Theorem 12.7

The expected number of probes in a successful search is at most

$$\frac{1}{\alpha} ln \frac{1}{1 - \alpha} \;+\; \frac{1}{\alpha}.$$

For example, if the table is half full, $\alpha$ = 0.5, the expected number of probes is 3.4.

If the table is 90% full, $\alpha$ = 0.9, the expected number of probes is 3.7.

If $\alpha$ is constant, the performance of a successful search is O(1).