But, the best strategy is the one which is most likely to win (or wins in the fewest possible moves.) Knowing that 'S' is the most likely letter to occur for a five-letter puzzle does not mean that it's the first guess you should make. Other letters might lower the depth of the search tree by providing a better branching structure.
Here's a toy example to make the point. Say you're playing with only the vocabulary SEE SAW SET SEX TEA ASH PAW SIS
'S' is the most frequent letter (6 words, 7 instances) compared to 'A' (4) or E (4 words, 5 instances). But if you guess 'S' first:
SxS -- SIS
Sxx -- SEE SAW SET SEX (need two guesses--- neither E T or X are sufficient.)
xSx -- ASH
xxx -- TEA PAW (guess 'A' next, done)
then the tree has depth 3. But if you guess 'E' first:
xEE -- SEE
xEx -- SET SEX TEA, guess T next and done
xxx -- SAW ASH PAW SIS, guess S next and done
