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Subject: Fire and Ice: First impressions rss

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Robin Munn

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Fire and Ice is an abstract strategy game that draws inspiration from Tic-Tac-Toe, but avoids the "Always ends in a draw" problem in some interesting ways. To start with, the basic board has seven spaces in it rather than nine, and draws are impossible: if the board is full, then someone has won the game.


Rules

The Fire and Ice board is composed of seven triangular "islands", arranged in a triangular formation: one "island" at the three points of an equilateral triangle, another "island" in the center of the triangle's three sides, and the seventh "island" in the geometric center of the triangle. Each "island" contains seven holes arranged in the same triangular formation. There are also seven lines on each island, and seven corresponding lines connecting the islands: the three sides of the triangle, three lines connecting one side to the opposite corner (via the center), and a circle connecting the three mid-side positions. (If this description doesn't make sense, simply look at one of the submitted images for this game to see the board).

The object of the game is to control three islands "in a row" (which means three islands along any one line or circle). One controls an island by getting three of one's own pieces "in a row" on that island. So to win the game, one must get three three-in-a-row formations in a row. A few moments' thought will show that if a seven-space board is full, there must be three in a row of one color along one, and only one, of the lines. Since the formation of the islands is the same as the formation of the spaces on each island, the same principle applies to controlled islands: when every island has been controlled by either Fire (red pieces) or Ice (blue pieces), the game will be over, because there will be one (and only one) line of three islands controlled by the same player. Therefore, Fire and Ice can never end in a draw.

So far this game sounds like merely a Tic-Tac-Toe variant. But there's one more game mechanic that we haven't covered yet: moving. The game starts with a single red (Fire) piece in the center hole of the center island, and Fire moves first. Each player selects one piece of his color and may either: a) move it to any other unoccupied hole on its current island, or b) move it to the corresponding hole on any other island (so a piece in the center of one island can move to the center spot of any other island), but only if that hole is unoccupied. And here's the interesting mechanic: a moving piece leaves behind a piece of the other color. So on the first turn of the game, Fire has only one piece available to move, in the center hole of the center island. After Fire has moved, the center hole of the center island is now occupied by an Ice piece. Since that's the only Ice piece on the board, Ice must move it, and at the start of the second turn, the center hole of the center island will be occupied by Fire again.


Strategy

Having played this game only once (at GenCon 2003), I feel inadequately prepared to comment on strategy. Still, I'll give it a try.

The basic strategy of Fire and Ice is like that of Tic-Tac-Toe: get as many two-in-a-row threats as possible, and block your opponent's threats before he can convert them to three-in-a-row. But the game's move mechanic adds a twist to that strategy: how do you block your opponent's threats? If you move a piece from the same island to block him, you've just handed him a new location on that island, and probably a new two-in-a-row threat that he can now convert (since it's now his turn). But if you move a piece from a different island instead, your opponent now has an extra piece on that island, and new possibilities over there.

Which islands will you fight for? Which ones will you give up? If you try to control too much territory, the pieces you hand to your opponent with your every move will work against you. You have to choose your fights carefully in order to win.


Replayability

Since Fire and Ice is a game of perfect information (no dice, no hidden cards), it could theoretically be solved. That would probably take quite some time, however. In the meantime, the move-and-leave-an-opponent's-piece-behind mechanic is new and interesting enough to hold your attention through at least four or five games. After that, it will probably depend on your gaming tastes. If you like abstracts, Fire and Ice may entertain you for quite some time.

Fire and Ice is easy to explain and learn, but deep enough not to be easily solved, and provides an interesting twist on an old and familiar (very old and familiar) game. Overall, I'd give it about a 7 out of 10.
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Daniel Danzer
Germany
Stuttgart
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rmunn wrote:
Since Fire and Ice is a game of perfect information (no dice, no hidden cards), it could theoretically be solved.


This sentence is obviously untrue. "Solved" is not equal to "perfect information". If you start a game of "Go", you have perfect information, but an empty board. Now, tell me the "best move". Even later in the game, there are lots of moves of equal "quality".
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Hubert Orlik-Grzesik
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...it could theoretically be solved...

Better?

Even Go is an alternative of conjunctions, so it has a solution. It's just a very huge alternative. Therefore this solution will be far beyond mankind knowledge for next few millenia or so.
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Jim "git yer stinkin' themes offa my mechanic" Puccio
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Exactly. Every perfect information abstract is a finite-state automaton (or graph), with every board position (and all its symmetries under the rules of the game) occupying exactly one of the states (or nodes), and the rules defining the possible state transitions (or edges). Its finiteness is what makes it theoretically solvable. But it's a "small matter of implementation" (ha ha) to actually do so. What is theoretically possible in a mathematical analysis can also prove to be intractable in practice (for example, NP-complete problems). But in any specific case, I wouldn't venture to hazard a guess as to the improvements either in the theory of computation, or actual computational resources (massively-parallel quantum computers, anyone?) that might come down the road, nor exactly when they may enable any given game, even the venerable Go, to succumb to analysis.

All that being said, even if a game is "solved" in every position, for a sufficiently complex solution, this will have no practical bearing on real players, nor their enjoyment of playing it.
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