George Tsavdaris wrote:
I knew that branching factor was how many child nodes someone considers in each node.
Your definition is equivalent if we assume that total child nodes per second someone thinks/calculates, is steady.
But humans don't think exactly in this way. Humans get's confused many times and slow or stop the process of searching.
Moreover, what matters is not that humans spend time to remember variations that they have analyzed-- and due to MUCH worse memory abilities from computers they have forgotten or have been confused and have to analyze the same thing again-- but that they really choose to analyze only 1-2 moves in each case discarding all others by intuition(and this intuition is correct in 99.99% of times).
This ratio is not worse for programs.
Do you now see why memorizing variations has a lot to do with the branching factor?
It gets worse for a human as search gets deeper.
Yes i understand that what you referred to, was the effective branching factor of a human, and the limited memory abilities of humans makes it much worse than the theoretical branching factor value.
But i was talking mostly about the ability of humans to eliminate almost all possible moves of a position and just search 1-2 moves that in most cases it's the right path.
This is because a human GM by just looking at a position and without searching at all, he feels what is the path that should be followed in the game.
While computer's first plies are compared to this, complete crap.
As this discussion is about comparing overall strength of humans and engines, it doesn't matter whether a human focuses only on 2-3 moves in the initial position of each game move while an engine considers all 36...38 moves.
Anybody talking about branching factor _in_this_discussion_ has to mean "how deep can I search in the limited time allocated ?".
That is when it becomes clear that the branching factor of GMs is not that golden compared to engines.
bob wrote:
In long chess, quite often a GM picks the move he is going to play after a second or so, although he spends a lot of time making sure that it does not fall to any tactical or positional flaw. Their branching factor is impossibly low compared to a computer chess program.
A program picks the move it is going to play even faster than a GM, although it too spends a lot of time making sure that it does not fall to any tactical or positional flaw.
Just watch the move it picks at ply 1 and see how long it survives to ply N where the search terminates. This number is very low compared to a GM..
A GM's branching factor is _NOT_ lower compared to a computer chess program. A GM has to invest at least the same extra relative time as a program to see one ply deeper.
As the search gets deeper, the GM has far greater problems than the program memorizing his variations as they increase in number and length. So the GM's branching factor RISES (and that is bad) more than the program's.
Perhaps you don't know the definition of "branching factor" and are confusing it with "effective branching factor". Branching factor is explicitly defined as the average number of alternative moves examined at any point in the tree. A GM looks at an average of less than 2 moves. The computer always looks at everything. That's a huge difference.
Bob, you know all this and shouldn't be writing the opposite.
Matthias.
Neither should you. You are using the _wrong_ terminology and should know the difference between the two. EBF != BF.
Matthias Gemuh wrote:
A GM's branching factor is _NOT_ lower compared to a computer chess program.
Sorry but this is completely ridiculous and wrong!
A GM's branching factor is thousands of times lower(more effective) than that of a top Chess engine.
A GM looks a position and "mysteriously" knows what move he should investigate and analyze. If he finds something bad for him with this move, he has another move in his mind and analyzes this.
Both 2 these moves, would almost certainly be the right path to the position.
Computer on the other hand, needs to search every single crap move of the board, even for just a fraction of a second, only to see it's crap and reject it.
The GM does NOT search any such crap moves. He rejects them automatically by intuition.
As the search gets deeper, the GM has far greater problems than the program memorizing his variations as they increase in number and length.
So the GM's branching factor RISES (and that is bad) more than the program's.
I don't understand how the first implies the second?!
I mean the difficulty a GM has, compared to a computer, in memorizing variations, what has to do with the branching factor?
Hi George,
you seem not to understand what a branching factor is.
Measure the time t1 that a GM needs to search 10 plys deep.
Measure the time t2 that he needs to search 11 plys deep.
His branching factor is the _ratio_ t2/t1.
This ratio is not worse for programs.
Do you now see why memorizing variations has a lot to do with the branching factor?
It gets worse for a human as search gets deeper.
Matthias.
AHA. It is _you_ that does not understand the term "branching factor". Hint: In Knuth/Moore "An analysis of alpha/beta pruning" they have the formula
N = W ^ D
where W is defined as "the branching factor or the average number of moves at any node. Has zero to do with the time to finish iteration N+1 compared to the time to finish N. That is the "effective branching factor"...
Claude Shannon used the same terminology for "branching factor" in his original paper on how to program a computer to play chess, and described full-width vs selective forward pruning to reduce the branching factor by looking at fewer moves at each position...
You can probably google "branching factor" and get many references to the proper use, and likely a few for the incorrect substitution for BF instead of EBF.
George Tsavdaris wrote:
I knew that branching factor was how many child nodes someone considers in each node.
Your definition is equivalent if we assume that total child nodes per second someone thinks/calculates, is steady.
But humans don't think exactly in this way. Humans get's confused many times and slow or stop the process of searching.
Moreover, what matters is not that humans spend time to remember variations that they have analyzed-- and due to MUCH worse memory abilities from computers they have forgotten or have been confused and have to analyze the same thing again-- but that they really choose to analyze only 1-2 moves in each case discarding all others by intuition(and this intuition is correct in 99.99% of times).
This ratio is not worse for programs.
Do you now see why memorizing variations has a lot to do with the branching factor?
It gets worse for a human as search gets deeper.
Yes i understand that what you referred to, was the effective branching factor of a human, and the limited memory abilities of humans makes it much worse than the theoretical branching factor value.
But i was talking mostly about the ability of humans to eliminate almost all possible moves of a position and just search 1-2 moves that in most cases it's the right path.
This is because a human GM by just looking at a position and without searching at all, he feels what is the path that should be followed in the game.
While computer's first plies are compared to this, complete crap.
As this discussion is about comparing overall strength of humans and engines, it doesn't matter whether a human focuses only on 2-3 moves in the initial position of each game move while an engine considers all 36...38 moves.
Anybody talking about branching factor _in_this_discussion_ has to mean "how deep can I search in the limited time allocated ?".
That is when it becomes clear that the branching factor of GMs is not that golden compared to engines.
Matthias.
<sigh>
Difficult to communicate without a standard vocabulary. But in any case, pick any public program you want, one you think is as good as a GM, and modify it so that at any node in the tree it can never search more than two possible moves, and see how it plays. And then realize that a GM doesn't even consider 2 moves on average. According to DeGroot, it was closer to 1.7. If you don't think that is a difference in understanding as opposed to a pure difference in speed, then there is not much more to say. But try the test first to see how good a human _really_ is...
bob wrote:
Perhaps you don't know the definition of "branching factor" and are confusing it with "effective branching factor". Branching factor is explicitly defined as the average number of alternative moves examined at any point in the tree. A GM looks at an average of less than 2 moves. The computer always looks at everything. That's a huge difference.
/
What does your "branching factor" then have to do with comparing the strength of humans and engines ?
You throw in terminology that is not relevant for an on-going discussion ?
When comparing the strength of humans and engines, it is their effective branching factors that matter, so "branching factor" in this thread _has_ to be understood as effective branching factor, and not some irrelevant stuff.
bob wrote:
Perhaps you don't know the definition of "branching factor" and are confusing it with "effective branching factor". Branching factor is explicitly defined as the average number of alternative moves examined at any point in the tree. A GM looks at an average of less than 2 moves. The computer always looks at everything. That's a huge difference.
What does your "branching factor" then have to do with comparing the strength of humans and engines ?
It has to do with how clever human GMs are in playing Chess and how well they can plan in Chess, out-planning and outplaying many times the computers(the other times it is just equal), but they just fail to put the nail in the coffin because of tactics, that computers handle perfectly while humans not....
Perhaps i'm a bit unfair to computers, since there are times where computers put pressure on GMs and even take the initiative, but you don't see this very frequently.
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bob wrote:
Perhaps you don't know the definition of "branching factor" and are confusing it with "effective branching factor". Branching factor is explicitly defined as the average number of alternative moves examined at any point in the tree. A GM looks at an average of less than 2 moves. The computer always looks at everything. That's a huge difference.
/
What does your "branching factor" then have to do with comparing the strength of humans and engines ?
You throw in terminology that is not relevant for an on-going discussion ?
When comparing the strength of humans and engines, it is their effective branching factors that matter, so "branching factor" in this thread _has_ to be understood as effective branching factor, and not some irrelevant stuff.
Matthias.
Extra info for whoever it may not be obvious :
A GM may focus on 2-3 moves on the visible board but to avoid stupid blunders, he has to look a bit more at the moves he intends to reject as he searches deeper.
So though he may still be focussing on 2-3 moves per node, more time is spent on the "moves to reject" than on the visible board which gets scanned without strain.
George Tsavdaris wrote:
Perhaps i'm a bit unfair to computers, since there are times where computers put pressure on GMs and even take the initiative, but you don't see this very frequently.
When computers exert pressure on humans, it is of course due to effective branching factor, and not "branching factor".
"branching factor" is good humans, but just a tool to arrive at a meaningful effective branching factor.
So to compare strength between humans and engines, "branching factor" is not the right thing to compare.
You must be kidding us Robert....
Very high quality chess at 1 second per move,the humans
Even if they move the piece with an eye click,they won't be able to play a high quality chess,sorry,in this life time....
No. I guess he means very high quality Chess in comparison with what computers do at 1 ply.
And he is right of course. Human intuition and ability for planning at these low depths is crucial.
something is wrong here,you can't compare time,1 second,with 1ply of a computer,he's comparing too totaly different things,or does he mean 1 second for the humans is comparable to 1-2 plys by the machines
Of course dumping the chess engines to 1-2 plys will affect horribly the playing strength,nothing new here....
What is wrong here is you are not reading. I said that at less than a second per move, a GM is _not_ searching. Yet he comes up with incredibly strong moves. Would you like to take me on using Rybka with a real search depth of one ply? Any player that has played a large number of games will overwhelm such a weak search, since it won't be very accurate tactically, and positionally it will be terribly weak...
When a human sees that envading a b2 hole with the queen is devastating he is searching by sight. He is aware of the defending pieces movements and just sees what is possible. He has conducted a search--not a deep calculation, but a type of search none the less, Qd8c8 Qc8a6 Qa6a3 Qa3b2. A computer has no sight. It must search in order to 'see' the board and the possibilities. Take away the computers search and then ofcourse the computer is stupid because it can not see that the queen can reach b2 and what it can do there. Search can not be excluded from the definition of what constitutes a computers positional understanding.
Sorry, but he is _not_ searching. He is doing something totally different. I have played chess for almost 50 years now. And while I don't use alpha/beta, I definitely "push pieces" in my head. But I push far _less_ when playing 5 minute chess. And even less when playing 1 second games. That is the difference between how the human brain works and how the computer works when both are playing chess. I can "feel" that my king is a bit unsafe without _any_ searching and play a move to shore up the defense without taking any time at all. GMs are so much better than that it is not funny... Just compare some GM blitz games to patzer blitz games to see how much better they are. Compare GM 1 minute games to patzer 10 minute games and see which is of higher quality...
In long chess, quite often a GM picks the move he is going to play after a second or so, although he spends a lot of time making sure that it does not fall to any tactical or positional flaw. Their branching factor is impossibly low compared to a computer chess program. Because the "hardware" is so different in what it can do and how it does it...
When a hunter is in the woods and then comes to a clearing he uses his sight to search the clearing for game (and obstructions). When the GM is presented a chess position he is much like the hunter in that the chess position is searched in much the same way. It is a type of search. Not a calculated search, but rather an awareness type of search. My point is that computers do not do this kind of awareness search and must rely on an alpha/beta search in order to 'see' the position and cull the same information that a GM just simply uses his sight to obtain. So I still maintain that it is proper to include alpha/beta search as a major source of positional understanding for a computer. Even you in Crafty apply the eval function only at leaf nodes (iirc) after a series of moves. There are not always tactics envolved at the end of those moves, but there is better positional understanding. That is what constitutes a computers "sight". To allow a comparison between a human playing at 1 second a move and a computer searching 1 or 2 ply is just taking a computers "sight" away.
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bob wrote:
Perhaps you don't know the definition of "branching factor" and are confusing it with "effective branching factor". Branching factor is explicitly defined as the average number of alternative moves examined at any point in the tree. A GM looks at an average of less than 2 moves. The computer always looks at everything. That's a huge difference.
/
What does your "branching factor" then have to do with comparing the strength of humans and engines ?
You throw in terminology that is not relevant for an on-going discussion ?
When comparing the strength of humans and engines, it is their effective branching factors that matter, so "branching factor" in this thread _has_ to be understood as effective branching factor, and not some irrelevant stuff.
Matthias.
If you would just pay attention for a minute, and follow the old proverb "put your brain in gear before putting your fingers in motion" you would get it. I discussed positional "judgement" and tactical "accuracy". And clearly the computers are more accurate over the long haul because they don't get tired, nor distracted, nor worried, nor any of a dozen other things that can distract a human just enough to create a tactical mistake.
But a human GM plays incredibly impressive chess if you force him into a game where he just chooses a move and plays it without searching, such as game in 1 minute type games. How can a human just look at one "node" and play so strongly when a computer can't keep up with a full 1-ply or 2-ply search? Because of the abilites the human brain has that computers do not yet come anywhere near...
So my point was that positionally, a human GM is _far_ more accurate. And in deep tactics, the human GM is far more accurate in general, except for the occasional mistake. But there are dozens of good positions that humans solved OTB that a computer can't solve in weeks of constant computation.
