> What are the chances?

We don't know! That's why this is an incomplete analysis. A comparison against other players of his caliber would answer that question.

Hikaru tried to answer just that:

https://www.youtube.com/watch?v=qjtbXxA8Fcc

Yes, that's the question that I wish she had tried to answer. What are the chances? Without checking for that pattern by other 2600+ GMs, we don't know the answer.

Hikaru, who ranges from high 2700s to 2800s, said only one of his games is at 100%, which was his best game. Hans having multiple 100% is suspicious.

How long was the engine run for those cases? Does the engine output change if you double or halve the depth?

100% correlation to an output that can be tuned doesn't seem that exciting

And then explains the odds, to both this one and the parent's question