(1) K+B+N - K

When I counsel "up and coming" players to concentrate on endings, I am usually ignored - even as I once ignored my own elders. This is quite common: improving players usually prefer to work on their openings, hoping to catch an unwary opponent early and get an easy win. Unfortunately, chess isn't like football - even if you "score" in the opening, unlike a 1st Quarter touchdown, it isn't still on the scoreboard in the 2nd Half. Only mate or resignation counts. You can learn all the opening tricks you wish, but if you can't figure out how to queen that P in the ending, you may not win the game. Also, opening theory is constantly changing, like fashions in clothing. Hold onto your bell-bottoms, Argyle socks, and Earth Shoes long enough, and they'll be back in vogue. Endgame theory is only very rarely subject to adjustment. Once you know endings, you know them, and whatever opening becomes the newest trend will not affect that knowledge. Let's look at a few "simple" Pawn endings which are frequently misunderstood, so we won't get "Pwned" - but first, the dreaded B+N mate. ` Many players worry over mating with only a B + N. Mating with a Q, a R, or two Bs is fairly easy, yet most players will not work on their technique with B + N, even though they realize they don't know it. When it turns up in a tournament game, they may regret this lack of attention. ` Set up the current position - designed to be difficult, with Black's King centralized and the White forces scattered. The only challenge to this ending is doing it within 50 moves, so we should start with an unfavorable situation. Note that Black's defensive strategy should be to stay in or near the center if possible, and to run to the corner NOT of the Bishop's color when chased (because mate can only be forced in a corner the Bishop controls). Play it out yourself, then consult the analysis (there are any number of ways to carry out the mate, not just the specific moves shown). The Pawn endings are on the "drop-down" menu beneath the board, as usual.

1.Kb2 Kf6
Black seeks to attack the N in the corner, but he is not really at risk since his good friend, the Bishop, can rush to his aid (which may explain why all Knights go to church)

2.Be4 Ke5 3.Bc2 Kf6 4.Ng6 Kg5 5.Kc3
It's not really "B+N vs K" at all, because White's King must also be part of the mating net.

5...Kf6 6.Kd4 Kg5 7.Ke5 Kh5
[But not 7...Kg4 8.Bd3 Kf3 9.Nf4 Ke3 10.Bg6 and Black is already stuck near the right corner]

8.Bf5 Kh6 9.Kf6 Kh7
[9...Kh5 10.Ne5 Kh6 (10...Kh4 11.Bg4 Kg3 12.Kf5 Kh4 13.Nd3 Kg3 14.Kg5 and the end is near, as Black is trapped near the fatal corner. ) 11.Ng4+ Kh5 12.Ke5 Kg5 This is a place many players get excited and stop thinking - but don't worry: the Black K isn't going anywhere. Notice how the B+N cut off the retreat towards the dark-square corner. 13.Ke4 Kh4 14.Kf4 Kh5 15.Bh7 Kh4 16.Bg6 Kh3 17.Ne3 Kh4 18.Ng2+ Kh3 19.Kf3 Kh2 20.Kf2 Kh3 21.Bf5+ Kh2 22.Ne3 Kh1 23.Bg4 Kh2 24.Nf1+ Kh1 25.Bf3# ]

10.Be6 Kh6 11.Bg8 Kh5 12.Ne5 Kh4
Here is where it is easy to panic and lose the thread, as Black's King escapes the h-file. But the important point is to restrict him to the corner area, and this is readily accomplished. [12...Kh6? only shortens the game after 13.Ng4+ Kh5 14.Kf5 Kh4 15.Kf4 Kh5 16.Bf7+ Kh4 17.Ne3 Kh3 18.Bc4 Kh4 19.Be2 Kh3 20.Bg4+ Kh2 21.Kf3 Kg1 22.Kg3 Kh1 23.Kf2 Kh2 24.Nf1+ Kh1 25.Bf3# ]

13.Kf5 Kg3 14.Ng4 Kg2 15.Bc4
Cutting off flight to the other dark-square corner at a1. I recall (then Chairman of the Joint Chiefs of Staff) Gen. Colin Powell's response to a reporter's question, in the 1991 Gulf War, as to how we would deal with Saddam Hussein's elite personal army, then beating their own hasty retreat from Kuwait: "First we're going to cut it off, and then we're going to kill it."

15...Kf3 16.Bd3 Kg3 17.Be4
The noose tightens.

[17...Kh4 again doesn't change the end: 18.Kf4 Kh5 19.Bc2 Kh4 20.Bg6 Kh3 21.Ne3 Kh4 22.Ng2+ Kh3 23.Kf3 Kh2 24.Bf5 Kg1 25.Ne3 Kh2 26.Kf2 & etc. as in the main line.]

18.Kf4 Kh4 19.Bg6 Kh3 20.Ne3 Kh4 21.Ng2+ Kh3 22.Kf3 Kh2 23.Kf2 Kh3 24.Bf5+
squeezing the Black King into the proper corner

24...Kh2 25.Ne3 Kh1 26.Bg4 Kh2 27.Nf1+ Kh1 28.Bf3#
It's not so hard if you know the method - but it would be very risky to assume you could find it over the board with the clock ticking if you are unprepared. A good exercise with a partner is to take turns playing offense and defense - one try each before you begin your usual speed chess session. Check the "drop-down menu" for some critical Pawn endings. 1-0