The Penults of Tak: Adventures in impartial, normal-play, positional games

by Boris Alexeev, Paul Ellis, Michael Richter, and Thotsaporn "Aek" Thanatipanonda

Abstract

For normal play, impartial games, we define penults as those positions in which every option results in an immediate win for the other player. We explore the number of tokens in penults of two positional games, Impartial Tic and Impartial Tak. We obtain a complete classification in the former case. We then explore winning strategies and further directions.

Approximate citation

Boris Alexeev, Paul Ellis, Michael Richter, and Thotsaporn Aek Thanatipanonda
The Penults of Tak: Adventures in impartial, normal-play, positional games
Integers, 25:Paper No. G1, 18, 2025.

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