King Of The Hill

There is a kid's game called King of the Hill. They don't play it much any more since video games have taken so much of youngster's time. Anyway, the idea is to find a mound of dirt and all the kids try to get to the top. The one who is there is the King of the Hill and the others try to knock him off and replace him with a successor.

Programmers have something similar; it is called the first pass of a “straight sort”. They have a bunch of numbers and need to find the largest (or smallest). They start by assigning the value of negative infinity to the King of the Hill and proceed to look at each number. Each time they find a number larger than the King of the Hill, it becomes the new King of the Hill until they find a larger one. Once they have examined all the numbers the King of the Hill is the largest.

In chess we have a saying, “If you see a good move, look for a better one – you are trying to find the BEST one!” During the time you are considering your move, the best one you have found so far is the King of the Hill. When you are finished your analysis of all your moves, the move you should play is the “final” King of the Hill. Every chess player should have this as part of their thought process each move, but they don't for various reasons.

Take the following diagram from a recent event. A student of mine, rated 1680 USCF, had White and was on the move:

White was sorely tempted by the smothering move 1.Nf7+ winning the exchange, and played it. However, after 1…Rxf7 2.Rxf7 axb3 he soon ran into some trouble (if 3.Nxb3 Qb2) and was actually losing at one point, but later pulled out the win.

When I reviewed the game with him, I did not yet know what he played, but I said, “Well, you can win the exchange with 1.Nf7+, but when you see a good move, look for a better one…Suppose you play 1.Rxf8, what then? If Black plays 1…Bxf8 then 2.Bf6+ Nxf6 3.Qxf6+ Bg7 4.Qd8+ Bf8 5.Qxf8# and if 2…Bg7 then (I paused for a second or two) 3.Nf7 is a smothered mate! So yes, I would play 1.Rxf8.”

Things like this happen all the time in games of weaker players. A player gets enamored with an idea or a type of attack and pursues it without regard to other, possibly better options.

Therefore, a good thought process needs to contain an efficient way to search for the best move. There are many ways to do this, but they mostly boil down to picking out the reasonable moves (perhaps the moves which implement your most reasonable plans), analyzing each, assuming the opponent will make his best move, finding which positions result, and then evaluating those positions. There is no way around it – in most positions this takes some time, which is why the best players are usually the last ones finished at Open events.

Suppose the first move you look at is OK, but you feel the position promises more. Then you should surely feel that a further search is worthwhile and that you might beat your King of the Hill. If the first move you look at results in a bad position and you feel your position is not bad to begin with, then you might not even assign this one as King of the Hill, knowing that another reasonable candidate is sure to emerge.

Suppose you find a move that exceeds all expectations. The temptation might be great to play the move immediately, but maybe you have underestimated your position and can get even more. Our example position above is a good one for this case. White thought he might be winning with 1.Nf7+ and stopped his search, but if he had thought the King of the Hill bar might be higher, he might have kept looking.

When you run a computer chess program and ask it to show its analysis, most programs will show one or more lines that look something like this:

11 ply (1/42) +0.83 19.Rhe1 d5 20.cxd5 exd5 21.Bh4 …

If there is more than one line of sequences (Fritz defaults to show the expected variations of the top three moves), then the top line contains as its first move the “King of the Hill” – in this case 19.Rhe1 - and the line of expected moves on that first line (the best moves for each side) is called the Principal Variation. Before the moves, the “11” indicates how many half-moves deep the computer is currently searching, the “(1/42)” means that it is analyzing its best current move out of the 42 legal possibilities, and the “+0.83” means the computer thinks White is better by about 0.83 pawns.

But once the computer finds a move it considers better, the first move of the sequence changes, e.g.

11 ply (7/42) +0.98 19.Rad1 d5 20.cxd5 Rxd5 21.Bf2

…and that means the new King of the Hill is 19.Rad1. Note that the new evaluation, in this case 0.98, must be higher than 0.83 or it would not have changed its King of the Hill. Since it is searching for White's best move, the higher the evaluation, the better.

Humans don't think exactly in this manner, but their intent should be similar: Consider reasonable moves, assume the opponent's best replies, evaluate what will happen, and then compare this evaluation with the one you estimated with your current King of the Hill. Replace your King of the Hill if the new move results in a superior position. Try and prove your King of the Hill is the best one you can find, given the time control restraints, and then play your King of the Hill move.