The game of Flipping Coins

Abstract

We consider Flipping Coins, a partizan version of the impartial game Turning Turtles, played on lines of coins. We show the values of this game are numbers, and these are found by first applying a reduction, then decomposing the position into an iterated ordinal sum. This is unusual since moves in the middle of the line do not eliminate the rest of the line. Moreover, when $G$ is decomposed into lines $H$ and $K$, then $G=(H:K^R)$. This is in contrast to Hackenbush Strings where $G= (H:K)$.