I like the concept but it's basically a bisect / binary search simulator. Guess a reasonable but definitely high number as a high bound, a reasonable but definitely low number as a low bound, guess the average of the two, then the average of that and the high or low bound, etc.

This is especially the case when the question is asking for a bounded number in the first place (eg a percentage). In fact I'm pretty certain you should _always_ succeed within 4 steps given +-10 on a percentage question and nearly always within 3 steps. ChatGPT says it's provably so but I'm not smart enough to verify. Rings true though.

Certainly made easier by knowing whether it's higher or lower, and especially with the yellow arrows if you're not too far off.

One UX change that might be nice is to have a "spoken" version of your guess live-update below the input. I keep having to count zeroes and it would be nicer to see "Eleven billion".

The UX change you propose would be quite an improvement and it is unfortunate that I haven't considered that myself. I'll implement that in the next few days.