Merging stacks of papers by hand isn't the same as exchange-based computer mergesort: if the cost of inspecting and comparing items is negligible relative to actually moving them the basic, unit cost operation is splitting a sequence into three possibly empty sequences and splicing the middle piece into an arbitrary position in another sequence. In some cases reversing the spliced sequence is free ("pancake" sorting).

This cost model is an important reason to merge bottom up, from sorted subsequences, without arbitrary splitting that can add work but not reduce it.