the worth of a king is infinite, because it is against the rules to put him of the board.
Btw. this is a funny trap for chess programmer. Because the most programs use integer numbers to represent the aktual score they have to set a checkmate value. Most work with centipawn as unit, so that a pawn is worth 100, most a queen is 900. Now you have to define the checkmate value. It has to be a number beyond the maximal sum of all the pieces together. And here the programer can make a simple error. All together a set of pieces have a value of about 3900 centipawns. So we let us set the checkmate value to 5000, because there are also positional bonuses and stuff.
Now we play againt the computer and get into a really bad endgame. We are lost!?! The computer has four passed pawns and a lot of his pieces left. We have a lone king. Now the computer let run his pawns and promote them to queens.
Should we resign? NO!!!
We should not, because now the computer uses all his resources to avoid checkmate. Because a checkmate is worth 5000 centpawns, but his pieces have a much higher value! So checkmate is not the best move ;-)
#14 Look here chessprogramming.wikispaces.com i actually do not find the pages, but last year i wrote a article about computer chess for the newspaper of my chess club and i found unbelievable endgames played by computers. Back in the good old1980's but sure they did that.
And by the way, me to, in another form but the same problem