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We study how often exceptional configurations of irreducible polynomials overfinite fields occur in the context of prime number races and Chebyshev's bias.In particular, we show that three types of biases, which we call "completebias", "lower order bias" and "reversed bias", occur with probability going tozero among the family of all squarefree monic polynomials of a given degree in$\mathbb{F}_q[x]$ as $q$, a power of a fixed prime, goes to infinity. Thebounds given improve on a previous result of Kowalski, who studied a similarquestion along particular $1$-parameter families of reducible polynomials. Thetools used are the large sieve for Frobenius developed by Kowalski, animprovement of it due to Perret-Gentil and considerations from the theory oflinear recurrence sequences and arithmetic geometry.

Exceptional biases in counting primes over functions fields