124. Chew (3k) vs Fuego (Bot)

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flOvermind
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by flOvermind »

emeraldemon wrote:
value: 50.7%
A slight decrease.
Click Here To Show Diagram Code
[go]$$Bcm37
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . . . . . . . . . |
$$ | . . . O . O . . . , . . . . . O 0 . . |
$$ | . . . . . . . . . . . . . . . 8 5 6 . |
$$ | . . X . . . . . . . . . . . . 3 O . . |
$$ | . . . . O . . . . . . . . . . X O 9 . |
$$ | . . X . . . . . . . . . . . X O X . . |
$$ | . . . . . . . . . . . . . . 2 O X . . |
$$ | . . . X . . . . . , . . . . . 1 . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . X X . X . . . . . . X O . . . |
$$ | . . X , X O . . . O . . X . 7 X O . . |
$$ | . . . . . O . O . . . . X O X 4 O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
As expected, Fuego isn't going to play out the ladder. They say "beginners play atari", but I think this is a good one, since it helps fix black's shape. I don't have time for too much analysis unfortunately.
Is it just me, or is there a lot of wishful thinking in the Fuego's reasoning? Why on earth would white play 40? Especially when Fuego itself thinks it doesn't need to be answered immediately...

That's not the first time I see that kind of move in the bot analysis. That may hint at a weakness in the bot, but I'm not quite sure what that weakness would be, and how (or even if) you can exploit it ;)
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by Chew Terr »

Click Here To Show Diagram Code
[go]$$Bcm31
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . . . . . . . . . |
$$ | . . . O . O . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . . O . . . . . . . . . . X O . . |
$$ | . . X . . . . . . . . . . . X O X . . |
$$ | . . . . . . . . . . . . . . 8 O X . . |
$$ | . . . X . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . X X . X . . . . . . X O . . . |
$$ | . . X , X O . . . O . . X . . X O . . |
$$ | . . . . . O . O . . . . X O X . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Okay, I suppose this buys Fuego's right-side group better shape. The only alternative I see is playing the ladder almost all the way out to get several forcing moves against my bottom middle group, but it doesn't feel worthwhile. So I'm assuming that black will not push more than one more time from each side before fixing the weak side's cut points and resuming the non-ladder game proper.
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by emeraldemon »

Click Here To Show Diagram Code
[go]$$Bcm31
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . . . . . . . . . |
$$ | . . . O . O . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . . O . . . . . . . . . . X O . . |
$$ | . . X . . . . . . . . . . . X O X . . |
$$ | . . . . . . . . . . . . . . O O X . . |
$$ | . . . X . . . . . , . . . 9 . X . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . X X . X . . . . . . X O . . . |
$$ | . . X , X O . . . O . . X . . X O . . |
$$ | . . . . . O . O . . . . X O X . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Fuego took 28:04 to decide this move, which is the longest its ever taken to decide a move.
Value dropped again to 49.8% .
Click Here To Show Diagram Code
[go]$$Bcm31
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . . . . . . . . . |
$$ | . . . O . O . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . b O . . |
$$ | . . . . O . . . . . . . . . . X O . . |
$$ | . . X . . . . . . . . . . . X O X . . |
$$ | . . . . . . . . . . . . . c O O X . . |
$$ | . . . X . . . . . , . . . a . X . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . X X . X . . . . . . X O . . . |
$$ | . . X , X O . . . O . . X . . X O . . |
$$ | . . . . . O . O . . . . X O X . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Moves by consideration time:
a - 51%
b - 44%
c - 3%

The time spent on c was mostly at the beginning I think, when it was still considering playing out the ladder. The reason it took so long was that Fuego couldn't decide whether or not to push at b or go directly for a.

Predicted sequence:
Click Here To Show Diagram Code
[go]$$Bcm39
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . . . . . . . . . |
$$ | . . . O . O . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . 6 O . . |
$$ | . . . . O . . . . . . . . . 2 X O . . |
$$ | . . X . . . . . 9 . . . . 3 X O X . . |
$$ | . . . . . . . . . . . . . 5 O O X . . |
$$ | . . . X . . . . . , . . . 1 . X . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . 7 . O . . . |
$$ | . . . . X X . X . . . . . . X O . . . |
$$ | . . X , X O . . . O . . X . . X O . . |
$$ | . . . . . O . O . . 4 . X O X . O . . |
$$ | . . . . . . . . . . . 8 . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by emeraldemon »

ez4u wrote:
For :b35: did it consider any plays around :b1:, which would create the alternative ladder shown? If so, how did it expect White to react?
Click Here To Show Diagram Code
[go]$$Bc "d" connects at 5
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . . . . . . . . . |
$$ | . . . O . O . . . 2 1 . . . . O . . . |
$$ | . . . . . . . . . . . . . . . 4 . . . |
$$ | . . X . . . . . . . . . . g 9 3 O . . |
$$ | . . . . O . . . . . . . . f 8 X O . . |
$$ | . . X . . . . . . . . . e b 5 O X . . |
$$ | . . . . . . . . . . . . . a 0 6 X . . |
$$ | . . . X . . . . . , . . . . 7 c . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . X X . X . . . . . . X O . . . |
$$ | . . X , X O . . . O . . X . . X O . . |
$$ | . . . . . O . O . . . . X O X . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
No it hasn't liked any moves around the top (except some plays in the upper left corner). I didn't see that latter either, it's a pretty sneaky one :tmbup:
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by emeraldemon »

flOvermind wrote:
emeraldemon wrote:
value: 50.7%
A slight decrease.
Click Here To Show Diagram Code
[go]$$Bcm37
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . . . . . . . . . |
$$ | . . . O . O . . . , . . . . . O 0 . . |
$$ | . . . . . . . . . . . . . . . 8 5 6 . |
$$ | . . X . . . . . . . . . . . . 3 O . . |
$$ | . . . . O . . . . . . . . . . X O 9 . |
$$ | . . X . . . . . . . . . . . X O X . . |
$$ | . . . . . . . . . . . . . . 2 O X . . |
$$ | . . . X . . . . . , . . . . . 1 . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . X X . X . . . . . . X O . . . |
$$ | . . X , X O . . . O . . X . 7 X O . . |
$$ | . . . . . O . O . . . . X O X 4 O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
As expected, Fuego isn't going to play out the ladder. They say "beginners play atari", but I think this is a good one, since it helps fix black's shape. I don't have time for too much analysis unfortunately.
Is it just me, or is there a lot of wishful thinking in the Fuego's reasoning? Why on earth would white play 40? Especially when Fuego itself thinks it doesn't need to be answered immediately...

That's not the first time I see that kind of move in the bot analysis. That may hint at a weakness in the bot, but I'm not quite sure what that weakness would be, and how (or even if) you can exploit it ;)
Well, Fuego isn't capable of wishful thinking in the way humans are: it uses the exact same algorithm do choose both white and black moves, so it can't hope for the opponent to play poorly, the way a human can. That said, it can certainly miss tesuji and play poorly in the tree and in the playouts. The hope is that it will make mistakes in roughly equal amount for both sides, so that the board evaluation is correct.
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by ez4u »

emeraldemon wrote:
ez4u wrote:
For :b35: did it consider any plays around :b1:, which would create the alternative ladder shown? If so, how did it expect White to react?
Click Here To Show Diagram Code
[go]$$Bc "d" connects at 5
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . . . . . . . . . |
$$ | . . . O . O . . . 2 1 . . . . O . . . |
$$ | . . . . . . . . . . . . . . . 4 . . . |
$$ | . . X . . . . . . . . . . g 9 3 O . . |
$$ | . . . . O . . . . . . . . f 8 X O . . |
$$ | . . X . . . . . . . . . e b 5 O X . . |
$$ | . . . . . . . . . . . . . a 0 6 X . . |
$$ | . . . X . . . . . , . . . . 7 c . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . X X . X . . . . . . X O . . . |
$$ | . . X , X O . . . O . . X . . X O . . |
$$ | . . . . . O . O . . . . X O X . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
No it hasn't liked any moves around the top (except some plays in the upper left corner). I didn't see that latter either, it's a pretty sneaky one :tmbup:
Generally how many alternative "next move" candidates does fuego consider? It obviously spends most of its time on a select few, but how many candidates receive at least some analysis in each turn?
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by emeraldemon »

ez4u:
Here's an image showing how many playouts each point on the board received. The larger numbers get cut off, for example the game move was visited 3114430 times. But this should give the basic idea.
playouts.png
playouts.png (405.14 KiB) Viewed 10406 times
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by ez4u »

@emeraldemon

Can you see the meaning of the 23 playouts that great majority of points receive? Is there some special pattern? Obviously 23 playouts is not going to go very far! :)
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by perceval »

@ez4u:

my guess would be that its a default minimal value, which seems rather low:
around 20-25 is the threshold where a bernouilli distribution begin to be approximated by a normal distribution so roughly:
(here we consider that a given move give a probaility p that a random playout after the move will give a won game for B, and we want to approximate p by playing a limited number of playout )
The error is of order 0.5/sqrt(23) which is approx 0.1. This is probably the reason why they picked 23 as the default value .This seems like a rather big error bar.

It might be interesting to check if this min number of playout can be tune up and if it would affect the result.

Maybe after those min 23 playouts fuego excludes all moves with a p less than 0.4 ? BUT considering the number of candidate moves it is probable than at least one as been wrongly estimated by more than 10%. (of course fuego implementors know their jobs so we can hope they have taken that into account)

Here the final evaluation for the best move is within 0.01 of 0.5 so it would be useful to have this kind of error bars on the estimation of all points as well.


having a 1% error interval means around 2500 playout.... which is a lot (to gain a factor of 10 in accuracy you need 100 times more playout). But it needs to be compared to the in depth exploration of the many variation for the preferred move: you have roughly 300 plays looking "not interesting" so exploring them all at 2500 playout would be 750.000 play out which is still far less than playout for the top move (around 3000000 according to esmeraldemon ).

So maybe fuego will run at roughly the same speed with this value tuned up to 2500 ?
Not sure, though, that it would bring a better playing strength.

Does esmeralddemon has the time and willingness to give it a a shot for 1 move ?

Edited out the most embarassing typos
Last edited by perceval on Fri Jul 01, 2011 7:25 am, edited 3 times in total.
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by topazg »

perceval wrote:@ez4u:

my guess would be that its a default minimal value, which seems rather low:
around 20-25 is the threshold where a bernouilli distribution begin to be approximated by a normal distribution so roughly:
(here we consider that a given move give a probaility p that a randaom playout after the move will give a won game for B, and we want to approximate p by playing a limited number of playout

the error is of order 0.5/sqrt(23) which is approx 0.1. This seems is a rather big error bar.
it might be interesting to check if this min number of playout can be tune up and if it would affect the result.
having a 1% error interval means around 2500 playout.... which is a lot (to gain a factor of 10 accuracy you need 100 more playout). but it needs to be compared to the in depth exploration of the may vars: you have roughtly 300 plays looking "not interesting" so exploring them all at 2500 playout would be 750.000 play out which is still far less than playout for the top move.

So maybe fuego will run at roughtly the same speed with this value tuned up ?
Not sure, though, that it would bring a better playing strenght.

Does esmeralddemon as the time and willingness to give it a a shot for 1 move ?
If we're talking about sufficient data points to improve play beyond chance, then I suspect 1 move won't tell us much ;)
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by perceval »

topazg wrote:
If we're talking about sufficient data points to improve play beyond chance, then I suspect 1 move won't tell us much ;)
What i meant was, for next move, try to run fuego twice, one with min playout 23 , the other 2500 min playout, and see if the chosen move ,and the rate between explored moves, changes.
i propose to do it only for next move because maybe esmeralddemon as a life and no time to run all those experiments for our enjoyment :scratch: .

Unfortunatly i don t have much time at home those days and compiling/running fuego at work might be a liiittle too much :D or i ll try it myself.
Very interesting thread anyway :tmbup:
I really wish i had some time to burn on that.

My previous job was on automated software translation base on statistical algos, it was really a blast, so if i have been able to work on translation without being a linguist, i hope i could work on a MC go engine without knowing how to play.
Unfortunatly i am not sure that go engine dev really pays up the bills ...
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by Chew Terr »

Click Here To Show Diagram Code
[go]$$Bcm31
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . . . . . . . . . |
$$ | . . . O . O . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . . O . . . . . . . . . . X O . . |
$$ | . . X . . . . . . . . . . . X O X . . |
$$ | . . . . . . . . . . . . . 0 O O X . . |
$$ | . . . X . . . . . , . . . X . X . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . X X . X . . . . . . X O . . . |
$$ | . . X , X O . . . O . . X . . X O . . |
$$ | . . . . . O . O . . . . X O X . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Ah, an easy decision. Keep strong, separate. Hope to capture the stones above, but only naturally and as part of a growing framework. Any running battle here seems to benefit me more than it does Fuego. Black can try to hane, but it would leave cutting points for later.
Someday I want to be strong enough to earn KGS[-].
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by emeraldemon »

I asked the Fuego development mailing list about this, and this is the reply I recieved:
Martin Mueller wrote:Thank you for sharing your experiment. I agree that intuitively, this focus on one move is excessive. There are also some theoretical arguments against it. Still, we do not have anything that works better at the moment. This is definitely worth studying.

One problem with doing this in the whole search tree is that because of the child selection formula, exploring bad moves by doing more exploration costs you performance because of the averaging process. I.e. assume the following situation:
you play Black and have two choices:
move a is very aggressive, but it works and it will win the game immediately by some complex tactics.
move b is solid, and will lead to a quiet, balanced situation, say a .50 score.

To simplify, let's also assume that the opponent's reply to a, White a2, is forced. So let's look at the position when it is Black's turn to play after Black a, White a2. Since the position is very tactical, there is probably only one way for Black to win from here. With low exploration and deep search, the program may discover this win, and most simulations use this move, so the weighted average looks good and move a is selected. But with higher exploration, the program will explore many more of the losing continuations in this subtree, and the average value of a will drop.

I think it is hard (but of course very interesting) to try to fix this problem in general. A simpler approach would be to force more exploration at the root node only. I agree it must be wrong to have say 100 million simulations and spend more than 99 million on the same move.
Here, the tradeoff is between exploring the top move deeper, and exploring alternative moves deeper. I believe that at some stage MoGo was using a different bandit formula for the root node, and they may still do that. But I do not know what they do, or if the details are published. I will meet Olivier next week so I will ask him.

As far as I know no one ever tried different root bandits in Fuego.

Martin
I can certainly still try it if people are curious.
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by emeraldemon »

Click Here To Show Diagram Code
[go]$$Bcm41
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . . . . . . . . . |
$$ | . . . O . O . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . . O . . . . . . . . . . X O . . |
$$ | . . X . . . . . . . . . . . X O X . . |
$$ | . . . . . . . . . . . . 1 O O O X . . |
$$ | . . . X . . . . . , . . . X . X . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . X X . X . . . . . . X O . . . |
$$ | . . X , X O . . . O . . X . . X O . . |
$$ | . . . . . O . O . . . . X O X . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Compared to last move, this one was an easy decision for fuego. Only took 15 minutes, and 99% of playouts were at that move. Value = 49.9%

Sequence:
Click Here To Show Diagram Code
[go]$$Bcm41
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . . . . . . . . . |
$$ | . . . O . O . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . . O . . . . . . . . . 4 X O . . |
$$ | . . X . . . . . . . . 5 . 2 X O X . . |
$$ | . . . . . . . . . . . . 1 O O O X . . |
$$ | . . . X . . . . . , . . 8 X 3 X . . . |
$$ | . . . . . . . . . . . . 0 . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . 7 . 6 . . . . |
$$ | . . . . . . . . . . . . . . . O . 9 . |
$$ | . . . . X X . X . . . . . . X O . . . |
$$ | . . X , X O . . . O . . X . . X O . . |
$$ | . . . . . O . O . . . . X O X . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
:w42: seems pretty much forced, and :b43: is solid, if a little slow. But I doubt white should play :w44: . It seems a bit too slow for the situation. Also I've noticed black often considers the slide at :b49: , it seems to be a large point to take.
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Re: 124. Chew (3k) vs Fuego (Bot)

Post by Chew Terr »

Click Here To Show Diagram Code
[go]$$Bcm41
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . . . . . . . . . |
$$ | . . . O . O . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . O . . |
$$ | . . . . O . . . . . . . 4 . . X O . . |
$$ | . . X . . . . . . . . . 3 2 X O X . . |
$$ | . . . . . . . . . . . . X O O O X . . |
$$ | . . . X . . . . . , . . . X . X . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . X X . X . . . . . . X O . . . |
$$ | . . X , X O . . . O . . X . . X O . . |
$$ | . . . . . O . O . . . . X O X . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Yeah, black gets a couple of good forcing moves here to harm my framework, but at least it will have to go back and fix the cutting point after. I know computer triggers don't work per se, but if black takes 43, I call dibs on 44.
Someday I want to be strong enough to earn KGS[-].
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