Nah, I think we ought to just delete stalemate, go back to the old rules. I argue if you've got more material in the endgame, you've played the board better.
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Now seems to be an appropriate time to raise the issue of the draw problem in Chess once again, given that the first three games in the Carlsen-Caruana World Championship have been draws, presumably leading to less than the hoped-for benefits in the popularization of Chess from this major event.
While I didn't think it would do much to solve the draw problem, it seemed reasonable to me to change the rules of chess so that the points would be split 3/5 - 2/5 in favor of the player who forces a stalemate. This would still mean a checkmate counted for much more, so endgame theory wouldn't be destroyed, but a new chapter would be added, the technique of forcing stalemate.
If one wanted to add other types of victory, I had thought not only of the historical "bare king" victory, but even of allowing credit for perpetual check, as that shows the player has managed to obtain some advantage.
I've been playing with such ideas for some time, but I've now come up with a combination with which I am particularly happy.
One player forces checkmate: a 1000 to 0 split of the 1000 points for a game in favor of the player forcing checkmate.
Forcing stalemate obtains a 600-400 points split.
Inflicting perpetual check obtains a 510-490 points split.
Finally, if a player succeeds in capturing all the opponent's pieces other than the opponent's King, then the player doing so has the option of replacing one of that player's own pieces (other than that player's own King) by a Pawn. Doing so forefeits the right to win by anything except checkmate, and if that player wins by checkmate, the points split is now 501-499 in that player's favor.
I think this finally puts the types of victory in the right order, and it makes the bare king victory still a dynamic victory rather than a material-based one.
Also, rather than reflecting the fact that it's harder for Black to win in the points schedule, I propose that, when appropriate, players recieve tiebreak points when winniing as Black. 1000 tiebreak points for a checkmate, 196 tiebreak points for a stalemate, 14 tiebreak points for perpetual check, and 1 tiebreak point for a checkmate after swapping in a Pawn after baring the opponent's King.