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.
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