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

TL;DR

This paper investigates penult positions in impartial normal-play games, specifically Impartial Tic and Tak, providing a complete classification for Tic and exploring strategies and future research directions for Tak.

Contribution

It introduces the concept of penults in impartial games and offers a complete classification for Impartial Tic, while analyzing strategies and open problems for Impartial Tak.

Findings

Complete classification of penults in Impartial Tic

Analysis of winning strategies in Impartial Tak

Identification of future research directions

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.