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I think Betza has his wording correct. More force DOES make the game more strategical, especially if one mistake can lead immediately to a mate in 1. An example is Suicide Chess (though it doesn't quite fit here.) Suicide for beginners is a very tactical game. However, among the masters (who became so by avoiding tactical mistakes,) it's a game of strategy. Betza in his page of Tripunch chess talked about Small Weaknesses, and how the Nightrider is useful in this matter. As I understand strategy, small weaknesses is all that matters.
'All of my old variants, from the 1970s, were designed for postal play, so they had a higher ratio of force to space than you see in FIDE chess.' - Ralph Betza
The same design philosophy led me to Lions and Unicorns Chess. Players need to have a strategic plan and carefully choose where they place each piece. The board is simply 'too small' for these powerful armies, so the players have to fight for space for their pieces. Shatranj, on the other hand, can be played as a game of pure tactics. The board is 'large' and there are always undefended pieces and pawns to attack.
I posted a series of comments relating to the 6x6x6 board on the 3D Chess thread last month. Many designers prefer 'Capablanca style' 3D variants, with many compound pieces. I was exploring the idea of special promotion rules that change the R, B, Q to 3D versions of Tripunch Chess pieces. Such pieces may be able to checkmate the lone King in the endgame.
I have also considered a different approach, keeping the strong King and weak Unicorn from Raumschach, then adding the stalemate and bare King victory conditions from Shatranj. The Raumschach Queen does not belong in a game like this, even the simple Rook+Bishop compound may be unsuitable.
Another way to project more force is multi-move designs. But they are tricky, both hard to balance and in need of certain constraints. Yet there are many interesting things you can do with multiple moves. One possibility is to allow one piece to make 2 moves or two pieces 1 move each, so that, for example, some shatranj variant with slow pieces could move 1 of them twice in a turn. [Yes, David, I decided to take your bait hook, line and sinker.] Would this make shatranj more strategic? Certainly, there are vast differences among one piece moving 6 squares, two moving 3 each, or six pieces moving only 1 square each. But consider some of the recent 2 and 3 square ranged pieces; if they could make 2 consecutive moves, how quickly could a game end? That easily fits Abdul-Rahman's criterion: 'especially if one mistake can lead immediately to a mate in 1.' Gotta continue this later, apparently we're getting a blackout. But I suggest a few trial games of shatranj with 2 moves might be interesting.
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Didn't Betza mean to say 'more tactical than strategical'? The bigger the force, as in Tripunch, the greater the tactics, no?
Perhaps he is saying that because of the greater tactical abilities of the pieces, more time must be spent on strategic considerations to compensate?
Tactics and strategy are intimately connected, as tactics arise naturally from proper strategy.