Locking a profit by hedging after the odds move

Earlier you backed outcome XX of a two-outcome event, staking $100 at decimal odds of 3.003.00 (so you collect $300 if XX occurs, and lose your $100 otherwise). The market has since moved, and you can now back not-XX at decimal odds of 2.002.00. You want to hedge so your net profit is the same whichever outcome happens — a locked profit. How many dollars should you now stake on not-XX, and what is your guaranteed profit? Give the guaranteed profit (in dollars).

Show hints (2)+
  1. Write the net profit on each outcome as a function of the hedge stake hh (total out is 100+h100 + h), then set the two equal.
  2. Solving 200h=h100200 - h = h - 100 gives h=150h = 150; plug back in for the locked profit.

Answer

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50

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