Further Hopping with Toads and Frogs

Abstract

We show the value of positions of the combinatorial game ``Toads and Frogs''. We present new values of starting positions. Moreover, we discuss the values of all positions with exactly one $\Box, \regT^{a}\Box\Box \regF^{a}, \regT^{a} \Box \Box \Box \regF \regF \regF,\regT^{a}\Box\Box \regF^{b}$, $\regT^{a}\Box\Box\Box \regF^{b}$. At the end, we post five new conjectures and discuss the possible future work.