arc046_b
https://gyazo.com/d9db142ea9bb9d964a6454189f0dacea
Thoughts.
If there is less than A remaining and it is the first move's turn, the first move wins.
If there is less than B remaining and it is the late player's turn, the late player wins.
Suppose B is less than A (wlog)
The first player wins if A+1 or less on the second player's turn.
In the first move, when A+2, even if 1 is taken, it is still greater than B, so the first move wins.
If it's 2A+1 or less, you can take the first move to win.
If the side with the highest number of moves wins the game...
Official Explanation
Your intuition is right, you just need to show it in a proper and comprehensive case study.
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