Namaste, Jude and I played a game of Lenga last night, which was an interesting experience, especially considering that Jude was not familiar with the notation of formal logic (he is more familiar now — and I hadn’t intended to make an educational game :-). Degeneracy (the “dicks” rule) is not an issue: there was no lack of interesting statements.
One of the biggest problems was that Namaste and Jude had trouble coming up with interesting ways to twist the game. I think this is more about people learning how to play the game than a flaw in the game. Namaste took 5 minutes on his turn when the only thing on the board was “There exists an object called 0”. What needs to be understood is that the game will not start twisting until we have some significant assumptions, so it’s better to just start writing some stuff down than to come up with something clever for the second move of the game. It’s kind of like playing pente: you can’t come up with a clever move for the second or third move of the game, because there are not enough pieces on the board yet.
Aside Jude’s frustration at the notation, the game was decently fun. It got fun when we got to something like 20 axioms, and the properties and operations started to become concrete. There was a problem with the competitive portion of the game, however, since if you were in a tough spot, you could just make a new definition. We tried to solve this by only allowing each player to introduce three new symbols throughout the game (if you said “∃x blue(x)” and blue hadn’t been mentioned before, you have introduced a symbol). We never finished that game because of dry-erase marker delerium.
Anyway, the biggest problem was the tyrrany of choice. At any stage in the game, there were far too many statements you could make. Namaste was thinking of making it a card-based game, and I tend to agree. More instructional cards than entire statements that you would play. Here are some examples of cards:
- ∃x blue(x) — write this statement when this card is played.
- ∀∃ — you may write a statement of logic with exactly these two quantifiers in this order.
- commutative — state that a binary function already defined is commutative. If no such function exists, introduce one.
On every turn you have to play something (and probably draw something). This means that you may just get screwed if, for example, there is only one function defined and the axioms already contradict it’s being commutative.
I’m going to make some cards now, so maybe we can play this game during GameDev.