I can't even get past turn 2 without getting trapped and none of the numbers you have can factor into 23,17, or 97
Okay, I finally found a sequence that leads to a win. At no point does it involve playing the large stones, so I still have no idea what people mean by that. The first two turns are crucial.
For turn 1, use the pickaxe on the 122 to play a 61 and a 2 like so:
Turn 2, use the pickaxe on 125 to get three 5s. Use them to lock the opponent out of the top-right:
This alone opens up many paths to victory. However, you can get an even cleaner win by holding onto the 5s on turn 2, not playing anything that turn, and instead waiting until turn 3 to play them along with additional stones, allowing you to lock the opponent out of the bottom left as well:
