Playing Yahtzee while you RP

[sparkletwist]

The question I'm trying to ask with my rather glib title is what you all think of games with interesting, weird, minigame-ish dice mechanics.

I personally kind of like them from a gamist perspective, but I can also see how they'd be distracting. I also think that they're a lot harder to balance probabilities-- it seems like if the designer tries to get too "clever" all that really happens is that a bunch of suboptimal options get put in that will always lead players to mathematically inferior outcomes when one analyzes the expected value. This seems undesirable, and the only conclusion I can draw is that the designers themselves didn't fully calculate the probabilities of the system they were designing.

Let's take Elegant10 for example. I'm not meaning to pick on it, as such, but I've analyzed the probabilities and it highlights the problems I'm noticing, so I'll be using it as an example. It is a basic sort of dicepool system where you roll a number of d10s and take the best value, with a sort of weakened exploding mechanism where if you roll any more 10's when you've already got one, you get a bonus +2. However, what you can also do is choose not to roll any number of your d10s and take a +1 to your roll instead. This means that if your pool is 3 dice, you can also roll 2 dice (keeping the best) and then add a +1 bonus or roll one die and add a +2 bonus. Sounds fun and gives the players interesting options, right?

Nope. Here's the problem. For one die, your expected value is 5.5. For two dice, your EV is 7.17 (the expected value of a standard roll 2d10 and keep the best is 7.15, this one is slightly higher because of the 1% chance of ending up with a 12). On the the other hand, the expected value of rolling one and using the other for a +1 bonus is only 6.5, i.e., the 5.5 from before +1. It's demonstrably mathematically superior to roll two dice so unless you will die if you roll a 1 and a 2 is ok, there's no reason to ever roll one die and take a +1 bonus. Rolling three dice gives an expected value of 8.03, whereas the expected value of rolling two dice and getting a bonus of +1 is 8.17. It's a close call, but two dice wins. Rolling four dice has an EV of 8.58, whereas rolling three and getting +1 has an EV of 9.03, and rolling two and getting +2 has an EV of 9.17. One die is forever left in the dust and is never something you want to do, adding more dice to the pool leads to ever more diminishing returns, and two dice will always retain its slight edge over three dice. In other words, all this seeming complexity and choice is pretty much reduced to roll two dice and add the rest of your pool as a bonus, because if you do anything else, you're getting a mathematically suboptimal outcome.

I think far too many systems that introduce fun, crunchy dice mechanics end up including false choice like this that makes the system completely fall apart under mathematical analysis. And in that light, it makes me wonder... is it even worth bothering with anything other than a simple system of picking up a dice, tossing it, and seeing what it says?

[beejazz]

I think the only uses a special roll might have are
a)cramming more information into the roll than pass/fail
b)offering a genuine apples to oranges choice (for example, in my last version of my homebrew, attack and damage were merged and players could pick the number of dice... ostensibly allowing a trade off between accuracy and damage)
c)something like exploding dice, actually doing something to probabilities of outcomes (in this example, opening the upper end)

[Lmns Crn]

I am hesitant to outright discount the notion of "dice gimmicks" because I think that, done right, they can potentially be fun and interesting. Elegant10 is perhaps not a great example, but the existence of one bad example isn't much of a condemnation of the whole general concept.

[LD]

Does any system use "imploding dice"?

Roll a 1 and then roll a d6 and add that as a negative to your roll bonus? :D Then repeat on a 1.

Or would that be too cruel a mathematical fate, even if paired with exploding dice?

[sparkletwist]

the existence of one bad example isn't much of a condemnation of the whole general concept.

I agree. My point was more to say "Look, the probabilities of this stuff are really hard to analyze. That in itself makes them a bit more difficult to use, and what's more, here's one that I've bothered to analyze, and the results weren't pretty. How many others are out there that also crumble under a rigorous analysis?"

Does any system use "imploding dice"?

Rolemaster actually did something like that. :P
(Of course the game with the infamously gruesome critical hit tables would do something like that...)

[Stryker25B]

Some players thrive on the metagames within tabletop RPGs. Have you ever had a session that was wholly dedicated to a single facet of the overall game? A lot of my D&D campaigns usually featured a night or two that was nothing but crafting, because I would inflate the crafting system a bit to make it more interesting for the players. Say the player was trying to craft a longsword +2, first we need a mastercrafted longsword. I kept that simple, but when it came to actually imbuing it with the magic, there would be a few arcana and spellcraft checks. A natural 20 would give a +1 bonus to the next roll. If they passed the player would then roll d10 to see if they manage the +2 bonus (9-10), only managed a +1(5-8), failed (2-4), or failed completely and melted the sword(1). They would get the previously mentioned bonus here and if they scored an 11 or 12 they could add another +1 bonus or a minor additional ability to the weapon. It's been years since I did this, so I don't have all the different tables I created in the course of campaigns. As the characters grew more powerful and added additional skills for crafting magical items, I would adjust the table to allow for more powerful items. At one point, a highish level PC fighter died, but rather than spend tons of treasure to have him resurrected, his faithful wizard buddy opted to try to put his soul into his greataxe "Because it's what he would have wanted." An hour of roleplay and successful rolls later, one of my players was now roleplaying a sentient greataxe.

It's this kind of emergent gameplay that makes me love these games, and my role as a DM, so much!

[Superfluous Crow]

Hmm, I will probably have more to say on this later, but if we take a full-blown exploding dice mechanic (roll 1dx, roll again and add if you roll x, continue ad infinitum) isn't this a 1) simple 2) fun 3) statistically valid dice mechanic, worthy of inclusion in a hypothetical game system?
It doesn't change the likelihood of rolling below x (and incidentally completely removes the chance of rolling x), but otherwise it just adds a dwindling probability of rolling very high numbers.
Without having to add an arbitrary "20 always hits" mechanic you have suddenly given the weakest-of-the-weakest a feasible chance at achieving the impossible.    

But yeah, I can see the issue with the above. Although it does make for a favorable lower margin to ditch a die, as you mention. Would it be possible to change the static bonus so it makes sense mathematically?

EDIT: Stryker, you mention Emergent Gameplay and this is a concept I really, really love - when a set of rules opens doors that you didn't even know existed!

[Ghostman]

Crow, the example given by sparkle is significantly more complicated than a simple roll 1dx system, because only the best die actually counts. It's essentially a roll-and-keep system, and that is something that makes the math rather difficult to figure out. Not to mention the rule where additional explosions after the first one are converted to flat numbers. That's hardly what I'd call "elegant" :P

[Superfluous Crow]

I study math and I realize that the elegant10 model is reasonably statistically complicated, I just wanted to offer the classic explosive dice mechanic as a "dice mechanic done right". An opposed example if you will, as a basis for further discussion. 

[Matt Larkin (author)]

Does any system use "imploding dice"?

Roll a 1 and then roll a d6 and add that as a negative to your roll bonus? :D Then repeat on a 1.

Or would that be too cruel a mathematical fate, even if paired with exploding dice?

Hearing the phrase "imploding dice" made my whole day a little bit better. Thanks for that :)

[sparkletwist]

Some players thrive on the metagames within tabletop RPGs. Have you ever had a session that was wholly dedicated to a single facet of the overall game? A lot of my D&D campaigns usually featured a night or two that was nothing but crafting, because I would inflate the crafting system a bit to make it more interesting for the players.

I agree with you about RPGs containing some fascinating little diversions like this. I recall long-ago sessions of AD&D being led on enjoyable tangents by the inclusion of various gambling games in town, not to mention the fun when we first ran across the potion miscibility table. However, these are systems that are but one part of the whole "game experience." This is fundamentally different than playing some sort of dice game every single time you pick up the dice and roll.

I will probably have more to say on this later, but if we take a full-blown exploding dice mechanic (roll 1dx, roll again and add if you roll x, continue ad infinitum) isn't this a 1) simple 2) fun 3) statistically valid dice mechanic, worthy of inclusion in a hypothetical game system?

Definitely. It's also a rolling mechanic that doesn't include any complicated "Yahtzee-like" tricks or any real (or illusory) player choice. The probabilities are also not that difficult to analyze. In other words, yes, but this is a "just pick the dice up, toss them, and see what they say" mechanic so it isn't what I was talking about.

[Lmns Crn]

Let's be clear: are you specifically talking about games where players are given choices about what to do with their dice that alter probabilities?

[Lmns Crn]

Also, hey, have you looked at Dogs In The Vineyard? Because that game is all about unusual dice strategy stuff.

[sparkletwist]

Let's be clear: are you specifically talking about games where players are given choices about what to do with their dice that alter probabilities?

Yes, sorry that wasn't clear before.

I have looked at DitV, and I can't say it made a lot of sense to me.