Twenty Questions Games Always End With Yes

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.

💡 Research Summary

The paper addresses a subtle but important mismatch between the classic Huffman coding solution for optimal binary questioning and the practical rules of the “Twenty Questions” game, where the game always terminates with a “Yes” answer. Traditional Huffman codes are optimal prefix codes for a given probability distribution P(X) in the sense that the expected code length E