The "math" of RPGs

[GMMichael]

In short, increasing your number of samples make the phenomenon happen more, ie alot.

But that's not how statistics work. The more you roll the dice is the more they average out. If the DM just gets more and more killer rolls because she's had more encounters, it means she's using loaded dice.

Moreover, to mitigate the chance of bad luck TPK occurring it means a significant number of combats are going to feel easy as the only lever the dm has to prevent it is overall encounter difficulty.

The DM has way more levers than that.

Blame the players plan for them missing in the first round? Really? This could happen with any plan.

No. If they all miss in the first round, it's the fault of the dice (or that cheating DM from above). I was saying that they shouldn't all be swinging in the first place. Some could be moving to high ground. Some could be summoning a dire kobold. Some could be kicking the fire pit into their faces. Some (and bear with me here), could be playing a motivational song.

I disagree. Sometimes, in the first round, everyone does "their opening move" and sometimes the dice work against them. Monsters make all their saves, attacks miss etc...

That's a lot of "sometimes," and I don't think we need to be lamenting about TPKs or redesigning games when "sometimes" happens. Especially in games that use dice.

 

[TwoSix]

I will agree with the posts that say that it's an art and requires knowing the game, the PCs, and the players.

And...it got me thinking about the most exciting combats are the ones that are on the knife edge, or maybe on the monster's side of the knife edge, and how to keep it there. I'm imagining a kind of rheostat in combat rules, with mechanics that make the losing party stronger. "Bloodied" condition, with concomitant powers, would be an example of that, but I'm wondering what else could be dreamed up.

(n.b.: Baldur's Gate III has a few magic items that kick in when HP are below certain % thresholds.)

I mean, it's really difficult in a turn-based strategy game. All of those games are meant to prioritize making good opening moves, which puts you in a stronger position for the next turn, until your advantages snowball to the point where victory is inevitable. 4X games are all like that, RTS games are like that, chess is like that, etc. (Contrast this with most physical sports, and board games without an "engine-building" component; the only benefit to an early advantage strategically is the psychological pressure on opponents of having tighter margins to achieve a victory.)

If you're playing a game wherein you still only have a ~50% chance to survive on turn 5 even after strong earlier moves, then you're in a position where either a) the initial chance of success was much lower than 50%, b) the game was always 50-50, and your moves didn't actually impact the chance of success, or c) the opponent has relatively symmetrical strength and has also made strong moves. (This would be the chess or other strategy games situation between similarly skilled players.)

 

[RenleyRenfield]

....

So, I don't know, are there any RPGs that somehow manage to do this better? Is there a better way to design encounters to hit this sweet spot?

There are so many...

It does help to step away from D&D, OSR, or adjacent, as all of those are not really tryin to solve the no-fun combat and no-result failed rolls stuff.

Draw Steel does a good job at making minis combat more action packed, and reduce the amount of dud/nothing rolls.

Cypher (such as Numenera) does a good job at making combat high energy with all rolls being player act or player react. So the GM need only narrate the cray fun things enemies do, and focus none on dice and bonuses, and such.

Apocalypse World is just about unrivaled for intense and action-packed combat. So much diversity in what characters can do and how it can play out makes combats in Apocalypse World feel cinematic.

Exalted 3e has a overly clunky and very poorly balanced set of rules, but it really can be a blast to play anyway since its all over the top and for wear someone down till you can decisively take them out, and all of the munchkin ability to build characters is pretty much unrivaled.... over 1000 powers and growing...

so many more...

 

[FrogReaver]

But that's not how statistics work. The more you roll the dice is the more they average out. If the DM just gets more and more killer rolls because she's had more encounters, it means she's using loaded dice.

That’s precisely how probability works. You are misapplying the average out concept here. If you have a 1% chance and have 10000 samples then on average that result will occur 100 times. If it’s 100,000 samples then it’ll occur on average 1000 times. More samples -> more occurrences.

 

[TwoSix]

That’s precisely how probability works. You are misapplying the average out concept here. If you have a 1% chance and have 10000 samples then on average that result will occur 100 times. If it’s 100,000 samples then it’ll occur on average 1000 times. More samples -> more occurrences.

Yep. And crucially, people remember unexpected occurrences, not the expected ones. Everyone remembers the time the 0.1% chance of catastrophic failure happens, not the 99.9% of the time the reliable success happens.

 

[Vael]

I think over-emphasizing balance, especially on an encounter-by-encounter basis is a mistake. I'm less interested these days in a balanced encounter, I just want it to be exciting or at least interesting. Did an early crit, a splashy power, or a clever tactic make an encounter less challenging than expected? That's fine, as long as the players are jazzed about it. To me, DnD and RPGs are often a bit of a power fantasy for players (certainly that's why I'm playing spellcasters 90% of the time I'm not GMing), and mowing through my elaborate challenges, while I might feel a little cheated, enables that.

That said ... I do want to be able to push and challenge the PCs without throwing an RPG's encounter guidelines completely out the window.

 

[TaranTheWanderer]

That's a lot of "sometimes," and I don't think we need to be lamenting about TPKs or redesigning games when "sometimes" happens. Especially in games that use dice.

Yeah, that’s what @FrogReaver said,

If dice rolls go lucky or unlucky, don’t change up your next encounter to compensate. It’s just dice rolls. I think you misinterpreted their post.