I need some DND 5E maths for a finals assignment

[GabesHorn]

Hey Giantitp members,

This is a senior high school student checking in. For maths, there's this gnarly project that I'm unfortunately obligated to do but it's an open ended exploration that I can do on anything so long as it takes into account a good bit of maths from my syllabus. I'd be bored to death doing some generic maths problem so I chanced on DnD for a better time, still, I'm not sure what maths specifically I could hone in on.

I've gone through a bit now, I'm pretty set that my primary focus will be on probability, with the dice rolling and all. I thought the advantage disadvantage stuff would be interesting. Does anybody know some interesting DnD mechanics or maths problems I could explore?

I need to actually have issues to resolve. I'm thinking about stuff like 'pick this feat or this feat' for optimising DPR but I'm not the most heavily experienced DnDer so I'm not sure what situation I could use to keep this feat choice problem relevantly open ended. Most likely a fighter base?

For the advantage disadvantage system are there any vexing problems which could bring up some more difficult probability maths based content? I already made a table about how likely you are to get certain values with adv/disadv but now I need problems to solve instead of just analysis to transcribe.

Finally, I always do need a bit of other content (in terms of topics) aside from probability. But it's gotta be a bit harder than just adding numbers so I do need some clarification on if there are other harder topic areas. I'll put a general list here:

1. Math fundamentals. 6. Triangle trigonometry.
2. Functions and equations. 7. Statistics.
3. Sequences and series. 8. Probability.
4. Exponential and logarithmic functions. 9. Probability Distributions.
5. Trigonometric functions and equations.

Thanks for reading and thank you for literally any help I get in advance. DnD is just a big game and I need a bit more of a direction as to where I'm steering this maths patchwork.

[Boverk]

One thing you could do with advantage would be disadvantage vs. Normal vs. Advantage, throw in elven accuracy for one more possibility.

You could do character creation 4d6k3 vs. Point buy.

Dual wield vs. 2handed damage

How valuable is extended crit range?

Health vs. AC for survival

You could also do some math on prep round vs. All out attack...i.e. for a hexblade, should you hex first? Or all out attack right off.

Is an asi more useful than a particular feat?

You could also throw in some simulations if you wanted to do that

[mgshamster]

DPR calculations give you multiple aspects of your project:

Deriving equations
Actually solving equations
Probability: must determine probability to hit in order to determine the DPR
Statistics: determine averages, range, mean vs median, etc...

For trig stuff, you could look at theater of the mind and try and determine just how far a fireball will extend around a corner, given that the corner is not a 90° angle.

[GabesHorn]

Thank you both. I forgot that ASIs would be the most logical comparison to a feat, silly.


Character creation vs point buy is brilliant and as concrete as I would need to make it easier on myself. Could be checking that in also.

Health vs AC... prep round vs all round.. all sound great. Problem is it's a 12 page project so I'll need to narrow it down. And I want to avoid looking scattershot looking like I just chose DND random topics and stuck them together willy nilly.




So it might also be difficult to link it to the theatre of the mind sort of content. Statistics + probability seems like the most natural combination and I guess since I already have equations that probably diversified my maths portfolio enough.

[Naanomi]

It isn’t super hard, but in terms of highschool level math; doing the math to find the damage breakpoints for Sharpshooter with Elven Accuracy would align with 12th grade common core statistics and algebra standards

[Kane0]

Table of attack bonus vs AC featuring four lines on the graph tracking chance to hit:
No -5/+10, no advantage
-5/+10, no advantage
No -5/+10, advantage
-5/+10 and advantage

That ought to do it.

[dreast]

The question if “what’s the expected value and distribution of 4d6-L” is actually pretty interesting mathematically, and comparing that to point buy to decide the optimal start could be fun.

[LudicSavant]

For triangle trigonometry, you could do the optimal usage of the Locate Objects spell. I even did a post about the trigonometry involved somewhere.

[MrStabby]

Game theory might be good. 5 simple pregen characters to chose from, two players pick one. What mixed strategy is a stable equilibrium.

Simpler might be death saves - use binomial theorem and different bonuses to see the effect on probability of death without other intervention. Or look at this as a markov process.

Not sure what country this is in or what is on the syllabus there.

[DMThac0]

Some of the maths involved with creature creation may be helpful here:

HP vs Effective HP and how it affects CR
AC vs Effective AC and it's effect on CR
Damage values toward CR
Traits and how they may or may not have an effect on CR

combining all of those inputs to a final CR, and how simple changes may adjust the final outcome.

(if Effective AC is 2 higher than the desired CR AC increase AC CR by 1) for example.

[qube]

barbarian vs monster - fighting reckless (both you & enemy have advantage) or not

[Foxhound438]

you could also do some more detailed analysis of effects like bless and bardic inspiration that add another die to the d20. it's pretty commonly accepted to add a flat percentage based on the average of the added die, and statistically speaking it works, but you could do a full tree diagram or something to prove that it works out. With this you could also put together a probability mass function table for each possible result. Maybe do a comparison of giving an ally advantage on one attack vs. giving them a 1d6 bardic inspiration to see if one is better in a given situation.

[Contrast]

You could also look at how some of these expectations change depending on if you used different dice instead of a d20 - 2d10, 4d5 (its a maths problem, you don't need to worry about weird dice :smalltongue:). Or weirder systems like pulling cards numbered 1 to 20 from a deck and reshuffling when you've pulled all the cards and how that changes things.

Honestly not sure there's really enough meat to sink your teeth into for a whole project but then I guess I don't know how in depth your project needs to be.

[Grog Logs]

...but now I need problems to solve instead of just analysis to transcribe...


...Health vs. AC for survival...Is an asi more useful than a particular feat?

SCENARIO A "Here be dragons": You are facing a solo dragon. The dragon will use its breath weapon attack whenever able to and use it's claws/bite when the breath weapon is unavailable. Should the Player (e.g., Fighter or Paladin) invest in Strength for Plate Mail, Dexterity for Saving Throws (and possibly light or medium armor), Constitution for health (which will help for both types of attacks), or Charisma (only applies if Paladin for aura)?

The dragon type will be somewhat dependent on the PC level. Currently away from book.

SCENARIO B1 "Orc Gauntlet": You are a level 8 Champion Fighter. You are about to face 6 waves of 3 Orcs each. Assuming that you can take a short rest between each wave, how should you spend your ASIs/feats? Compare the relative benefits of Durable vs. Constitution ASI vs. Strength ASI.

SCENARIO B2 "Infinity (Orc) Gauntlet": Same as above but now there are infinity waves of Orcs. What ASI/feat combination will last the most battles? Long rests after every 6 waves (or 10 waves if we need to up the difficulty).

Adjust the number of waves and monsters per wave, if needed, to result in different answers.