mathematicians and stats geeks hate to hear that, but I've been doing tabletop game design professionally for ten years now, and that's just the truth of it.

These statements, of course, don't remotely hold up when talking about computer games, which are far better random number generators than dice.

...and after I typed all that I re-read your initial post to discover that what you were asking had nothing at all to do with what I wrote. *blush.* Still, the statements stand.

As to whether one should round up or down, down is the common factor in 99.99999999% of games, but you can always choose to round fractions up if you want to favor the players. It comes down to how difficult a game you want to play.

Rounding down will penalize the players more than their opponents, who exist as a one-off fight while players' characters go on and on.

Rounding the players down and the opponents up will make for an extremely harsh, gritty game.

Rounding both up will benefit the players for the same reason as rounding down penalizes them.

Rounding the players up and the opponents down will create an epic-hero environment where the players have a great advantage.

[Deleted]

Well as a game designer and former stats and math professor I say always go with the simpleist rolls.

The amount of time saved rolling and doing mental math is translated into more play. *Maybe* you sacrifec "realism" but not enough to matter in the long run.

Tim

[cooper]

Thanks for the feedback. I think default I will use initialism+ratio, with occasional uses of italic descriptive language.

AF4d6/6 (3:1) 4s vs. HH4d6/5-6 (1:2) 4c

this stands for:
Armored Foot Hero rolls 4d6 counting each 3rd 6 as a hit and himself takes 4 simultaneous hits to be removed from the battle vs. a Heavy Horse Dragon rolls 4d6 counting each 5 and 6 as two hits and itself takes 4 cumulative hits to be removed.

reducing the ratios gives us:

4th level hero:
att/def: AF
hits: 4s
dmg: 4d6/6
vs.
Dragon:
att/def: HH
hits: 12c
dmg: 8d6/5-6

Somewhat arbitrary, because I can't divide the heroes 4 attacks by 3, I simply tripled the hits required to kill the dragon.

Lets look at a giant vs. dragon.


HF/AF12d6/6 (1:4) 12c vs. HH4d6/5-6 (1:2) 4c

Where: The Heavy Foot offense/Armored Foot defensive Giant rolls 12 dice counting each 4th 6 as one hit and itself requires 12 cumulative hits to be removed vs. Heavy Horse dragon rolls 4d6 with each 5-6 counting as two hits and itself requires 4 cumulative hits to be removed from battle.

Reduced without ratios:

Giant
att/def: HF/AF
hits: 12c
dmg: 12d6/6
vs.
Dragon
att/def: HH
hits: 16c
dmg: 8d6/5-6

last one 1:10 ratio (where one figure represents 10 men)

30 gnolls vs. 10 sword masters note: the 3nd level fighters are not heroes and thus does not get multiple attacks, nor the benefit of simultaneous hits to kill. Gnolls are a 2 hit dice monster in d&d.

2 units HF gnolls 1d6/6 (2:1) 2c vs. 1 unit AF swordmasters 1d6/5-6 (1:1) 3c

where: the Heavy Foot gnolls roll 2d6 counting every 2nd 6 as one hit, themselves requiring 2 hits to remove 1 unit vs. Armored foot swordmasters roll 1d6 counting each 5-6 as one hit and themselves require 3 hits to remove from the field of battle.

reduced without ratios:

2 units of Gnolls
att/def: HF
hits: 2c
dmg:1d6/6
vs.
1 unit Swordmasters
att/def: AF
hits: 6c
dmg: 1d6/5-6

instead of counting every other gnoll hit, I simply doubled the hits required to remove the singe unit of swordmasters.

round 1: gnolls roll 1d6x2=1, 6
round 1: swordmasters roll 1d6=5

result: gnolls reduce the sword masters to 5c, next round if the swordmasters score another hit, one unit of gnolls will be removed from play.

[cooper]

I think the best option for dispelling confusion would be this: hero vs. dragon as an example.

4th level Hero
Att/def: AF
hits: 4s
dmg: 4d6/6 (3:1)

Dragon
Att/def: HH
hits: 4c
dmg: 4d6/5-6 (1:2)

If you didn't know what your unit was fighting and just wanted to stat them out it is even simpler

just for fun you could list the CHAINMAIL hero and dragon but add d&d nomenclature:

Hero:
Att/Def: AF
Hits: 4s
Dmg: 4d6
AC: 2
Thac0: 13
hp: 28
att: 3/2
dmg 1d6+4

Dragon:
Att/Def: HH
Hits: *4c
Dmg: *4d6+special
AC: -1
thac0: 11
dmg: d6/d6/2d6+special

*Dragons can range in size from 1 horse for small or up to 6 horses for ancient wyrms.

notice I did not list 4d6/6 or 4d6/5-6 because this number changes based on what creature it is fighting, so too there is no ratio because the ratio changes based on what creature you are fighting. you have to look up the attack matrix of armored foot vs. heavy horse to find your ratio and of course all of these fights could be resolved quickly on the Fantasy Combat table rolling a 2d6 and determining the probable outcome. Alternately you could use the man-to-man tables (as modified by d&d) and get into even more detailed fights. Note: if you do not use the greyhawk supplements introduction of extraordinary strength in your conversion, nor variable weapon damage the hero translates poorly and will have a much reduced chance of defeating the dragon than that which is shown on the Fantasy Combat Chart or in CHAINMAIL.