BreakthroughSolver

[mtaktikos]

Hello friends,
have added to Fairy-Stockfish the variants breakthrough5 (on 5x5 board), breakthrough6 (6x6), breakthrough7 (7x7) and of course the predefined breakthrough on 8x8 board, have compiled and attached the file here
BreakthroughSolver.zip

After the first tests, here are some results:

*** breakthrough5 (5x5 board) ***
SF finds in 3 seconds, that it is a second player win (a proof by Abdallah Saffidine is mentioned in Wikipedia), and plays this:

1. e3 {-9.59/24} dxe3 {+16.31/25} 2. dxe3 {-1000.12/35} d4 {+1000.12/32} 3. exd4 {-1000.11/47} exd4 {+1000.11/60} 4. ed2 {-1000.10/59} a3 {+1000.10/76} 5. ab3 {-1000.09/85} cxb3 {+1000.09/103} 6. cxb3 {-1000.08/126} c4 {+1000.08/191} 7. bxa3 {-1000.07/240} bxa3 {+1000.07/245} 8. bxc4 {-1000.06/245} bxc4 {+1000.06/245} 9. ab2 {-1000.05/245} axb2 {+1000.05/245} 10. cxb2 {-1000.04/245} e3 {+1000.04/245} 11. dxe3 {-1000.03/245} dxe3 {+1000.03/245} 12. ba3 {-1000.02/245} ed2 {+1000.02/245} 13. a4 {-1000.01/245} de1=. {+1000.01/245}

*** breakthrough6 ***
For the 6x6 board, the evaluation of FSF with a breakthrough6 nnue, went at depth 31 at +3.17 in favour of White, see https://discord.com/channels/779317816897699850/784418118503235625/967428814852481095 (waiting for confirmation). No proof in Wikipedia is mentioned, yet, it appears that FSF is the first engine that quasi solves this game. Edit 2022-06-24: Have adapted the engine KataGo fork hzyhzy (https://github.com/hzyhhzy/KataGo) to breakthrough6. Although no dedicated net is used, the evaluation of the 8x8-hzyhzy-net, generalized to 6x6 board, looks good enough for a proof. In analysis KataGo vs KataGo and also KataGo vs FSF, KataGo gives itself after 6 moves, over 95% win probability, confirming the first player win, see https://discord.com/channels/719576389245993010/752554748208611439/990019561246044190

*** breakthrough7 ***
With a NNUE for breakthrough7, the evaluation remains balanced for > 10 moves. Edit 2022-06-24: Have adapted the engine KataGo fork hzyhzy (https://github.com/hzyhhzy/KataGo) to breakthrough7, here again the general 8x8-hzyhzy-net is used instead of a training of a dedicated 7x7-net. In KataGo vs KataGo, the evaluation is shown as about 70% in favour of the first player, and when the game continues further, KataGo wins as the first player. Also in a test FSF with breakthrough7.nnue vs KataGo, FSF as first player could manage to reach decisive advantage in move #14, here the output of FSF:

1. fe3 {+0.00/32} gf5 2. ef3 {+0.10/32 6} cd5 3. bc3 {+0.05/30 5} ab5 4.
   gf2 {+0.05/30 8} bc5 5. de2 {+0.06/28 6} ab6 6. ab2 {+0.02/28 6} fe5 7. g3
   {+0.00/25 4} ba4 8. ab3 {+0.15/28 16} b5 9. g4 {+0.18/28 9} gf6 10. d3
   {+0.16/27 10} dc6 11. ed2 {+0.21/25 11} fg5 12. ba3 {-0.35/27 20} cb6 13.
   ba2 {+0.12/23 1.7} ba5 14. bxa4 {+3.68/24 6}
   This can be taken as another indication that breakthrough7 is a first-player-win. However, we have to wait for a stronger proof until a dedicated 7x7-net is trained

*** breakthrough ***
KataGo finds with the 8x8-net immediately 97.7%, so it is a first player win