He is saying this (I think): to read m moves deep with a branching factor of b you need to look at p positions, where p is given by the following formula:
p = b^m (actually slightly different, but this formula is close enough) which is: log(p) = m log(b) m = log(p) / log(b) We assume that a doubling in time should double the number of positions we can look at, so: m(with doubled time) = log(2p) / log(b) m(with doubled time) = log(2) * log(p) / log(b) So, as we can see we get a linear relationship no matter what b, the branching factor, is. However, the slop on the line changes accordingly. We are also assuming that the number of moves deep that one reads is proportional to playing strength. This is in fact simply a way of defining playing strength. There are many scales that could be constructed where this is not the case, however, this is a good one to pick from a theory perspective because the formula holds with any game that has a branching factor. What you are talking about in terms of using "sense" is another factor is strength that isn't really addressed by the above math (in my opinion). There are certainly ways in which one could say that by having a better sense of the game one can effectively reduce the branching factor, but one could also say that sense could be capable of restructuring the way people read a situation so that it is possible to read much deeper than is allowed by simple brute force search strategy. That is an issue for psychologists to address. I am looking forward to good data from experiments on this subject to answer some of these questions. I think until we have good data for go, we won't really know. Just my opinion (guess it is the scientist in me...) - Nick On 1/22/07, Matt Gokey <[EMAIL PROTECTED]> wrote:
[EMAIL PROTECTED] wrote: >>What if we look at it mathematically by looking at the branching >>factor? >>Go's branching factor is generally considered to be about an order >>of >>magnitude greater than chess – perhaps a bit less, right? That >>means >>that after each ply go becomes another additional order of >>magnitude >>more complex. > > > Mathematically a bigger branching factor does not matter. If the level > increase is proportional to the 2log of time, then it is also > proportional to the 10log of time. The only difference is the > proportionality factor. I'm not sure I follow your logic here. Sounds like you are using the hypothesis to support itself in a circular argument. Perhaps you could elaborate. _______________________________________________ computer-go mailing list [email protected] http://www.computer-go.org/mailman/listinfo/computer-go/
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