algebra and DND

[tokonaut]

what kind of algebra is there in DnD i ask because it is for a very important school project also I this the correct thread for this kind of question??

[Gaiwecoor]

It's sparse, really. Typically, you just do basic arithmetic. (3+5+6=14! Yay!) The closest thing that actually comes to algebra that immediately springs to mind would be spells with a dice/level effect. Something like magic missile would do it for you:

For every two caster levels beyond 1st, you gain an additional missile—two at 3rd level, three at 5th, four at 7th, and the maximum of five missiles at 9th level or higher.

It's pretty simple, really.

[Dublock]

unless you want to get into more heavy duty math that I would be hesitant to call Algebra, for example figuring out the difference of the mean and the standard deviation of the result of rolling 3d6+2 appose to rolling a 1d20. That falls under Probability and Statistics.

Then if you want to figure out the falling damage/charging damage for a few situations, that got into some heavy math...I don't remeber the exact situation/spell but that got complex.

Also you can figure out how WoTC came up with the equation to determine the exp costs per level :p.

[Maerok]

A series of graphs for an Empowered CL 10 inflict X wounds versus a Maximized one and a normal one, for various spell levels (minor, moderate, serious, etc.). This would show which is the best choice for average damage.

My dread necromancer would appreciate it.

[Artanis]

You can figure out the CL of a multi-enemy encounter for a party of non-standard size.

...though that might require calculus.

[SirGhandi]

any attempt to optimize damage (for instance, power attack) could be treated as an algebra problem. X would be the number to take off the attack roll and 2X would be the resulting damage addition. For kicks, consider multiplying the expected average damage (including the +2X) by the expected probability of hitting (similarly affected by -x) and boom, a nice little quadratic emerges. Hope that helps.

P.S. Using 3.x rules... if you're strictly 4.0, you'll have to adjust.

[Prometheus]

The grid movement rule is a simplification of the Pythagorean theorem. Investigate whether or not this is a good approximation, and if so, under what circumstances. Also, generalize to 3D (in which case, the 2D hypotenuse forms one of the two sides).

Power attack, already mentioned, is a good problem, very reachable with algebra.

Attempting to optimize the best action for a PC in a given combat scenario will get as complicated as you like it to be. It is choosing between multiple options, each with a certain probability of contributing to your ultimate success, which is contingent upon succeeding in other options with a certain probability etc etc until you win or are defeated. Than select which path gives you the highest probability of winning, the quickest path to winning, or winning comfortably with the least expenditure of resources.

[Maerok]

Two-handed combat versus two-weapon combat.

I had this whole set-up for SW Saga to study whether using Double/Triple Attack and Double Weapon Fighting and rapid Strike all together is sane or not. Total average damage per round, etc. I even had it rigged to test it against various ACs and employed adjustable Strength and Dexterity. I love Excel. Made some really nifty stuff with it.

[seedjar]

I think some of the above posters were correct; there's algebra in playing D&D, but not in the system itself.
You can use algebra for optimization purposes with D&D, but the way that attributes and attack rolls and such are related isn't regular and I would be reluctant to call anything in the D&D rules real 'algebra.' There's no solving for unknown variables or first-class expressions; D&D is value-based. If there were any significant algebra to D&D, it would quickly fall apart with all of the contradictory rules.
~Joe

[Heliomance]

For more algebra than you can cope with, try here.

Warning: Degree in advanced mathematics required for full comprehension.

[Artanis]

For more algebra than you can cope with, try here.

Warning: Degree in advanced mathematics required for full comprehension.

*looks*
Feh, that's second- or third-year stuff. Now, if they were doing the stuff where 8+7=6 is actually true, we'd be talking

[Heliomance]

I've seen a thread which had even more horrible maths. Currently looking for it. Long story short, you got infinite attacks per round - sometimes.

[Sstoopidtallkid]

Once when falling we had to break out physics to figure out how many chances to save against Hold Person the flier got. Good times. But very little algebra. I did figure the odds of monsters making their Sense Motive checks against my Malconvoker, which is opposed d20 rolls, but that's Stat, not Algebra.

[tokonaut]

so anything using the formula y=ax(2)+bx+c?

[Heliomance]

The quadratic formula has sod all to do with D&D, I'm afraid. Not sure why you thought it would.

[tokonaut]

just wishful thinking

[ShneekeyTheLost]

Well, there are several variables involved in D&D, which can be used with algebraic expressions...

for example, level-dependent effects are good choices

Short range = 25+ 5*level or r=25+5x
Medium range = 100+ 10*level, which is to say r=100+10x

There is no squaring in D&D, though, so quadratic formulae are not used. You want that, go see GURPS.

[Yakk]

You can generate quadratic formula solutions as part of analyzing D&D.

Try doing an analysis of Twin Strike -- you end up with a square in the probability. So if you want to work out when Twin Strike intercepts the average damage of, say, Reaping Strike, you need to solve an equation involving a square.

[tokonaut]

i talked to my teacher and he said there are numerous examples such as the volume of a fireball or was it area? The slope of shooting an arrow from a cliff into a kobold the chance of success and so on.

[ShneekeyTheLost]

i talked to my teacher and he said there are numerous examples such as the volume of a fireball or was it area? The slope of shooting an arrow from a cliff into a kobold the chance of success and so on.

The problem is the volume of a fireball is constant, because the diameter of the fireball is constant. The slope of shooting an arrow from a cliff into a kobold is a quadratic equation, however it does not in any way impact the chance of sucess, which is a simple D20+variables. Distance may be a factor, but not a square.

I think Yakk has it best. How about this, why don't you try expressing the effectiveness of Power Attack vs normal attack at various AC? Then you can also express the value of Power Attack for a 2h weapon vs a 1h weapon.

[tokonaut]

well isn't a fireball well a ball and what is the volume of a flaming ball of ...fire with a radius of 20ft also all the applications algebra can be used in real life could be applied in DnD so why not?

[ShneekeyTheLost]

well isn't a fireball well a ball and what is the volume of a flaming ball of ...fire with a radius of 20ft also all the applications algebra can be used in real life could be applied in DnD so why not?

The problem is that there are no variables, they're all constants. It's a 10' radius fireball. That would make the volume a constant 314.16 (rounded to two decimal places) cubic feet. Every fireball ever cast (baring some shaping nonsense) has that same volume.

[monty]

The problem is that there are no variables, they're all constants. It's a 10' radius fireball. That would make the volume a constant 314.16 (rounded to two decimal places) cubic feet. Every fireball ever cast (baring some shaping nonsense) has that same volume.

If, however, you found a spell with a radius of X feet per level (I'm sure there are some, but I'm too lazy to check), then it would be a quadratic function with a variable.

[Frosty]

If, however, you found a spell with a radius of X feet per level (I'm sure there are some, but I'm too lazy to check), then it would be a quadratic function with a variable.

Otiluke's Resilient Sphere?

[monty]

Otiluke's Resilient Sphere?

Well, that would be cubed, but if you wanted to find the area of the great circle, it'd work, I guess.

Edit: or surface area. Calculus is making me forget my geometry.

[tokonaut]

On the note of the shooting from a cliff, I'm sure if we got into more specific details such as race, class, height, height of cliff and how far away the target is, algebra will show up. Also with a firball spell if you cast it in a room of a certain size how much room will the monster's inside have to move around freely in without being burned. There are lots of algebra concepts that i'm just begining to notice. I also feel i may have phrased the question wrong i meant to algebra in the game itself not the d20 system, which is why i asked if this was appropiate for this thread. It is not the system but how algebra can be applied to DnD within the world of DnD. Am I making sense, i'm usually told i'm not so i like to make sure.

[Gamiress]

I don't get into the combat number crunching, but I have used a little basic algebra for roleplay purposes to compare relative age for non-human characters. It helps to know that your century and a half old elf is about 17 as elves would count things.