What does it mean to be half a pawn ahead?
It's convenient to have a simple way to evaluate the material on-board, so many chess players use rules of thumb like a rook is worth 5 pawns, a knight or bishop is worth 3.25 pawns, and having both bishops is worth an extra 0.5 pawns. If I have R+B+B (5 + 3.25 + 3.25 + 0.50 = 12.00) and you have R+B+N (5 + 3.25 + 3.25 = 11.50), I'm up by half a pawn.
But be skeptical of such simple evaluations, because it's possible to be ahead materially but still losing because your opponent has a strong attack, a lead in development, or some other positional advantage to compensate for your material plus.
Yip and what might have happened is that a pawn's head might have been lobbed off by the opposition and he is staggering forward (involuntarily), so for a short period of time there is a "half pawn" advantage....
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