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What is a good spot in the queue worth?

The bid is 30.0030.00 with 50,00050{,}000 shares already queued ahead of you (time priority). Your fair value is 30.0530.05, so a fill at 30.0030.00 earns you a 55-cent edge. You can:

  • Join the queue at 30.0030.00, free, but you're behind 50,00050{,}000 shares, so you estimate only a 20%20\% chance of filling your 1,0001{,}000 before the price moves.
  • Step ahead to 30.0130.01, costs you a cent of edge, but you're first in line, so you fill about 75%75\% of the time.

Which is better in expectation, and what does the comparison say about queue value?

Your answer

This one is open-ended. Work it through, then check your reasoning against the full solution.

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