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If Billy is required to halve until one letter remains, this would take 4-5 selections. It might be more efficient to make two cuts so three letters remain, and let Billy choose from one of the three. People who play video games often remember short key sequences as combination moves in games, and might be quick to remember the key presses for word combinations.
Tertiary Search
Tertiary search would be similar to binary search, except instead of just using the "left" and "right" keys, a user could also use the "down" key. This would require only three key presses for each letter. A space could no longer be the "down" key and would likely be simply appended after "z" ie. hitting "right" three times. This would not be obvious to a user, and would have to be indicated somehow.
