Odds across books

Book $1$ offers decimal odds of $2.2$ on outcome A and $1.7$ on outcome B. Book $2$ offers $1.8$ on A and $2.3$ on B. Exactly one of A or B happens, and a winning bet returns stake times odds. A bettor places a total of $1000$ split between A at the best odds and B at the best odds, choosing the split so that the payout is the same whichever outcome occurs. What is the guaranteed profit, rounded to $2$ decimal places?

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