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Nelphine



Joined: Apr 01, 2011

Post   Posted: Jul 20, 2019 - 02:55 Reply with quote Back to top

Yup, I was just running numbers to show that it is complex, it's in the vicinity of other complex games like go, and therefore an AI could be written, even if it took a long time to get orrect.
thoralf



Joined: Mar 06, 2008

Post   Posted: Jul 20, 2019 - 04:37 Reply with quote Back to top

Speaking of Go, I just stumbled upon a great page on counting legal positions. This paragraph made me smile:

Quote:
Large numbers have a way of popping up in the game of Go. Few people believe that a tiny 2x2 Go board allows for more than a few hundred games. Yet 2x2 games number not in the hundreds, nor in the thousands, nor even in the millions. They number in the hundreds of billions! 386356909593 to be precise. Things only get crazier as you go up in boardsize. A lower bound of 10^{10^48} on the number of 19x19 games, as proved in our paper, was recently improved to a googolplex.


https://tromp.github.io/go/legal.html

***

I made some mistakes in my earlier calculations. I now think what I was looking for should be (11 x 390) ^ 40, and not 22 ^ 390 ^ 40. This still gives:

19,874,292,963,417,118,236,266,862,254,841,696,414,242,421,816,860,
696,451,432,693,625,001,345,613,236,841,303,143,020,070,472,606,145,
448,010,000,000,000,000,000,000,000,000,000,000,000,000,000

which isn't shabby, but less surprising than earlier.

Also, I misspecified the puzzle problem I had in mind. A perfect 50-pieces puzzle solver could do it into 50! possible permutations. My solution overestimated the number of possible paths by a factor of 292,028,571,691,918,698,419.

This may explain why Fumbbl broke down earlier.

***

I forgot to mention that part of the AI's learning could be race-relative. Its evaluation function could evolve differently if it learns Dorfs of Woodies. In the end it should not matter, but we could expect longer training.

More generally, I suspect ball control will take time to learn properly. This could imply a few 2-1 wins for the carbon-based lifeforms until it does.

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