Branching Factor of top engines
Posted: Sat Jun 15, 2013 2:13 am
Shredder GUI has a nice feature that it shows BF of the engines analyzing an EPD file. I fed a neutral EPD file of 30 middlegame positions without solutions bm or am, to such depths that on average an engine analyzes for around one minute or a bit more each position on an i7 core. So BFs are shown for relevant plies, where engines spend from seconds to minutes.
I took three top engines, and an oldie, Shredder 6PB from 2002. If BF is the branching factor, then 1/Log(BF) is proportional to the depth the engine searches.
Houdini 3
Ply:15 Positions: 30 Avg Nodes: 4474464 Branching = 1.54
Ply:16 Positions: 30 Avg Nodes: 9993292 Branching = 2.23
Ply:17 Positions: 30 Avg Nodes:16583899 Branching = 1.66
Ply:18 Positions: 30 Avg Nodes:29529725 Branching = 1.78
Ply:19 Positions: 30 Avg Nodes:59452946 Branching = 2.01
Ply:20 Positions: 30 Avg Nodes:100502642 Branching = 1.69
Ply:21 Positions: 30 Avg Nodes:226412605 Branching = 2.25
Average BF: 1.86
1/Log(BF)=1.61
Stockfish 3
Ply:17 Positions: 30 Avg Nodes: 5738272 Branching = 1.51
Ply:18 Positions: 30 Avg Nodes: 9495564 Branching = 1.65
Ply:19 Positions: 30 Avg Nodes:14927319 Branching = 1.57
Ply:20 Positions: 30 Avg Nodes:25380846 Branching = 1.70
Ply:21 Positions: 30 Avg Nodes:37913346 Branching = 1.49
Ply:22 Positions: 30 Avg Nodes:58287426 Branching = 1.54
Ply:23 Positions: 30 Avg Nodes:105041456 Branching = 1.80
Average BF: 1.61
1/Log(BF)=2.10
Komodo 5 CCT
Ply:15 Positions: 30 Avg Nodes: 3132997 Branching = 1.74
Ply:16 Positions: 30 Avg Nodes: 5471869 Branching = 1.75
Ply:17 Positions: 30 Avg Nodes: 9833793 Branching = 1.80
Ply:18 Positions: 30 Avg Nodes:16946370 Branching = 1.72
Ply:19 Positions: 30 Avg Nodes:28120847 Branching = 1.66
Ply:20 Positions: 30 Avg Nodes:57150190 Branching = 2.03
Ply:21 Positions: 30 Avg Nodes:93519346 Branching = 1.64
Average BF: 1.76
1/Log(BF)=1.77
Shredder 6
Ply: 8 Positions: 30 Avg Nodes: 515591 Branching = 2.68
Ply: 9 Positions: 30 Avg Nodes: 1347856 Branching = 2.61
Ply:10 Positions: 30 Avg Nodes: 3997429 Branching = 2.97
Ply:11 Positions: 30 Avg Nodes: 8540293 Branching = 2.14
Ply:12 Positions: 30 Avg Nodes:19868716 Branching = 2.33
Ply:13 Positions: 30 Avg Nodes:51275681 Branching = 2.58
Ply:14 Positions: 30 Avg Nodes:119957110 Branching = 2.34
Average BF: 2.51
1/Log(BF)=1.09
I took three top engines, and an oldie, Shredder 6PB from 2002. If BF is the branching factor, then 1/Log(BF) is proportional to the depth the engine searches.
Houdini 3
Ply:15 Positions: 30 Avg Nodes: 4474464 Branching = 1.54
Ply:16 Positions: 30 Avg Nodes: 9993292 Branching = 2.23
Ply:17 Positions: 30 Avg Nodes:16583899 Branching = 1.66
Ply:18 Positions: 30 Avg Nodes:29529725 Branching = 1.78
Ply:19 Positions: 30 Avg Nodes:59452946 Branching = 2.01
Ply:20 Positions: 30 Avg Nodes:100502642 Branching = 1.69
Ply:21 Positions: 30 Avg Nodes:226412605 Branching = 2.25
Average BF: 1.86
1/Log(BF)=1.61
Stockfish 3
Ply:17 Positions: 30 Avg Nodes: 5738272 Branching = 1.51
Ply:18 Positions: 30 Avg Nodes: 9495564 Branching = 1.65
Ply:19 Positions: 30 Avg Nodes:14927319 Branching = 1.57
Ply:20 Positions: 30 Avg Nodes:25380846 Branching = 1.70
Ply:21 Positions: 30 Avg Nodes:37913346 Branching = 1.49
Ply:22 Positions: 30 Avg Nodes:58287426 Branching = 1.54
Ply:23 Positions: 30 Avg Nodes:105041456 Branching = 1.80
Average BF: 1.61
1/Log(BF)=2.10
Komodo 5 CCT
Ply:15 Positions: 30 Avg Nodes: 3132997 Branching = 1.74
Ply:16 Positions: 30 Avg Nodes: 5471869 Branching = 1.75
Ply:17 Positions: 30 Avg Nodes: 9833793 Branching = 1.80
Ply:18 Positions: 30 Avg Nodes:16946370 Branching = 1.72
Ply:19 Positions: 30 Avg Nodes:28120847 Branching = 1.66
Ply:20 Positions: 30 Avg Nodes:57150190 Branching = 2.03
Ply:21 Positions: 30 Avg Nodes:93519346 Branching = 1.64
Average BF: 1.76
1/Log(BF)=1.77
Shredder 6
Ply: 8 Positions: 30 Avg Nodes: 515591 Branching = 2.68
Ply: 9 Positions: 30 Avg Nodes: 1347856 Branching = 2.61
Ply:10 Positions: 30 Avg Nodes: 3997429 Branching = 2.97
Ply:11 Positions: 30 Avg Nodes: 8540293 Branching = 2.14
Ply:12 Positions: 30 Avg Nodes:19868716 Branching = 2.33
Ply:13 Positions: 30 Avg Nodes:51275681 Branching = 2.58
Ply:14 Positions: 30 Avg Nodes:119957110 Branching = 2.34
Average BF: 2.51
1/Log(BF)=1.09