Statistics on one-sided chess
Below are statistics on "one-sided" (or "series") chess games in which only White plays, starting from the initial position. Here are the rules:
White plays as before and still cannot walk into check. Black has only one legal move, "pass", which can be played only if Black is not in check (if Black is in check then Black has 0 legal moves and the game stops).
With this viewpoint the concept of "ply" still makes sense. If you're confused by this, then you probably want to look at odd plies only. What is traditionally called "move n" in a one-sided game is ply 2*n-1.
Statistics on one-sided chess games
Number of one-sided chess games ending...
| |
without check nor checkmate |
in check |
in checkmate |
total |
| ply 0 |
1 |
0 |
0 |
1 |
| ply 1 |
20 |
0 |
0 |
20 |
| ply 2 |
20 |
0 |
0 |
20 |
| ply 3 |
445 |
0 |
0 |
445 |
| ply 4 |
445 |
0 |
0 |
445 |
| ply 5 |
11025 |
23 |
0 |
11048 |
| ply 6 |
11025 |
0 |
0 |
11025 |
| ply 7 |
300369 |
1506 |
16 |
301891 |
| ply 8 |
300369 |
0 |
0 |
300369 |
| ply 9 |
8868077 |
72203 |
1516 |
8941796 |
| ply 10 |
8868077 |
0 |
0 |
8868077 |
| ply 11 |
280048753 |
3137018 |
94385 |
283280156 |
| ply 12 |
280048753 |
0 |
0 |
280048753 |
| ply 13 |
9355829804 |
131589294 |
4959938 |
9492379036 |
| ply 14 |
9355829804 |
0 |
0 |
9355829804 |
| ply 15 |
327589464141 |
5460695559 |
240296331 |
333290456031 |
| ply 16 |
327589464141 |
0 |
0 |
327589464141 |
| ply 17 |
11928048036653 |
226577974916 |
11173375530 |
12165799387099 |
| ply 18 |
11928048036653 |
0 |
0 |
11928048036653 |
| ply 19 |
448720553497923 |
9446335911562 |
508994865393 |
458675884274878 |
| ply 20 |
448720553497923 |
0 |
0 |
448720553497923 |
| ply 21 |
|
|
22970475309696 |
17767780801369461 |
| ply 22 |
|
|
0 |
|
| ply 23 |
|
|
1033380994914771 |
|
| ply 24 |
|
|
0 |
|
| ply 25 |
|
|
46508527926770458 |
|
Breakdown according to the type of check
| |
direct check only |
single discovered check only |
direct and discovered check |
double discovered check |
total |
| ply 1 |
0 |
0 |
0 |
0 |
0 |
| ply 3 |
0 |
0 |
0 |
0 |
0 |
| ply 5 |
23 |
0 |
0 |
0 |
23 |
| ply 7 |
1506 |
0 |
0 |
0 |
1506 |
| ply 9 |
72203 |
0 |
0 |
0 |
72203 |
| ply 11 |
3136351 |
667 |
0 |
0 |
3137018 |
| ply 13 |
131494952 |
93906 |
436 |
0 |
131589294 |
| ply 15 |
5452511913 |
8109778 |
73868 |
0 |
5460695559 |
| ply 17 |
226011394682 |
559060977 |
7519257 |
0 |
226577974916 |
| ply 19 |
9411729227810 |
34004883409 |
601800343 |
0 |
9446335911562 |
Breakdown according to the type of checkmate
| |
direct checkmate only |
single discovered checkmate only |
direct and discovered checkmate |
double discovered checkmate |
total |
| ply 1 |
0 |
0 |
0 |
0 |
0 |
| ply 3 |
0 |
0 |
0 |
0 |
0 |
| ply 5 |
0 |
0 |
0 |
0 |
0 |
| ply 7 |
16 |
0 |
0 |
0 |
16 |
| ply 9 |
1516 |
0 |
0 |
0 |
1516 |
| ply 11 |
94293 |
0 |
92 |
0 |
94385 |
| ply 13 |
4948327 |
35 |
11576 |
0 |
4959938 |
| ply 15 |
239372712 |
7549 |
916070 |
0 |
240296331 |
| ply 17 |
11113417890 |
946724 |
59010916 |
0 |
11173375530 |
| ply 19 |
505501012812 |
90268176 |
3403584405 |
0 |
508994865393 |
Statistics on one-sided chess positions
See my page on chess positions to see my definitions of "position" and "diagram".
Number of distinct one-sided chess positions
| |
uniquely realizable |
all |
| ply 0 |
1 |
1 |
| ply 1 |
20 |
20 |
| ply 2 |
20 |
20 |
| ply 3 |
93 |
268 |
| ply 4 |
93 |
268 |
| ply 5 |
426 |
3036 |
| ply 6 |
416 |
3021 |
| ply 7 |
1289 |
30042 |
| ply 8 |
1231 |
29675 |
| ply 9 |
3191 |
262132 |
| ply 10 |
2944 |
256717 |
| ply 11 |
8958 |
2041089 |
| ply 12 |
8279 |
1980098 |
| ply 13 |
22237 |
14376296 |
| ply 14 |
20332 |
13805300 |
| ply 15 |
50339 |
92740688 |
| ply 16 |
45560 |
88096797 |
| ply 17 |
114014 |
553842653 |
| ply 18 |
102509 |
520114684 |
| ply 19 |
251018 |
3089610246 |
| ply 20 |
224015 |
2866694649 |
| ply 21 |
530514 |
16220185259 |
Statistics on one-sided chess diagrams
Number of distinct chess diagrams
| |
uniquely realizable |
all |
| ply 0 |
1 |
1 |
| ply 1 |
20 |
20 |
| ply 2 |
20 |
20 |
| ply 3 |
93 |
268 |
| ply 4 |
93 |
268 |
| ply 5 |
414 |
3022 |
| ply 6 |
404 |
3007 |
| ply 7 |
1267 |
29744 |
| ply 8 |
1209 |
29377 |
| ply 9 |
3155 |
258118 |
| ply 10 |
2912 |
252718 |
| ply 11 |
8824 |
1998859 |
| ply 12 |
8155 |
1938340 |
| ply 13 |
21926 |
14007252 |
| ply 14 |
20038 |
13443893 |
| ply 15 |
49860 |
89969218 |
| ply 16 |
45163 |
85412961 |
| ply 17 |
112885 |
535494808 |
| ply 18 |
101482 |
502567600 |
| ply 19 |
248654 |
2980424024 |
| ply 20 |
221771 |
2763682061 |
| ply 21 |
525245 |
15627174928 |
One-sided checkmate diagrams
Number of checkmate diagrams
| |
uniquely realizable |
with 2 solutions |
all |
| ply 1 |
0 |
0 |
0 |
| ply 3 |
0 |
0 |
0 |
| ply 5 |
0 |
0 |
0 |
| ply 7 |
0 |
4 |
6 |
| ply 9 |
2 |
8 |
167 |
| ply 11 |
13 |
21 |
2545 |
| ply 13 |
44 |
60 |
28331 |
| ply 15 |
158 |
180 |
257744 |
| ply 17 |
393 |
412 |
2028029 |
| ply 19 |
1145 |
1050 |
14270412 |
| ply 21 |
3049 |
3328 |
91774294 |
| ply 23 |
7794 |
8678 |
547487865 |
| ply 25 |
18343 |
22036 |
3061404218 |
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