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Steven Streetman wrote on Sat, Oct 30, 2010 01:09 AM UTC:
-----From the rules------------
4.12 Persian Victory - The Persian (white) wins once one of the Spartan Kings is captured and the remaining Spartan King is checkmated or when both Spartan Kings are placed under simultaneous attack (duple-check) and neither King can be removed from attack on the next move (see 4.4 Duple-Check and Mate).

4.4 Duple-Check & Mate If both Spartan Kings are placed under simultaneous attack this is called duple-check (d+). It is illegal for the Spartan to make a move that will place his Kings in duple-check. The Spartan loses if on his move he is unable to escape duple-check in which case the game ends in a duple-checkmate (d#).
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As you can see the Spartan need merely to remove one King from duple-check.

As for the values of pieces.... boy oh boy do opinions vary and I am always open to learning what people have to say on the subject. On another site there is a pretty detailed analysis.

The beginning of this analysis shows values for the Queen: 8.75, the Chancellor (my General): 8.25 and the Archbishop (my Warlord): 6.50. At the end he shows the calculations done by Reinhard Scharnagl on a 8x8 board as Queen: 8.9531, the Chancellor: 8.3750 and the Archbishop: 6.5781.

I certainly did take liberties in rounding the figures off in my presentation which can be found here: http://spartanchessonline.com/values.html which I imagine from your comments you may have already looked at.

As for duple-check (I could not use double check since this is a term already understood in orthodox to mean something else) the balance and 'fun' of the game was improved in version 1.06 when duple-check was introduced. Once the minor pieces are traded off the Spartans can plod across the board shepherding the forces with their 2 Kings. Once duple-check was introduced there were some very dynamic games. The Spartans in the center of the board with the White Queen and rooks circling them from both flanks and the rear ranks duple-checking the Spartans frequently and eventually being able to work out a White win.

As for the value of 'simple' check immunity for the Spartan, that is a puzzler. It's worth something, maybe a lot. I do know that the first time a Spartan King played the move Kc4-b3+ (since it was then next to the White King) we did a lot of laughing.