Improving upper and lower bounds of the number of games born by day 4

TL;DR

This paper significantly refines the bounds on the number of combinatorial games born by day 4, advancing from previous estimates to much tighter and larger bounds.

Contribution

It provides improved lower and upper bounds for the number of games born by day 4 in combinatorial game theory, using novel methods.

Findings

Lower bound improved to 10^{28.2}

Upper bound improved to 4.0·10^{184}

Bounds are substantially tighter than previous estimates

Abstract

In combinatorial game theory, the lower and upper bounds of the number of games born by day $4$ have been recognized as $3.0 \cdot 10^{12}$ and $10^{434}$, respectively. In this study, we improve the lower bound to $10^{28.2}$ and the upper bound to $4.0 \cdot 10^{184}$, respectively.