If you explained the rules carefully and asked it to respond in paragraphs rather than a grid, it might be able to do it. Can't test since it's down now.
Neglecting that (only because it's harder to navigate whether I should expect it to handle state for an extremely finite space; even if it's in a different representation than it's directly used to), I know I saw a post where it failed at rock, paper, scissors. Just found it:
https://www.reddit.com/r/OpenAI/comments/zjld09/chat_gpt_isn...