7th row template

Motivated by recent discussion on double ladder tactics, I started verifying a 7th row template, which is based on the 3-5 double ladder escape. Note that trmph only goes up to 19x19 boards, so it cannot display the full template, which has a base of 25. However, the template is symmetric, so you can imagine it extends symmetrically to the left. So far this template checks out, so I'm now reasonably sure it is correct (and likely minimal as well). Let me know if you find a bug or if you want to help verify (back in this thread, Phillip was looking for a 7th row template to check using a computer solver; I recommend checking this one).

Actually, I now think that template is not minimal, and that a template with base 23 is minimal instead (where you should imagine 4 extra columns on the left). I haven't verified this template 100%, but it seems to work. I will try to prove it correct using jhex. The shape of this template is a symmetric 3,6,15,18,21,22,23, so the increases in each row are 3,9,3,3,1,1. Compare this to the 6th row symmetric template, which has shape 3,6,9,12,13,14, so the increases are 3,3,3,1,1. The only difference is an extra increase of 9 in the middle.

I wouldn't be surprised if this pattern can be extended to higher symmetric templates, so the 8th row template might have increases of 3,9,9,3,3,1,1, the 9th might have 3,9,9,9,3,3,1,1, etc. That would mean the nth row symmetric template has base 9n minus 40 for n>=6. However, even verifying the 8th row version seems really hard to do by hand.

Here's how to counter some basic attempts to block the 7th row template:

4th row stone

5th row stone

6th row stone

I would just like to add that all the positions Shalev is referring to here are taken from the recent size hex19.ch.15.1.1. tournament, which gives you a superb idea of how size 19 games are ought to be played!

Kokosz, do these positions really occur in the hex19 championship? In which games?

Certainly not an easy question to answer Ben, however I feel I almost can assure you that none of this examples are played by David since he would have gone in the complete opposite direction with his windmilling technique.  I don't know double ladder might seem strange, however it reminds me of cluster bombing in Havannah. Maciej? At least he is a very strong Havannah player.