Yes, Fuego uses just the 3x3 patterns; its strength is surprising. :-)
Someone conjenctured it is because of how well-tuned its constants are.
I also think large part of it is that it seems to use perfect nakade
solver in playouts, so it should be very strong at playout tsumego; at
least in my experiments I'm finding that crucial to strength of my
bot...

It is true that Fuego has no larger patterns. However, playouts also use a number of other rules, e.g. for low liberty and selfatari.

Regarding parameter tuning, I am not so sure. This may have been true in the past. However, there have been many changes to Fuego in recent months, but the parameters have not been re-tuned, so there is probably room for improvement.

Fuego is unfortunately also far from perfect in nakade playouts. It only implements a simple but effective rule of moving single stone selfataries to the adjacent point. This "solves" most stretched nakade shapes. However, "bulky" shapes are misplayed with high probability (and some with 100% probability...)

A related problem is that even basic false eyes do not necessarily stay false during playouts, which leads to optimism about dead groups. I recently won a 9 stone test game rather easily after killing a medium-size group, which Fuego thought was about 40% alive until almost the end of the game. So it played as if it had 20 points more than it really had.

So there are still many systematic weaknesses in life and death in Fuego, even in pretty simple situations. However, the worst weaknesses in 19x19 in my opinion are for tactical fights. It is very surprising to me that this program, which plays many tactical blunders that no 15 kyu would make, can sustain a strong 3 kyu rating on KGS.

I should also mention that we have an experimental version (FuegoEx) that uses blunder filtering, tactical searches and larger patterns from Explorer for "heavy" nodes in the tree. I believe it applies such "classical" knowledge in a similar way to Many Faces. This version is probably 1-3 kyu stronger, but not very well tested. FuegoEx was used for 19x19 at the Olympiad in Pamplona.

        Martin (just back from holiday, still catching up on all these posts)
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