The theoretical max is 16, but I'm thinking the practical max is probably closer to 14, since even that would take crazy luck.
Edit: OK yeah, so, I can consistently get to 10 (occasional bad luck puts me below, but 10 is average at this point). Anything above that requires good luck. I'll let yall know if I break the 12 barrier.
One more thing, do you think you could add a tiny update with a 'restart game' button (preferable accessible even if you didn't run out of moves)? (I'd understand if you didn't want to, but I'd be super thankful for it)