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Random idea for a strategy game. You, and the other player, both have three pins, and five discs of different sizes that fit on the pins, all in ascending order of size on pin 1. Your goal is to have all your discs on a pin 3. Towers of Hanoi, in other words. But you can also move your discs onto their pins, still obeying the "no big disc on a small disc" rule. Is there an obvious winner?

@sil Presumably moving "red" onto a "blue" stack blocks "blue" from moving that stack? Can discs be placed on discs of the same size? If so, player 1 wins every time, of course, by simply blocking player 2 on the first move.

@neil I think that anyone can move any piece (which is in a position to be moved). Your goal is to get all your pieces "out" (on to the two pin 3s) before the other player does.

@sil Wouldn't it immediately degenerate? As first player, my first move is to place my smallest piece on the enemy's goal. Second player does the same to me. Neither of us will ever have any incentive to move those pieces unless it guarantees us the win. And neither will ever have that opportunity since the other player's piece is there. So no one ever wins and the game is a draw.

(Possible rules change: You can't play onto your opponent's goal space. Might fix this problem?)

@nickwedig yup, that's fair! So the game idea doesn't work. :)
The altered approach you suggest seems maybe more workable? I'm not really sure how to analyse this sort of thing...!

@sil Based on a little modelling of 1, 2 and 3 discs, I think the first player is in a dominant position and can always guarantee a win. I'm not 100% sure on that, and there might be some dynamics that emerge with more discs. But I don't think so. I think a good first player, familiar with the Tower of Hanoi's basic principles, can play a perfect game and always beast the second player.

@nickwedig ah, then you are right and it isn't fun. The idea just sorta popped into my head last night; clearly it didn't pop in from a source that invents self-consistent fun rulesets! Cheers for the investigation, though!

@sil It's really, really hard to make a 2 player abstract strategy game of perfect information where the first player doesn't have a huge advantage or a guaranteed win.

There might be ways to save this. (Rolling dice to determine which towers you can move to on a given turn? The board is a web of towers to build on, and you can only move so far from the towers you're already on? special powers for different discs?) But you'd probably lose some of the elegance of the idea in the process.

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