# Transfinite Version of Welter's Game

## TL;DR

This paper extends Welter's Game to transfinite ordinal positions, providing a straightforward solution by leveraging known results from transfinite Nim and the original game.

## Contribution

It introduces a transfinite version of Welter's Game and offers a simple solution method based on existing transfinite combinatorial game theories.

## Key findings

- Established a transfinite version of Welter's Game.
- Provided a straightforward solution approach.
- Connected the game to transfinite Nim results.

## Abstract

We study the transfinite version of Welter's Game, a combinatorial game played on a belt divided into squares numbered with general ordinal. In particular, we give a straight-forward solution for the transfinite version, based on those of the transfinite version of Nim and the original version of Welter's Game.