Good forum for Dice/Boardgame/RPG mathematics?

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Yakk
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Good forum for Dice/Boardgame/RPG mathematics?

Postby Yakk » Tue Jan 08, 2019 4:41 pm UTC

I'm looking for a place I can chat about probability & dice & board game mathematics with other people who are at least nominally interested and useful.

Googling for such a forum I keep on running into "board games that involve math to play". I'm looking for a place where I could ask or even meaningfully discuss, say:

Spoiler:
In a risk-type dice pool game (two or more sides roll pool of dice, you match dice in order from highest to lowest, higher die wins), how much better are d8s than d6s? Ie, in what way would d8+2d6 beat Nd6? How does Xd8 vs Bd6 compare to Ad6 vs Bd6? Can we form upper/lower bounds on the worth of a bigger die compared to a smaller die? Does this generalize, so d10s vs d8s, and in what way? How about d6s where you can reroll 1s and 2s, how do those compare? Is the effect sufficiently exponential? What if a d6 beating a d8 only caused 1 point of damage, while d8s where worth k points each, does that change things?

(The goal is to have dice pool based conflict resolution that handle larger ratios of power without blowing up the number of dice rolled)


or

Spoiler:
In D&D 4e wealth XP follows a 2x every 4 levels scale. XP in encounters maps +4 levels to being as hard as 2x as many creatures. +4 levels has affine effects on damage and HP, and linear effects on ATK/DEF. It may also have effects on number of limited expressions and special abilities (definitely on the player side, maybe on the monster side).

A: If we strip out the +1/2 level bonus to ATK/DEF, what is the most correct XP curve?

B: Is there a way to do away with having to build a master XP chart that obeys this new curve? Ie, even-level monsters (for the party) are worth 20 XP, +/- 5 XP for every difference in level, and gaining a level requires 200 XP. What if it was monsters are worth 20+2*Level XP, +/-3 per level different than the party, does that work better? (insert graphs)


To get either type of question to a point where it is worth "asking" would require hours of work; hence the desire to look for a forum with interested counter parties. :)
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Re: Good forum for Dice/Boardgame/RPG mathematics?

Postby Xanthir » Tue Jan 08, 2019 5:22 pm UTC

The Math subforum should do just fine, actually. We've gotten those sorts of questions before.
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Re: Good forum for Dice/Boardgame/RPG mathematics?

Postby Deva » Tue Jan 08, 2019 8:04 pm UTC

Question 1
Ran 50000 simulations each time. Pitted highest die versus highest die. Continues until one side runs out of dice. Called all ties in favor of defense.

Reported the average number of offense wins. Example: 5 4 4 2 for offense. 4 4 3 for defense. Yields two offense wins.

d6 (offense) versus d6 (defense). Used up to five offense dice and two defense dice. (Remembered the maximum number of offense dice incorrectly. Decided to leave the extra information in.)

Code: Select all

        1       2
1 0.41700 0.25556
2 0.58130 0.77874
3 0.65740 1.07582
4 0.70702 1.25032
5 0.73796 1.35690


d8 (offense) versus d6 (defense).

Code: Select all

        1       2
1 0.56132 0.43964
2 0.76288 1.15000
3 0.85482 1.51532
4 0.90570 1.69862
5 0.93664 1.80702

Pushed up match-ups a fair amount. Increased one-on-one from 41.7% to 56.1%. Favors the attacker now. Shows 2d8 to be more effective than 3d6, also.

d6 (offense) versus d8 (defense)

Code: Select all

        1       2
1 0.31126 0.14312
2 0.43468 0.53750
3 0.49674 0.76134
4 0.53196 0.89644
5 0.55426 0.97714

Goes very poorly for offense, unsurprisingly. Sees better odds for defense, even with two dice against five. Reached about 50-50 odds at 3d6 versus 1d8.

d10 (offense) versus d8 (defense)

Code: Select all

        1       2
1 0.55198 0.42052
2 0.74358 1.12032
3 0.83964 1.47680
4 0.88908 1.66084
5 0.92354 1.76624

Appears to be similar to d8 versus d6, although slightly worse. Met expectations. Tried a few different dice two apart. Brought it to 0.50096 for one-on-one for d124 versus d122. Ought to approach d6 versus d6, with sufficiently ridiculous dice.

d8 (offense, no rerolls) versus d6 (defense, one reroll). Only rerolled 1’s and 2’s once.

Code: Select all

        1       2
1 0.48040 0.38158
2 0.69648 0.95978
3 0.81214 1.33388
4 0.88012 1.56378
5 0.91800 1.70786

Notes the largest effect on even match-ups. Erases most of the benefit as inequality increases.


d8 (offense) versus d6 (defense). No rerolls. Inflicts damage equal to (offenseroll – defenseroll) on an offensive win. Used averages, once again.

Code: Select all

Offense Damage
        1       2
1 1.74116 1.10330
2 2.58652 3.06240
3 3.09018 4.41570
4 3.41460 5.36510
5 3.64372 6.06972

Defense Damage
        1       2
1 0.43398 0.56218
2 0.23738 0.84054
3 0.14238 0.48914
4 0.09270 0.30436
5 0.06302 0.19438

Looks bad for the defenders. Suffered considerable damage, even with two defenders against one attacker. Won ~56.2% of the time. Took 1.1033 damage on average, including the zeroes from the losses. 1.1033 / (1 - 0.56218) = 2.519985 damage on an average offensive victory. Ouch.
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Re: Good forum for Dice/Boardgame/RPG mathematics?

Postby Mannequin » Thu Jan 17, 2019 12:52 pm UTC

Giantitp forums have people who like this sort of thing, op. It's a webcomic forum, but the comic is based on a roleplaying game, so.. Just remember to read the rules.

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Re: Good forum for Dice/Boardgame/RPG mathematics?

Postby Quizatzhaderac » Tue May 28, 2019 4:27 pm UTC

Regarding the second question.

My first suggestion would be to take the scalability of each factor and multiple them together to get an approximate effectiveness at each level. So, based off my understanding of DnD:
hit ≅ level
armor ≅ level
HP ≅ level^2
damage ≅ level^2
effectiveness ≅ Hit* armor * HP * damage ≅ level^6
or rather (constant+ level)^6 because level one is special.

Additional finicky details spoiler-ed
Spoiler:
The effectiveness of armor is actually hyperbolic. Versus a +0 hit attacker, changing armor from 12 to 16 has the same effect as 18 to 19 (halving the number of attack that hit you and doubling your survivability). Hit is also a hyperbolic curve, but the other way around.

I made HP and damage squared because you said they were non linear. That holds if constitution ≅ level. As for damage, I would think it's merely linear for a physical character.

Also, doubling the number of monsters doesn't make the encounter twice as hard. Doubling monsters doubles both the enemy's hit-points and attacks, so it's approximately squared.

I forget the rules about how much equipment one can have in D&D, but as I recall it's loose enough that an infinite wealth character is seriously overpowered for level. Therefore, the wealth by level is a serious contributor to one's power at any given level. Wealth has diminishing returns in how much of each stat it can buy (or how powerful each consumable item is), but the multiple contributions might be multiplicative.
I'd say this is already complicated enough to include a chart. Also a chart allows one to account for the fact that the power(level) curve might not be smooth in reality.
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Re: Good forum for Dice/Boardgame/RPG mathematics?

Postby SecondTalon » Wed May 29, 2019 12:50 pm UTC

For the record - D&D doesn’t exactly have rules about equipment ownership. There are a few items that have rules about use - the famous one being the Holy Avenger which is a +2 Sword for everyone else and a +5 Flaming Undead Slaying fuckoff killsaber for Paladins, but it’s mostly a matter of what you have found and can afford.

That said, there are rules about how much you can haul with you and how much you can use at any given time.

An infinite wealth level 1 character may be able to kill an appropriately wealthed level 20 character if they’re clever, as they’ll have access to all the tricks.
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Re: Good forum for Dice/Boardgame/RPG mathematics?

Postby commodorejohn » Wed May 29, 2019 1:19 pm UTC

RPG.net deals with pretty much every existing angle of pen-and-paper roleplaying in their main site content, and they have forums which look to still be active; that said, I've never actually hung out there myself, just read some of their hilarious articles on SenZar and World of Synnibarr.
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Re: Good forum for Dice/Boardgame/RPG mathematics?

Postby Quizatzhaderac » Thu May 30, 2019 3:30 pm UTC

SecondTalon wrote:For the record - D&D doesn’t exactly have rules about equipment ownership.
I know there's no unified system (as a game with a DM doesn't need them) , but I think there' some de facto ones. Like, (I believe) one can't stack the effects of ten amulets of natural armor, or stack magical equipment bonuses to any stat. Also, I'd expect (even without a written rule) that most GMs would say a person can't wear multiple sets of boots at once. Looking it up, some versions had a limit of two rings.

5e apparently has a system of "attunement" for items. A character can only have three attuned items at once. Items that don't require attunement seem to be non-combat, like a ring of water breathing.
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Re: Good forum for Dice/Boardgame/RPG mathematics?

Postby SecondTalon » Thu May 30, 2019 4:06 pm UTC

That's equipment in use, not ownership.

You can have ten amulets of natural armor in your pocket. There's literally nothing saying you can't do that.

You can even wear all ten at once.

But only one of them works at a time.

Effect =/= Ownership.

There are game systems out there that, for reasons of balance, do stress rules of only allowing characters to own X amount of gear, where X is a derived power level, currency figure, or some other factor. Given the context of what I was replying to, that's the question I was answering - that D&D lacks such a system of balance. If you can afford it, you can own it. You can also probably use it. Whether or not you can use all of it at once is another question entirely.

Which was already addressed by the single line second paragraph.
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