boardgames

I love Death in Space's turn order style. One of the players goes first, then they decide which enemy goes next. Then when the enemy is done, they decide which player goes next. This repeats until one side is out of participants, and then the other team's participants go in whatever order they like.

This avoids any discussion for who goes next, and helps cut down on long winded strategy discussions because there's no guarantee to the turn order. Gameplay becomes way more focused around taking advantage of the current situation, but you can still plan a strategy.

Interesting challenge! Its curious how programming leads to this systematic analysis and the revelation of complexity even for “simple” things

There are some games where the turn order can be influenced that I am not sure are covered by your rules:

5 tribes has a auction-style system by players committing a certain amount of currency to occupy a specific slot in the turn. For 2 player game each player goes twice and auctions twice for the upcoming turn

Bot factory is using a rotating worker placing mechanic with 4 sections with each 2-3 worker position, with the limitation that you cannot remain in the same section

Castles of Burgundy player order divided in 5 turns divided into 5 phases which changes depending on playing certain tiles (ships and specific monasteries)

Rather than trying to define abstractions for turns and rounds, maybe you could implement the game state (and possibly individual players) as a finite state machine.

In this model, the way you set up the states and transitions for a particular game will capture its idiosyncracies in turn and round order.

In Galaxy Trucker, there is a "distance" or "race" track that manages turn order.

Once all players have built a space ship (simultaneously picking and laying tiles), players place markers on a race track. The first player to finish building their ship is in first, the second player behind them, and so on. I believe there is one empty space between them all as well.

The rest of the game is flipping over event cards one by one and resolving them. Some events are resolved by all players simultaneously. Others are resolved in the order on the race track. First player resolves part of the event. If there's anything left to resolve, second player resolves part, and so on.

Part of resolving an event might involve moving a certain number of steps up or down the race track, skipping over any occupied spaces.

So turn order here would be complicated to work out, especially in a FSM. Effect cards may change turn order, but not always. There may be empty space between two players in the turn order that gets reduced or increased instead. I suppose you could model it with N real players and then X place-holder players that don't actually take their turn.

Looks quite comprehensive! Some cases that may or may not fit in already:

• Turn order for the rest of the round determined by an early simultaneous step of the round: Gloomhaven, Undaunted, Khôra: Rise of an Empire
• Player gets an immediate extra turn due to an action: Mottainai "Frog" card
• Game ends immediately (mid-round) due to player action: Mottainai again.
• Round ends immediately due to a player's action skipping the other players' turns: Cubirds
• Parts of the round are timed: Bullet♥︎, Flatline

Action selection games might ruin your idea, like in Race for the Galaxy, everyone picks actions and everyone gets to do all actions selected. Puerto Rico is similar, but actions are selected in turn order instead of simultaneously.

Dominion has the possession card, which gives player A control over player B's turn, and player A gets all cards acquired by player B. There's also cards that grant extra turns, with varying conditions.

Red Dragon Inn has a basic turn order, but every player have many cards that can be played anytime or in reaction to certain events. There's also the gambling mechanic which gives everyone a turn in a mini game that doesn't affect the main turns.