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D&D 5E Game theory, D&D, and infinite games

pemerton

Legend
I wasn't sure what the "game theory" was that is being referred to in the OP. Some posts - eg referring to the prisoner's dilemma - have made me wonder whether we're meant to be thinking of game theory in that sense.

If so, before we even start talking about single-play vs iterated, and whether the number of iterations is known in advance or is open-ended, where are the pay-off tables? And what preferences are under analysis - just those that are defined by the logic of play (eg a preference to win combats my PC is part of), or all the preferences that a player brings to the table (eg maybe I have a reason to throw the chess game because that way my opponent will buy me lunch)?

Also: it's certainly possible to reason about payoffs in an open-ended series of iterated plays.
 

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There are clearly finite games nested within the infinite game of D&D, such as combat, exploration, interaction, character creation, missions, quests, modules, adventure paths, etc. But those are not the whole game. They are mini games. Finite games nested within the infinite game. You the player create your character. Your character can win a combat. Your character can complete a quest. Your character can explore a dungeon. Your character can charm the duke. You the player have input, of course, because you're controlling your character in the game. But to think of the infinite game of D&D as a finite game creates a mismatch of expectations. Which leads to a lot of problems within the community. When some people focus exclusively on the finite mini games within the infinite game, it's frustrating to almost everyone involved. There’s nothing wrong, per se, with focusing on one of the mini games in D&D, but focusing on one or two mini games to the exclusion of the others and the infinite game as a whole misses the forest for the trees.

The mismatch of expectations becomes a problem because it leads to arguments and recriminations and endless threads debating the particulars or this or that stye of play, i.e. focusing on one of the finite games nested within the infinite game. We see it all the time when a power gamer (focused on "winning" the character creation mini game) and a deep-immersion roleplayer (focused on "winning" the immersion mini game) try to talk about character. Or a deeply tactical players (focused on "winning" the combat mini game) butts heads with a storygamer (focused on "winning" the mini game of emulating a story). None of these styles are right, or wrong, but knowing which mini games you like (and which you don't) are a great way to focus your play and find a group that will work well together. A beer & pretzels combat-focused game is just as valid as a deep-immersion game which is just as valid a hexcrawl.

Or maybe you want both, but those things are in tension. That is, you want a character that is "3d," with a rich interiority and ties to the world, but when you translate this character into the mechanics of the game, they end up ineffective or not "optimal" in some ways. Or, more prosaically, sometimes an option for your character might be more interesting but less than optimal; feats, especially the more niche ones, are an oft-cited example in 5e.

From what I can gather, there appears to be much debate about how to approach this, with some saying that a Paladin Warlock multiclass character, for example, should make sense within the narrative before being allowed, while others saying that it's not the DMs or anyone else's business how a Paladin Warlock character makes sense, because it's the right of the player to meet their goals of being optimal.
 

Fanaelialae

Legend
Those aren't win conditions for the game, though. They are win conditions for the PCs, with an addition of a reward for the players' next characters.
I disagree. If the win conditions are completed, then the players "win" the campaign. In that the game ends (the campaign is over) and the players are considered to have won.

The characters might "lose" but the players still win, assuming the conditions are met. For example, in the dragon rescue scenario, the party might die bravely while fighting against the evil princess, buying the dragon time to successfully escape her clutches. The characters don't really win that scenario. Yes, they achieved their goal but at the ultimate cost. Their victory, if it can be said to be such, is pyrrhic at best. The players, on the other hand, all get to high five and celebrate because they've won that campaign, despite their characters being dead.
 

Maxperson

Morkus from Orkus
I disagree. If the win conditions are completed, then the players "win" the campaign. In that the game ends (the campaign is over) and the players are considered to have won.

The characters might "lose" but the players still win, assuming the conditions are met. For example, in the dragon rescue scenario, the party might die bravely while fighting against the evil princess, buying the dragon time to successfully escape her clutches. The characters don't really win that scenario. Yes, they achieved their goal but at the ultimate cost. Their victory, if it can be said to be such, is pyrrhic at best. The players, on the other hand, all get to high five and celebrate because they've won that campaign, despite their characters being dead.
These are the unconventional, "we all win if we have fun" type wins, though. In the first example, they still have those characters and can use them in further campaigns or adventures, because D&D really doesn't end, even if the campaign does. They may never do that, but it's a possibility. In the latter, they still all had fun and even though the PCs lost, they still all had fun and had that unconventional win.
 


Argyle King

Legend
One of the struggles I sometimes have when trying to ignore the "finite" mini-games in D&D is that some of those mini-games are somewhat clearly favored as being more correct ways to interact with (and "win") the game.

I believe this is due to the heavily-vertical nature of D&D advancement.

For example, there are a lot of feat choices, magic items, and etc which I find to be cool, flavorful, and interesting. However, the structure of the game tends to punish my character's ability if I choose those options over the +N options too many times.

In some ways, 5E is better at that than 3.5. Characters aren't magic-item Xmas trees like they were before, but D&D still tends toward rewarding a more-vertical approach to character building.
 

Fanaelialae

Legend
These are the unconventional, "we all win if we have fun" type wins, though. In the first example, they still have those characters and can use them in further campaigns or adventures, because D&D really doesn't end, even if the campaign does. They may never do that, but it's a possibility. In the latter, they still all had fun and even though the PCs lost, they still all had fun and had that unconventional win.
That's not what I was referring to. The DM sets a win condition for the players. Rescue the dragon.

If the PCs rescue the dragon, the players achieve the goal and the players win.

If the PCs fail to rescue the dragon, the players have failed to achieve the goal, and the players lose.

It is irrespective of whether they "win because they had fun". They could successfully rescue the dragon but have a miserable time of it. Or fail to achieve the win condition but have a great time of it.

It's also irrespective of whether the characters win. The players can achieve the goal but the characters all die. Presumably, most if not all of the characters would not consider their own death a win condition. Their goal was more than likely to achieve the goal AND live to tell about it. Which distinguishes it from the players' win condition.
 

Maxperson

Morkus from Orkus
That's not what I was referring to. The DM sets a win condition for the players. Rescue the dragon.
Okay, but that's not typical RPG play. I've never had a DM in any RPG tell me that he's setting win conditions on the game. But okay, if the DM wants to invent win conditions, he can.
 


Lanefan

Victoria Rules
That's true of basically everything numerical on a character sheet? Your character probably can't walk up to an npc and say, "I have a 13 wisdom, what's yours?" or anything to that effect.

Anyway, I don't mind giving out of character XP rewards if I think they are useful. For example, for writing the recap in a shared google doc.
You do you. :)
Do you create narration for level ups? Does the character know they've gotten better in some way, or do they even train during downtime as a way of narrating leveling up?
In order: often yes, usually yes and almost-without-exception yes.
 


clearstream

(He, Him)
In game theory there are two types of games: finite games and infinite games. Finite games are bound by specific rules about how players win and lose, how many players there are in the game, time limits, etc, and the goal is definite: to win. Infinite games, on the other hand, are not bound by specific rules about how players win and lose, there are no time limits, no limits on how many players, etc, and the goal is indefinite: to continue playing.

One example is the difference between a formal debate (finite game) and a conversation (infinite game). One interesting point is you can have finite games nested within an infinite game.
Working from your overview, it seems to me straightforward to say that infinite games can also be nested in finite games. Imagine we are playing classic Risk, and some players decide to play out the story of a cannon crew.

So, for example, within a conversation you can have a mini informal debate, but once that's over, you can shift back to the conversation. This is also why having an unmoderated debate is such a waste of time. There's no external score keeper or timer, so informal debates can simply keep going ad nauseum. Another interesting point is that when you have a mismatch of expectations, one person thinks they're playing a finite game when they're really in an infinite game, the finite players will inevitably get frustrated by the actions of the infinite players...or two players focusing on different finite games nested within an infinite game butt heads. This stems from the fact that the finite player is trying to win, whereas the infinite player is trying to continue the game...or two players have defined mutually exclusive personal win conditions. You see this all the time in conversations. One person is trying to have a conversation while another is trying to have a debate. As posters on internet forums, I think we can all relate.
Another way I have seen this put is as games with closure and without. One concern would be to ask how the proposed model treats the metagame? For example, in a Chess tournament I may indeed play closed games of Chess, and yet the tournament is not closed based on a given game. "Ah" one might say, "but the tournament itself is closed!" But then there is the matter of my Elo, which carries over - spanning games and tournaments.

So, without using game theory terms, D&D defines itself as an infinite game, not a finite game. Some people object to that statement, pointing out that there are win conditions in D&D. But, the crux of their argument relies on conflating the player with the character. There are indeed win conditions for the characters within the game but there are no win conditions for the players at the table. The player doesn't win but the character can. The player doesn't level up but the character can. The player doesn't gain XP but the character can. The player doesn't gain treasure but the character can. The player is meant to simply enjoys the game. Now, a fair few players choose to impose win conditions on the game themselves, but again, this is by conflating the player with the character. "I win as a player at the table when my character wins within the game." Which is a perfectly valid approach, but that is an explicitly self-imposed choice, not a function of the game itself. The game itself defines exactly one condition under which the players at the table win: "if everyone had a good time and created a memorable story, they all win." The character succeeds or fails, lives or dies based on the player's decisions and the dice, but the player can just keep on playing the game. The goal of D&D is the players asking the DM: "When can we play next?" The goal of D&D is to continue playing. Exactly like any other infinite game.
The relevant game theory terms are zero and non-zero sum, and what is described is very different from how finite and infinite seems to be being used. Win conditions don't tell us a game is closed, but can tell us the game is zero-sum. You can see that by supposing that the win condition is something so elusive, so remote, that the putatively finite game will prove to be infinite.

The distinction between the player and character goes down a misleading path. In games, players always control pieces that hold their state and translate their intents into events (or attempts at events) in the game world. We still speak of the player winning. The line of argument would have it that the Rook and Queen that checkmate the King win, rather than the player! An ontological distinction between sport and game might be that player and piece are identical in sports, but then we have esports...

There are clearly finite games nested within the infinite game of D&D, such as combat, exploration, interaction, character creation, missions, quests, modules, adventure paths, etc. But those are not the whole game. They are mini games. Finite games nested within the infinite game. You the player create your character. Your character can win a combat. Your character can complete a quest. Your character can explore a dungeon. Your character can charm the duke. You the player have input, of course, because you're controlling your character in the game. But to think of the infinite game of D&D as a finite game creates a mismatch of expectations. Which leads to a lot of problems within the community. When some people focus exclusively on the finite mini games within the infinite game, it's frustrating to almost everyone involved. There’s nothing wrong, per se, with focusing on one of the mini games in D&D, but focusing on one or two mini games to the exclusion of the others and the infinite game as a whole misses the forest for the trees.
It's an interesting area for discussion. The terms I am drawn to are zero and non-zero sum from game theory (to describe whether all that do not win must lose) and closure (to describe if the game has no consequence.) Games that genuinely have closure are rare, and generally not found to be satisfying. Most games have a metagame that gives meaning to the individual outcome.

Which is where one can see that 5e is not an infinite game, but rather one where the metagame is explicit. So that a given combat has closure (at the end of the final turn of the final round of the combat), but an explicit metagame carries forward consequences.

The mismatch of expectations becomes a problem because it leads to arguments and recriminations and endless threads debating the particulars or this or that stye of play, i.e. focusing on one of the finite games nested within the infinite game. We see it all the time when a power gamer (focused on "winning" the character creation mini game) and a deep-immersion roleplayer (focused on "winning" the immersion mini game) try to talk about character. Or a deeply tactical players (focused on "winning" the combat mini game) butts heads with a storygamer (focused on "winning" the mini game of emulating a story). None of these styles are right, or wrong, but knowing which mini games you like (and which you don't) are a great way to focus your play and find a group that will work well together. A beer & pretzels combat-focused game is just as valid as a deep-immersion game which is just as valid a hexcrawl.
It seems to me that there is ample evidence of that mismatch being observed sans the finite-infinite games mental model. Therefore it would seem that finite-infinite might be being introduced as an explanation for that mismatch. I fear it might rather act to obfuscate. I don't need to play Chess with a goal of winning, and yet according to the model the finite nature of Chess ought to explain my behaviour... I expect you can see the problem,

And while it's clear that there are some incredibly good and quite targeted (limited scope) RPGs that would count as finite games, with explicit win and loss conditions for the players, it's also just as clear that most RPGs are not like those few. Most RPGs have a wider scope and can, at least in theory, cover any kind of story. They also don't have win conditions spelled out for the players. The characters in most RPGs can win or lose certain tasks, goals, missions, quests, modules, etc...but there are simply no rules about how a player wins or loses D&D. Quite the opposite. D&D and several other RPGs explicitly state there are no win conditions for the players...because D&D is an infinite game.

So...with all that said...how about we try something completely different for a change?

Why don't we try to have a conversation about all of this instead of a debate?
I appreciate you introducing this interesting mental model or theory for conversation! Above I've tried to lay out a few initial concerns that I have relating to the concept as I grasp it.
 

clearstream

(He, Him)
1.) Finite and infinite games are not the coomon diction used in game theory, but they do differentiate between games that end and games that repeat or cycle. Prisoner's dilemna, for example, has different expected results if you assume the game will be repeated than if you play it only once.
Exactly! Games require a metagame to have meaning. Repeated play. It strikes me that a useful framing could be (stepping away from finite/infinite) games that contain a metagame within them, and games that do not. We might want to reserve "metagame" for only what happens outside sessions of play, but then RPGs seem to blur that boundary, e.g. with the campaign.

2.) Game theory, in general, is about optimization of results. While some gamers focus on optimization of damage, control, etc... for their PCs, the core of the game is a story telling game and there isn't really one optimal path in good storytelling. Often, it is when a PC does something despite not being great at it that creates a fond memory.
Specifically, optimisation where there are other actors who also want to optimise (for some goal). I think game theory could be applied to story-telling. It just requires analysis of the stakes and payoffs: there is nothing to say that stakes and payoffs can't be social or cultural etc.
 

pemerton

Legend
I think game theory could be applied to story-telling. It just requires analysis of the stakes and payoffs: there is nothing to say that stakes and payoffs can't be social or cultural etc.
There are philosophers, behavioural (and other) economists, etc who do this sort of analysis. I'm not persuaded that it is successful.
 

FrogReaver

As long as i get to be the frog
It seems to me that there is ample evidence of that mismatch being observed sans the finite-infinite games mental model. Therefore it would seem that finite-infinite might be being introduced as an explanation for that mismatch. I fear it might rather act to obfuscate. I don't need to play Chess with a goal of winning, and yet according to the model the finite nature of Chess ought to explain my behaviour... I expect you can see the problem,
One can avoid that problem by simply saying that you aren't playing chess if you aren't playing with a goal of winning. Your playing something similar to chess, but not chess.

That is, what does it mean to play a particular game?
 

clearstream

(He, Him)
One can avoid that problem by simply saying that you aren't playing chess if you aren't playing with a goal of winning. Your playing something similar to chess, but not chess.

That is, what does it mean to play a particular game?
Suppose that I accept a contention that I am not playing a game if I am not playing with the goal of winning. On surface, that could imply that so-called infinite games are not actually games, because one is expected to play them without the goal of winning. If so, then it turns out that only players at the table who are trying to win, are really playing an RPG as a game.

The infinite games theorist might grasp the horn of the dilemma, and uphold that infinite games are games, but for some reason they get a pass on the goal of winning. I think that will make their arguments less compelling, as they have built their result into their definition, whereas so far as I can make out they might have hoped that their concept was going to explain or entail that result. Seeing as they have now defined that a game can be a game without being played with a goal of winning, they might also be expected to explain why finite games must have that goal?

Alternatively, they can say that a game can be a game without being played with a goal of winning. Perhaps then the best place to land will be to concede that I can play Chess as a game without a goal of winning, but that players ordinarily would not. They can say it is an expectation about so-called finite games that you try to win them. It is hard to see though, why I couldn't have the same expectation about infinite games. In any case, their theory becomes one about behavioural norms, rather than ontology. I assume that is the case, and am asking what power the infinite/finite theory delivers to that discourse given it comes with some rather messy baggage?

Or they could accept the dilemma, and say that infinite games are not games. Our third sentence above is right (or RPGs are not 'infinite'.) I don't see that leading to a theory that will be widely embraced by those seeking to understand games.
 
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Fanaelialae

Legend
Okay, but that's not typical RPG play. I've never had a DM in any RPG tell me that he's setting win conditions on the game. But okay, if the DM wants to invent win conditions, he can.
I've never had a DM say they were setting win conditions either.

However, I have had plenty DMs say, "We're getting near the end of the campaign. I am going to conclude things once you face the BBEG that you've been gunning for the last few sessions (regardless of the outcome)". I've had some additionally say that if we were successful we would receive some reward in the next campaign (typically some benefit for the characters we create for the next campaign). I've also had it where a win condition was set, but the reward was tied to an optional bonus win condition (in one instance, slaying a very dangerous blue dragon who had continuously been a thorn in our side). In at least one campaign there was a secret win condition that rewarded us in the following campaign, which was only revealed after we had achieved it (it was associated with a particular character's goals).

In none of those cases did the DM say they were setting win conditions. Nonetheless, that's what they effectively were.

That said, obviously, this is not necessary for playing an RPG. You can play and have fun without any win conditions at all (except, arguably, those self-imposed by the players themselves). I've simply been making the case that RPGs are not "infinite" by necessity, and can certainly be played as "finite" games.
 

FrogReaver

As long as i get to be the frog
Suppose that I accept a contention that I am not playing a game if I am not playing with the goal of winning. On surface, that could imply that so-called infinite games are not actually games, because one is expected to play them without the goal of winning. If so, then it turns out that only players at the table who are trying to win, are really playing an RPG as a game.

The infinite games theorist might grasp the horn of the dilemma, and uphold that infinite games are games, but for some reason they get a pass on the goal of winning. I think that will make their arguments less compelling, as they have built their result into their definition, whereas so far as I can make out they might have hoped that their concept was going to explain or entail that result. Seeing as they have now defined that a game can be a game without being played with a goal of winning, they might also be expected to explain why finite games must have that goal?

Alternatively, they can say that a game can be a game without being played with a goal of winning. Perhaps then the best place to land will be to concede that I can play Chess as a game without a goal of winning, but that players ordinarily would not. They can say it is an expectation about so-called finite games that you try to win them. It is hard to see though, why I couldn't have the same expectation about infinite games. In any case, their theory becomes one about behavioural norms, rather than ontology. I assume that is the case, and am asking what power the infinite/finite theory delivers to that discourse given it comes with some rather messy baggage?

Or they could accept the dilemma, and say that infinite games are not games. Our third sentence above is right (or RPGs are not 'infinite'.) I don't see that leading to a theory that will be widely embraced by those seeking to understand games.
I didn’t say you weren’t playing a game. I said you weren’t playing that particular game - but instead something similar to it.
 

Ovinomancer

No flips for you!
I didn’t say you weren’t playing a game. I said you weren’t playing that particular game - but instead something similar to it.
Cool, so what are the default win conditions of D&D, and what games are people really playing if they don't do that?

This is the reductio of the argument in context of the OP. I'm a proponent of D&D having win conditions embedded in the playloop and I don't find this argument persuasive.
 

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