What you're describing is an interpolated binary search (where you don't divide in two, you pick a point based on a guesstimate of where the key will lie). It

What you're describing is an interpolated binary search (where you don't divide in two, you pick a point based on a guesstimate of where the key will lie). It turns out that interpolated binary searches are useful in computers, in cases where the structure being searched has a significant overhead for each read - for example, seeking in variable-bitrate-encoded video streams is such an application.