"Has yet to win" vs. "has yet won"?

Question

I was doing some SAT English problems and came across this one:

Find the error in the sentence, or state that there is no error. Each possible error is in parentheses.

Chess players find that playing against a computer is helpful (to improve) (their) skills, (even though) no chess-playing computer has yet (won) a championship.

I picked up the idiomatic error: "is helpful to improve" should be "is helpful in improving". However, I also saw a problem with the last choice, because I remember hearing the words "has yet to win".

According to the solution, I'm wrong. "Has yet won" is correct. The website says this:

There is no error at (D). The word "won," the past participle of the verb "to win," combines with the word "has" to produce the appropriate verb tense.

However, this means that "has yet to win" is incorrect due to the conflicting tenses.

Is "has yet to win" gramatically incorrect? Or are both okay?

Answer 1

Has yet to [infinitive] is perfectly correct, and there is no conflicting tenses in it. Remember, the verb have can combine with a past participle to form perfect constructions (present perfect and past perfect, respectively, for present and past have), but it can also combine with a to-infinitive.

Usually, have to X means ‘must X’, but if you add yet, the meaning changes. It is in fact a slightly different collocation of verbs, and it works with both be and have, though have is much more common. The meaning of X is/has yet to happen is “X has not happened yet”.

This is why it does not fit your sentence here: “No chess-playing computer has yet to win a championship” means “No chess-playing computer has not yet won a championship”… and that’s frightfully difficult to parse. Presumably it would mean that every chess-playing computer has won a championship already, but it’s basically nonsensical.

The following two are more or less equivalent, though:

…even though no chess-playing computer has yet won a championship.
…even though chess-playing computers have/are yet to win a(ny) championship(s).

The way this idiomatic phrasing works is probably easiest to understand if you use be as the basis: “He is to do it” means either a) ‘he must do it’ or b) ‘it is expected/known that he will do it’. Consider “He is about to do it”—that means that he will do it in just a moment. Yet here means ‘still’, so if you say “He is yet/still to do it”, it means that it is still expected/known that he will do it; in other words, he hasn’t done it yet.

Answer 2

I think the best way to look a this is to simply accept 'to have yet to' as an idiom. However here is my attempt at a partial explanation.

I have won is past perfect. The winning has already taken place.

I have to win is an idiom that refers to the future. These days it is synonymous with I must win.

By inserting 'yet' we revert it to its original sense of futurity but without a sense of compulsion.

So, I have yet to win, means I have not won yet. I may (or may not) win in the future.

I'm not sure if that helps. I hope so.