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The bot has completely different ideas. For either option, it does a cascade attack from the upper right, and finishes you off in the same number of moves.
|22.i6 23.s5 24.t6 25.l6 26.l9 27.j7 28.l11 29.q6
or
|22.i7 23.s5 24.t6 25.r3 26.r7 27.p8 28.p6 29.k6
For what it's worth, in that position, the bot chooses |22.i5... and still loses.
Of course, your actual opponent, as a human, was clearly playing differently. Maybe you could have hustled him.
Then I tried to figure out how far back I had to go until Twixtbot could find a winning move for Black... Oof. You were in a losing position for a long time.
Move 6. It does not like your |6.k13. Alternative line:
|6.m14 7.q14 8.q19 9.u19 10.u21 11.p17 12.n12 13.q10 14.n18 15.s20 16.p21 17.v21 18.r17 19.u14 20.s15 21.v16 22.t9 23.s11 24.p7
If there's a lesson here, maybe it is just the classic advice: avoid early battles. Claim territory instead.
My thought would be that White has 2/3rds of his pegs in the upper left quadrant. My focus, then, would be to create space for myself in the lower half of the board -- ideally, enough space to drive a truck through.
One way to do that is to block that L12 peg, and 6.m14 does that. (It also has the nice perk of being a nice distance from your n8 peg.)
I might explore some far solutions, like 6.l17 or 6.m17, but the in-your-face block 6.m14 looks better. Now White is forced to claim territory on the right side of the board, but has to block that m14 peg at the same time, which leaves a large gap for you to work with in the bottom right (while that n12 threat to n8 remains). If White has to block 6.m17, Black will probably have to move to the upper right, and get around that L12 peg.
This is working so strongly in Black's favor because White's |5.l12 was such a timid move. It doesn't block your |4.i14 peg and it doesn't threaten any new paths to the top. The territory it claims is the upper-left of the central octagon, which isn't much.
Does that clarify?