User blog:Edwin Shade/Can Chess Ordinals Produce Functions With Uncountable Growth Rates ?

\(\omega_1^{{\mathfrak{Ch}_{\!\!\!\!\sim}}_3}\) has been proven to equal \(\omega_1\), the first uncountable ordinal. If I am correct, it is the supremum of the values of all the positions from which white can force a win in three-dimensional chess with an infinite number of pieces. Defining \(f_{\omega_1^{{\mathfrak{Ch}_{\!\!\!\!\sim}}_3}}(n)\) is trivial then, as it can be equal to \(f_{\mathfrak{Ch}_n}(n)\), where \(\mathfrak{Ch}_n\) is equal to the supremum of all the values of all the positions from which white can force a win in three-dimensional chess with a finite number of pieces, (which is countably infinite). Ignoring the fact I have not defined a system of fundamental sequences for the large countable ordinals that would be produced, have I not just created a function with a growth rate of \(f_{\omega_1}(n)\) ?

In addition, can someone please explain to me how chess ordinals are even calculated ? Because although I read the article on them, (both on this Wiki and Cantor's attic), and watched the following video by PBS Space Time, I still cannot understand how transfinite numbers can be associated with chess games. So if there is someone with an intuitive explanation of this, please elucidate.