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Knight Probability in Chessboard
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Input
3×3, 2 moves
4×4, center
3×3, 1 move
5×5, center
Custom
n
=
3
,
k
=
2
,
row
=
0
,
column
=
0
move
0
/ 2
P(on board) =
1.00000
each move splits a square's probability across its 8 knight jumps
move
0
/ 2
P(on board) =
1.00000
each move splits a square's probability across its 8 knight jumps
move
0
/ 2
P(on board) =
1.00000
1
start square holds probability
1.0
move
1
/ 2
P(on board) =
1.00000
♞
off
off
off
off
off
+.125
off
+.125
1
/ 8 =
.125
to each on-board jump; off-board jumps are lost
move
1
/ 2
P(on board) =
0.25000
.125
.125
after move 1, on-board total =
0.25000
move
2
/ 2
P(on board) =
0.25000
♞
.125
off
off
+.016
off
+.016
off
off
off
.125
/ 8 =
.016
to each on-board jump; off-board jumps are lost
move
2
/ 2
P(on board) =
0.25000
.125
♞
+.016
+.016
off
off
off
off
off
off
.125
/ 8 =
.016
to each on-board jump; off-board jumps are lost
move
2
/ 2
P(on board) =
0.06250
.031
.016
.016
after move 2, on-board total =
0.06250
move
2
/ 2
P(on board) =
0.06250
.031
.016
.016
P(on board) = 0.06250
algo
master
.
io
Step:
Knight starts at (0, 0) on an 3×3 board and makes 2 random knight moves. Find P(still on board).
0 / 7
Input
3×3, 2 moves
4×4, center
3×3, 1 move
5×5, center
Custom
n
=
3
,
k
=
2
,
row
=
0
,
column
=
0
0 / 7
algo
master
.
io
Step:
Knight starts at (0, 0) on an 3×3 board and makes 2 random knight moves. Find P(still on board).
