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I agree, Rich. But the concept is essentially the same. For example a Queen of 9 points fighting a Rook of 5 points... or having 9 (1 unit pieces) fighting 5 (1 unit pieces). In both cases statistics come into play with chance favoring the stronger piece (or group of pieces).
If all units are the same value, or there is a bunch of them, you can do single combat (this is Risk). When you decide a queen is worth a LOT more than another piece, it leads to things being exponentially worse.
Risk Godstorm and Risk 2210 A.D by Avalon Hill, (as well as the original Risk) boardgames seem to have already employed the concept that Single Combat Chess aims at; of course, without using chess pieces.
A problem when you propose game rules for literary or 'artistic' reasons, is that the foundation doesn't come from gameplay. If your idea is to have a unit challenge another unit to a duel, add another game level of play, where the battles can be fought out, and based on skill of players at the mini-game, one unit or another can win.
The points below are well taken. What I was really trying to do was express a concept from literature - the idea of chess capturing moves as ritualised single combats, with the attacker formally challenging the defender. This naturally excludes multiple attacks and the element of surprise. I accept that these things might make for a better game, but then the literary concept would be lost.
In most cases piece A has the same chance of beating piece B whichever attacks, and this seems too much of a change. It would be less of a change if each piece had a better chance when attacking than when attacked, e.g. a Queen attacking a Queen requiring a score of 4 or more on 8-sided dice. In wargaming terms this could represent the attacked piece being taken by surprise, not knowing from which direction the attack will come.
In wargames, you have combined units attacking a single unit that is more powerful to eliminate it. You don't have that, as far as I can tell, with this game. This makes, in my assessment, a game where pieces are exponentially more powerful than they would be normally. I don't see what issue is 'addressed' here at all. Chess is an abstract strategy game, where combat/capture is deterministic in nature. This proposal stops making it chess, or chess-like, in my assessment. It becomes a simple wargame. If you want to go this route then have it so that pieces move next to others and then can attack multiple against one. You also need to allow multiple pieces to move. In other words, make it more wargame-like.
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