Twenty Questions Games Always End With Yes

TL;DR

This paper clarifies the relationship between Twenty Questions games and Huffman coding, proving that the average number of questions remains within a specific bound despite the game’s ending constraint.

Contribution

It demonstrates that the average questions in Twenty Questions games are bounded by entropy, even when the game always ends with a 'Yes,' addressing a gap in previous understanding.

Findings

Average questions are between H(X) and H(X)+1

Twenty Questions always end with 'Yes' but still relate to Huffman bounds

The bound holds despite the ending constraint

Abstract

Huffman coding is often presented as the optimal solution to Twenty Questions. However, a caveat is that Twenty Questions games always end with a reply of "Yes," whereas Huffman codewords need not obey this constraint. We bring resolution to this issue, and prove that the average number of questions still lies between H(X) and H(X)+1.