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Chess - Programming - Perft

Perft does a raw node count, up to some specified depth, by doing a full tree search.

Draws by threefold repetition are ignored.

Perft Values

Start Positition

Perft against normal opening position:

FEN-string: rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1

Depth	Nodes	Captures	E.p.	Castles	Promotions	Checks	Checkmates	Total Nodes
1	20	0	0	0	0	0	0	20
2	400	0	0	0	0	0	0	420
3	8902	34	0	0	0	12	0	9322
4	197281	1576	0	0	0	469	8	206603
5	4865609	82719	258	0	0	27351	347	5072212
6	119060324	2812008	5248	0	0	809099	10828	124132536
7	3195901860	3320034396				32668081	435767
8	84998978956					959129557	9852036
9	2439530234167					35695709940	400191963
10	69352859712417					1078854669486	8790619155
11	2097651003696806					39147687661803	1078854669486
12	62,854,969,236,701,747					1224448528652016	8361091858959

Depth	Checks	Single Discovered Check Only	Direct and Discovered Checks	Double Discovered Checks
1	0	0	0	0	0
2	0	0	0	0	0
3	12	0	0	0	12
4	469	8	0	0	461
5	27351	347	0	0	27004
6	809099	10828	46	0	798271
7	32668081	435767	1628	0	32668081
8	959129557	9852036	147215	0	959129557
9	35695709940	400191963	5547221	10	35695709940
10	1078854669486	8790619155	302900733	879	1078854669486
11	39147687661803	1078854669486	11721852393	57443	39147687661803
12	1224448528652016				8361091858959

Perft Estimates

Depth	Nodes
13	1.9810e+18
14	6.187e+19
15	2.015e+21
16	6.507e+22
17	2.175e+24
18	7.214e+25
19	2.462e+27
20	8.350e+28

NOTE: These estimates are done by randomly pruning the game tree.

Good Test Position

The startposition is not a very good test position as it does not uncover flaws that might still be hidden regarding promotion or castling.

Therefore the following position should be a better test.

FEN-string: r3k2r/p1ppqpb1/bn2pnp1/3PN3/1p2P3/2N2Q1p/PPPBBPPP/R3K2R w KQkq - 0 1

Depth	Nodes	Captures	E.p.	Castles	Promotions	Checks	Checkmates	Total Nodes
1	48	8	0	2	0	0	0	48
2	2039	351	1	91	0	3	0	2087
3	97862	17102	45	3162	0	993	1	99949
4	4085603	757163	1929	128013	15172	25523	43	4185552
5	193690690	35043416	73365	4993637	8392	3309887	30171	197876242
6	8031647685							8229523927

Discover promotion bugs

The following position does not look very realistic but nevertheless helps to uncover promotion bugs.

FEN-string: n1n5/PPPk4/8/8/8/8/4Kppp/5N1N b - - 0 1

Depth	Nodes	Total Nodes
1	24	24
2	496	520
3	9483	10003
4	182838	192841
5	3605103	3797944
6	71179139	74977083

Position 2

FEN-string: 8/2p5/3p4/KP5r/1R3p1k/8/4P1P1/8 w - -

Depth	Nodes	Captures	E.p.	Promotions	Checks	Checkmates
1	14	1	0	0	2	0
2	191	14	0	0	10	0
3	2812	209	2	0	267	0
4	43238	3348	123	0	1680	17
5	674624	52051	1165	0	52950	0
6	11030083	940350	33325	7552	452473	2733
7	178633661	14519036	294874	140024	12797406	87

Position 3

FEN-string: r3k2r/Pppp1ppp/1b3nbN/nP6/BBP1P3/q4N2/Pp1P2PP/R2Q1RK1 w kq - 0 1

Or mirrored (with the same perft results):

FEN-string: r2q1rk1/pP1p2pp/Q4n2/bbp1p3/Np6/1B3NBn/pPPP1PPP/R3K2R b KQ - 0 1

Depth	Nodes	Captures	E.p.	Castles	Promotions	Checks
1	6	0	0	0	0	0
2	264	87	0	6	48	10
3	9467	1021	4	0	120	38
4	422333	131393	0	7795	60032	15492
5	15833292	2046173	6512	0	329464	200568
6	706045033	210369132	212	10882006	81102984	26973664

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References

http://web.archive.org/web/20120420061542/http://www.rocechess.ch/perft.html

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