The game Ghost is a game where players take turns appending letters to the end of a word. The first person to form a complete word with at least four letters, or give a string of a letters that no word begins with, loses.
An example game might go:
Player 1: A
Player 2: AC
Player 1: ACC
Player 2: ACCO
Player 1: ACCOM
Player 2: ACCOMP
Player 1: ACCOMPA
Player 2: ACCOMPAN
At this point, player 1 realizes he loses because all variants of ACCOMPANY (all of which begin with ACCOMPANI-) have an odd number of letters. If he'd gone with ACCOMPL instead of ACCOMPA on his fourth turn, he could have forced player 2 to spell ACCOMPLISH or ACCOMPLICE or ACCOMPLETIVE, all of which have an even number of letters, thereby winning.
Therefore, we call ACCOMP a non-winning string for Player 1, in which there are both odd-length and even-length words that begin with that string, and therefore it's not a sure thing that Player 1 wins yet. (He many have the winning strategy by choosing ACCOMPL, but he still has to make the right choice in order to win here.)
A friend and I came up with a variant in middle school in which you could insert a letter anywhere within the word itself. We called it Insertion Ghost due to its insertion mechanic (the Wikipedia article linked above calls it Xghost or Superduperghost and attributes it to a man named Daniel Asimov).
In this game, a string like XVZ is valid because you can still make the word EXTRAVAGANZA out of it. Thus, the potential for words, and the capacity for strategic thinking, is much larger.
A game might go like this:
Player 1: X
Player 2: XF (thinking of "EXFOLIATE")
Player 3: XFD (thinking of "EXFOLIATED")
Player 4: XMFD (now thinking of "EXEMPLIFIED")
Player 5: ... ... ... EXMFD (also thinking of "EXEMPLIFIED", but stalling)
As you can see, the target words get convoluted really quickly, and even switch a lot of letters almost all the way (the change from EXFOLIATED to EXEMPLIFIED being the target word inserted five letters between the X and the F that weren't there before, just to change the target word), and it becomes much harder to determine whether you've won in advance or not. An example of a five-letter non-winning string might be CLAMT - both CLAIMANT (8) and EXCLAMATION (11) are possible target words.
What's the longest non-winning string (i.e. a string that can have both odd-length and even-length target words) in this variant, for either player?
For the purpose of this question, our word list is the 2012 CSW.
