Forced To Make A Move In Games.

You are getting ready to play chess or a math game and you have the choice of going first or second.  Which should you choose even though everything in you is screaming to go first? 

In some games, going first provides only a small advantage but in other games, it is better to let your opponent go first. Either way, there are circumstances in some games where a person is forced to make a move.  That is what Zugswang is about.  Zugswang is a German word meaning "move compulsion" and was explored by some researchers.  One game to think about letting the other person go first is Chess.  

There are situations in chess where the person must make a move such as in the 1971 game between Bobby Fischer (white) and Mark Taimanov (black).  White had a bishop while black has a knight but white also has a pawn that can go all the way to the other side and become queen. In order to prevail, black must capture white's pawn by possibly sacrificing his knight but the best this leads to is a draw.  This is circumstance where he must move (Zugswang) either the knight or his king. In addition, white has the opportunity to make a move that doesn't lead to anything so that black must make another move.  In the end, White won since black had to make moves at various times.

In the game of Nim where two players are engaged in subtracting from a starting number selected by the second player.  In this game, players must subtract at least one but no more than one more than the tens digit of the number.  Player B must choose a starting number between 90 and 99 so that player A can begin subtracting. There are a few numbers that when chosen will automatically lead to player A being forced to make a move so they loose. If player B starts with any of the following numbers or gets the subtraction to any of these numbers - 93, 82, 72, 63, 55, 48, 42, 36, 31, 26, 22, 18, 15, 12, 9, 7, 5, 3, 1 player A will loose.  If on the other hand, player A is able to get the total to one of these numbers, player B will loose.  

Then there is Sim which is played on a hexagonal shaped playing board with lines going from all points across the center to the other points and along the outside.  There are two players, red and blue. The idea is to color in the lines across the middle or outside but they can't make three edges that form a triangle or they lose.  So picture if you will the hexagon is labeled A, B, C, D, E, F.  The first player starts by choosing AC, the blue EC and continuing on alternating until the red colors in the lines AC, AE, AF, AD, and AB and the blue has chosen lines EC, EB, ED, EF and it is blue's move.  No matter what move they make next, they will complete the third leg of the triangle and lose.  They are forced to make the move (Zugswang) and will lose.

On Friday, we'll look at this in terms of sharing a pizza so one person might be able to get more of the pizza than the other.  Let me know what you think, I'd love to hear.  Have fun with the idea of Zugswang and enjoy your day.