Ken's blog

every checkmate in orthodox chess requires at least two pieces (plus the enemy king).  often, one or more of those pieces is an enemy piece ...

chess variant: each player has one king, worth 2^N points.  each player has 2 pieces (names and abilities TBD) each worth 2^(N-1) points. ...

compose an initial chess position and sequence of moves which do not repeat positions (position includes player to move).  how long of such ...

how would a sport change if distance from the one team's goal side to the other team's goal side were decreased?  basketball and soc...

pawn allowed on 8th rank: N.  (orthodox chess: promotion forced) Y. pawn is allowed to move to 8th rank and remain a pawn: N.  (...

did anyone find all Koroks in Zelda BOTW before the first object map was published? when was the total number first known? vaguely related...

consider a mate in N chess problem.  how many paths through the game tree end in checkmate in exactly N moves?  (also consider less than N m...

incomplete information version: at the beginning of a turn, you see your opponent's attack.  you choose a defense, which is revealed t...

if a baseball batter is awarded a base on balls, let the manager have the option of instead having the next batter ("batter on deck...

rate chess players by how often they turn a drawn position into a lost one, and by how often they turn a winning position into a drawn one. ...

below are the 129 primes less than 27^2 = 729, written in big-endian base 27, using the following straightforward encoding of base-27 digits...

suit major, rank major (2 possibilities) ordering of suits (4! = 24) king high, ace high (2) low instead of high (i.e., reverse the ra...

define the ranged pieces queen, rook, and bishop to be female. define the non-ranged pieces king, knight, and pawn to be male. but I can...

apply neural network machine learning on positions of a theoretically drawn but hard to defend chess endgame such as KRBKR.  can an AI playi...

create a deck of cards representing the 48 elements of the symmetry group of a cube (isometries of a cube) (automorphism group of a cube).  ...

in the following chess position (FEN), white has 44 possible moves that get out of check: r6K/QPPPPPPB/NNNNNNNN/8/8/8/8/7k w - - 0 1 is ...

at the end of a season, determine the pitchers and batters who are good by some statistic (in opposing ways) and compile a highlight reel of...

chess variant: ranged pieces can travel through pawns of their own color. 1.Rxa7, etc. become valid opening moves, perhaps problematic. ...

a square (or rectangle) fundamental polygon is good for 2D games. previously on the various spaces (manifolds) that a fundamental polygon c...

transposition table is the other elegant improvement to minimax (after alpha-beta): elegant in principle, hairy to implement in practice. ...