# KBN v K

• 5 years ago · Quote · #1

Hey all. So I 'm looking at this KBN v K endgame, and I think I've got it mastered, but I had an unusual question about this part....

So, it looks comical to me. It appears that the bishop is over extending itself and by some miracle the bishop, knight, and edge of the board cover just the squares they need to to keep the king from escaping. So my question is this:

If chess were played on a 10x10 board, would KBN v K be a draw?

• 5 years ago · Quote · #2

I don't think so, but there's a way to find out.

• 5 years ago · Quote · #3

go on...

• 5 years ago · Quote · #4

Set up a ten by ten board.

• 5 years ago · Quote · #5

well, following the traditional method, I think it would in fact be a draw, I don't see how I can "find out"

• 5 years ago · Quote · #7

Assume Black is the player with the bare king.  Whether or not KBN vs K is drawn on a 10x10 board depends on whether Black's king can successfully run from one "wrong corner" to the other, I figure.  There is a winning technique for White that makes me think Black can't do this.  It goes like this:

Let's start with the standard KBN vs K position BK on a1, WK on c3, WN on d4, WB on d5.  The winning procedure I have in mind starts with 1. Nc2+ Kb1 2. Bc4 Kc1 3. Ba2 Kd1 4. Nd4 Ke1 (4...Kc1 5. Ne2+ Kd1 6. Kd3 makes progress) 5. Bd5 Kf2 (making his break for the other corner) 6. Nf5!  This sets up the key barrier that makes me think KBN vs K is won on a 10x10 board.  With the g2 and g3 squares unavailable to the Black king, he has to play 6...Kg1 to try for the opposite corner, but then 7. Kd3 Kh2 8. Ke3 Kh3 9. Bf3 Ki4 (we'll call the ninth and tenth files i and j) 10. Kf4 Ki5 11. Kg5 Kj6 12. Kh6, and the Black king cannot reach j10.

So, I'm thinking the ending is still winnable on a 10x10 board, but not a 12x12.  Of course, the way to prove this conclusively would be to build a 10x10 tablebase for KBN vs K.  Surely this has been done - wish I could find one on the Internet!

• 5 years ago · Quote · #8

10 by 10 board you say? If it exists.