One way to understand biology is by finding genetic sequences that are related to each other. Often, a family of related sequences has position-varying probabilities of substitutions, insertions, and deletions: we can use these to find distant and subtle relationships. Current software tools for this task either do not use all probability evidence (e.g. PSI-BLAST, MMseqs2), or have excessive complexity and minor biases (e.g. HMMER). This complexity inhibits fertile development of alternative tools. This study describes a simplest reasonable way to find related sequences with position-specific probabilities, using all probability evidence. The algorithms likely use the fewest operations that such algorithms possibly could. A full version of this paper is available at bioRxiv: https://doi.org/10.1101/2025.03.14.643233