If John is the brother of Pete, and Pete is the brother of Sam, we know that John and Sam are also brothers. The “is the brother of” relationship is called transitive. Transitivity is a logical, mathematical relationship. There are a lot of transitive relationships, such as “heavier than,” “taller than,” etc.
There are a lot of relationships that are not transitive. Let’s say George is in love with Mary, and Mary loves her mother. We can’t conclude that George loves Mary’s mother. Whatever else it is, love is an intransitive relationship.
Video poker strategies are usually transitive. If we know that a 4-card straight flush is more valuable than a 3-card royal flush in a particular game (which is true in most, but not all games) and that in this game a 3-card royal flush is more valuable than a pair of 7s, we can conclude that a 4-card straight flush is more valuable than a pair of 7s if the strategy is transitive, but not if the strategy is intransitive.


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