Break-even uninformed fraction against pick-offs

Market-making a name, you earn +$0.50 on an uninformed fill but lose $2.00 whenever an informed trader picks you off. What fraction of your fills must be uninformed for you to break even? Give a decimal to two places.

Show hints (2)+
  1. Let pp be the uninformed fraction; write E[P&L]=0.50p2.00(1p)E[\text{P\&L}] = 0.50p - 2.00(1-p) and set it to zero.
  2. The +0.50+0.50 vs 2.00-2.00 asymmetry pushes the break-even fraction well above one-half.

Answer

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0.8 (± 0.001)

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Asked at: Timed Mental-Math & Sequences, ETF Market-Making

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