The Three-Player Problem
- Essay by Kevan, March 2025
Nomic is a game where players vote as a group to change the rules. How does the proposal aspect of the game change at small player counts?
One player
Solitaire Nomic is winnable in one move: the player unanimously passes a proposal saying that they have won.
To make the process more complex, they can either:
- Use proposals to solo design some non-Nomic solitaire subgame, then try to win it without using proposals to help them.
- Start by proposing constraints on their own proposal ability ("I cannot propose to say that I have won"), and challenge themselves to escape from those bounds and propose victory.
The first isn't meaningfully distinguishable from just designing a non-Nomic solitaire game to your own satisfaction and then testing it.
The second is an exercise in finding loopholes in a ruleset, where the player is the arbiter of whether or not any given edge case or scam succeeds, and they only have to convince themselves. It can be an interesting puzzle, but it's questionable whether it would count as a game of Nomic.
Two players
In a two-player Nomic, a proposal can only pass if both players agree to enact it. Assuming that both are playing to win, a proposal to say that one person wins the game, or gets any kind of clear advantage, will be voted down by the other.
Such a pair of players will only agree to enact a proposal which is either:
| Perfectly fair | Typically early-game stuff where the game is not yet complex enough and the gamestate not developed enough for there to be any question over whether a proposal advantages one player more than the other. |
|---|---|
| Close enough to fair | Once the game is more complex, the players may be able to negotiate their way to an agreement by changing clauses and tweaking numbers until both are happy that the scales are sufficiently balanced. Perfect balance isn't necessary, if neither player is genuinely sure whether the proposal is, in total, strictly better for one player than the other. (The size of this "close enough" zone will vary according to how seriously the two players are taking the game, and how much time they have to think about proposals.) |
| A trap | Although a proposal looks better for the proposer's opponent (possibly being written subtly enough that the opponent thinks the proposer may have overlooked this), it's actually hiding a larger advantage for the proposer. |
| A callout | In a game that supports long-term strategies or hidden information, a player may propose something that would be mildly detrimental to some potential plan or secret gamestate of their opponent, to see if they object enough to veto it. An opponent may tactically take the hit and vote it through, to make it appear that the proposer was wrong about that hidden information. |
| A called bluff | With hidden information or strategies, a player may bluff by proposing a rule change that's actually bad for them ("aces can't be used in sets" while they have an ace in hand), to attempt to mislead their opponent. Their hope would be that their opponent takes the misleading message on board, and votes it down for some other reason (the opponent possibly bluffing in response that they have an ace in their hand). But the opponent may, to the proposer's disappointment, call the bluff and vote it through. |
"Perfectly fair" is easy at the start, and can be extended by delaying the point at which gameplay actually begins. "Close enough to be fair" has potential, but can be slow unless negotiated in real time conversation. Traps, bluffs and callouts are tactically interesting even when they fail, but require some subtlety.
In practice, a two-player Nomic is likely to run on "perfectly fair" and "close enough" proposals until the gamestate becomes complex or hidden enough for a player to believe that they are in the lead - at which point they have a strong incentive to maintain that status quo by not allowing the other player to pass any more proposals, in case they turn out to be traps or callouts.[1]
A two-player Nomic having a period of pre-game rule design and then locking into a fixed ruleset as soon as one player feels that they are ahead is still a meaningful game, but it can mean that most of the play duration doesn't meet the "a game in which changing the rules is a move" definition of Nomic.
Three players
In a three-player Nomic, the same pattern is there as with two players. Initially, it's easy to say whether each proposal is fair, but after a while, one player will feel that they have a meaningful lead and will be content with the status quo: they will tend to stop supporting proposals from the other players. (They might be wrong about having a lead, but will still act as if they have one. It may even be that two players both believe themselves to be slightly in the lead, and both act in this way.)
At this point, one of two things can happen:
| An alliance | If any pair of players made a sufficiently strong agreement to work together earlier in the game (perhaps when it had more players and "I agree to support all of your proposals" seemed a smaller commitment), that pair can now win by controlling all proposals against the objections of the solitary player. It doesn't matter who was in the lead: two lagging allied players can propose to overtake the leader; a supported leader can shut down all proposals, or make one that would accelerate ending the game.
If no strong pre-agreed alliance exists then then players might try to form one now - the plainest one being the two lagging players teaming up to win instantly by proposal. But this is likely to be regarded by all as an uninteresting way to end the game. |
|---|---|
| A standoff | If no alliances were made, the game will enter a standoff.
If the two lagging players are considering a milder alliance ("I won't support your proposals, but I'll choose game actions that harm the leader rather than you"), the lead player is in a good position to make a counter-offer to one of them: the leading player is usually the better person to ally with, since by definition they're in a stronger game position. Any smaller punish-the-leader agreements are likely to be deterred by the prospect of tit-for-tat retaliation - if two players agree to diminish the leader to the point where they are no longer in the lead, then that process can be repeated for the new leader.[2] |
So it either plays out as a two-player Nomic, with proposals largely being switched off and the game playing out unamended, or it is revealed to be a much simpler game of whether or not two players can form (or had already committed to) an alliance.
Four plus players
With more than three players, standoffs and strong alliances start to diffuse. The wider spread of player positions also gives the game a more complex dynamic, including a greater focus on whoever is in second place.
Adding just a fourth player balances some of the 2-vs-1 problems of a three player game. If two players happen to have an alliance, the other two can form their own alliance to maintain a proposal stalemate (rather than the fourth player joining a 3-vs-1 pileon against the leader, or a 3-vs-1 crackdown from the leader and their existing ally). That second alliance will likely cut them a better deal (a 50% share of whatever can be offered, rather than 33%) and would be generally seen as more sporting gameplay than three players easily ganging up against one to directly end the game.
The likely presence of a clear second-place player also focuses the group to consider the consequences of any strong (but not game-ending) proposal that punishes the current leader: they will just be setting up a new leader, who could also be punished in turn.
2-vs-2 is still a stalemate, especially if both sides form ironclad voting alliances of "I will copy your vote on all proposals", which makes it a two-player game. But if alliances are even slightly looser, the proposal game can continue.
Less active players
The above analysis assumes a game between engaged players who are each trying to win the game, and who discuss each proposal before voting on it, and who talk about those votes.
If less active players aren't proposing and are only voting passively (i.e. waiting for everyone else to vote and then casting whichever vote wouldn't change that outcome), then any given proposal simply drops to a lower player count, and - if that count is now below four - likely ends up at one of the stalemates.[3]
If less active players vote and propose but don't follow or react to discussions and attempts at negotiation, this is more of a problem. At higher player counts it doesn't make much difference, but in smaller games - crucially in three-player ones - it can swing the game's outcome heavily or completely in favour of whichever of the active players they happen to have acted in the interests of (by voting for one player's proposal before the other can make a counter-argument or counter-offer, or by proposing something unbalanced and not responding to the disadvantaged player's reaction).[4]
See also
- The history of the Dormancy rule in BlogNomic, which (at time of writing) pauses the game when it drops below four players
- The BoardGameGeek page for Nomic considers it (through a poll of its users) to be a game for at least four players ("best with 6-11")
Footnotes
- ↑ For example, the Life Goals dynasty ended with only two active players, its winner Josh saying in the post-game discussion that "I didn't bother proposing at all in the back half as anything I would have wanted on the books would have been correctly viewed as partisan."
- ↑ When applied to proposals in BlogNomic this is sometimes called the Munchkin Effect, which may merit its own essay on why straightforward "let's just eliminate the leader" proposals never really happen in Nomic.
- ↑ For example, the Simulation dynasty ended with three active players and a fourth who hadn't taken a dynastic action in over a month and was just voting passively. Active player Bucky said in the washup that "There wasn't a whole lot I could do to compete 2v1 in such a small group."
In the Life Goals dynasty example above, the game had two active players who were trying to win, and two inactive ones who were not. The outcome of that (with the inactive players supporting anything that the active two agreed on, and presumably demurring on anything that was controversial) was the same as if the two inactive players had not been there.
In the Alien DNA dynasty, the Dormancy threshold was temporarily raised by 1 when the fourth player seemed to be acting passively. As proposer I noted that (with game actions being anonymous) "I can't tell if I'm playing a three-player Nomic or a four-player one right now." - ↑ The Freight Shipping dynasty ended with two active players and three significantly less active ones. The Emperor proposed a coin-flip to pick a winner from the two most active players: those two players both supported the idea, and agreement of the least active player (who had immediately voted DEF) was enough to take the proposal to quorum before the other two players responded in any way.