User blog comment:Edwin Shade/Can Chess Ordinals Produce Functions With Uncountable Growth Rates ?/@comment-1605058-20171222153040

I'm afraid I do not understand the definition of \(\mathfrak{Ch}_n\) (the parenthetical remark confuses me) - is it the supremum of the values of positions with \(n\) pieces? If this is so, then \(\omega_1^{{\mathfrak{Ch}_{\!\!\!\!\sim}}_3}\) is not the supremum of \(\mathfrak{Ch}_n\). You can do strictly better with infinitely many pieces than you can do with a limit of finite numbers.