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Subject: maximin strategy and Tzaar rss

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Alan Kwan
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When applied to 2-player abstracts (with typical alternating turns and such), the game theory concept of "maximin strategy" means that, you should assume that your opponent is smart and will make his strongest response, when considering what move to make now.

If we follow this principle, then it follows that the basic strategy in Tzaar is as what I explained: make a stacking move most of the time, and don't make a double capture unless you have a clear reason. For example, on black's first move, he should *always* stack and *never* capture two white Tzaars. The reason? Your chance of a quick win with the double capture relies on your opponent being dumb. If white is smart and responds by stacking up his Tzaar, you won't have any reasonable chance of capturing that Tzaar stack (since it's the tallest stack on the board), and you're now behind in stack strength.

When I play white, I start by capturing a black Tzarra, not a Tzaar. Why? Because black should stack a Tzaar on his first turn; why should I encourage him to do what he should do? No matter how many of his other Tzaars I pick off, he just need to defend that Tzaar stack (which starts as the highest stack on the board) and he'll be fine. But if I start reducing his Tzarras, in a few moves he will have two weak types to defend instead of just one; I can force him to play a 2-stack game instead of giving him a free choice. (Reducing his Tzaars doesn't force him into a one-stack game, because it is hard to chase down that stack using just one stack of mine, as it is unlikely that I can build up more than one stack high enough to threaten it. So he can still start other stacks if he wants.)

In short, a move that relies on your opponent being dumb, and fails when your opponent plays smart, is not a good move. And any double capture move without a clear reason is like that. It is generally useless to reduce an enemy piece type unless the opponent has difficulty building a stack (ensnare or encirclement); it doesn't hurt to use your first capture to do so (since you have to capture something anyway), but it's not worth sacrificing a stacking move to do that.
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Breno K.
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After 60 or so matches, I must say that "rarely do double-captures" is about as close as I got to an axiom in this game. It's a fantastic design, incredibly dynamic.
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Russ Williams
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I agree with your general tips about TZAAR strategy.
Alan Kwan wrote:
In short, a move that relies on your opponent being dumb, and fails when your opponent plays smart, is not a good move.

And of course general advice like this is valid for every strategy game! It is interesting how often people make irrational "wishful thinking" moves.
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Joe Gola
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Right. Towards the end game the double-capture moves can be useful, but otherwise you want to stack.

I've come to realize that Tzaar is similar to Dvonn in that you always want to be reducing your opponent's options, and stacking accomplishes this goal just as well as removing pieces. I've played games against someone who was trying out a "capture" strategy, and what he discovered in the end was that while he had many more stacks than I did, my few tall stacks had lots of possible captures to make while his plentiful short stacks had none.
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Jeremy Yoder
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Gola wrote:
what he discovered in the end was that while he had many more stacks than I did, my few tall stacks had lots of possible captures to make while his plentiful short stacks had none.

Did he realize he can stack his stacks?
 
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Joe Gola
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JYoder wrote:
Did he realize he can stack his stacks?

Yep, but he had lost so much ground that he couldn't set up future moves faster than I could take them away.
 
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Alan Kwan
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Unlike Dvonn, in Tzaar every stack moves the same, so if one stack can move onto the other, the converse is also true. The only thing that breaks the balance and allows the capture one way but not the other is stack height. Thus for the goal of winning the game by running the opponent out of moves, it is most important to build your stacks. (There are occasional exceptions for positional reasons, but in general one should stack.)

If both players play wisely and make stacking moves, then position becomes very important. I think both the "a few tall stacks" and the "many shorter (2+) stacks" strategy have a chance to win, and it depends on position: if you let the tall stack threaten the short stacks, the tall stack will win, but if you manage to isolate the tall stack and get the short stacks to ensnare seas of single pieces, the tall stack will lose. In any case, double captures (without a clear reason) don't win.
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