Is it worth improving the price by one tick?

Question

You want to buy, and there's a long queue resting at the $20.00$ bid. You can join that queue at $20.00$ , or step ahead to $20.01$ , jumping everyone.

At $20.00$ your edge (versus your $20.03$ fair value) is $3$ cents, but the queue is long so you only fill about $30\%$ of the time. At $20.01$ your edge drops to $2$ cents, but by leading the book you fill about $70\%$ of the time.

Which has the higher expected value? When would improving not be worth it?

Accepted Answer

Compute EV = (fill probability) × (edge per share) for each. 	ext{Join at } 20.00: \quad 0.30 	imes 0.03 = 0.009 = 0.9 	ext{ cents per share (expected).} 	ext{Improve to } 20.01: \quad 0.70 	imes 0.02 = 0.014 = 1.4 	ext{ cents per share (expected).} Improving wins: 1.4 cents beats 0.9 cents in expectation. You give up a penny of edge per fill, but you more than double your fill probability, and the extra volume at a still-positive 2-cent edge outweighs the thinner margin. When improving does not pay. The math flips if the edge you'd give up is large relative to what's left. Suppose your…

Is it worth improving the price by one tick?

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