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.

  • $\begingroup$ So no infinity with PHP.... :( $\endgroup$ – Mark N Jun 19 '15 at 16:05
  • $\begingroup$ Note: OED might be a bad idea because it's behind a paywall. But I'll see if I can find a better one. If not, we'll have to limit it to words of length 15 or less, which sorta sucks. $\endgroup$ – Joe Z. Jun 19 '15 at 16:07
  • $\begingroup$ How about Moby as recommended over on Stack Overflow? $\endgroup$ – Engineer Toast Jun 19 '15 at 16:13
  • $\begingroup$ Do I understand that the word must be as least 4 characters long? $\endgroup$ – Engineer Toast Jun 19 '15 at 16:17
  • $\begingroup$ SOWPODS was superseded by CSW a while ago. $\endgroup$ – Joe Z. Jun 19 '15 at 16:18

Since the CSW only contains words with 15 letters or less, it's quite trivial. I go for one of many:


which I presume is in the 2012 CSW.

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  • $\begingroup$ I guess it's the same no matter what word length I choose. sigh $\endgroup$ – Joe Z. Jun 19 '15 at 17:20
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    $\begingroup$ @JoeZ. I thought something like this would happen....I guess Puzzling has become too smart :p $\endgroup$ – Mark N Jun 19 '15 at 17:21
  • $\begingroup$ @Joe Z It's this damned internet makes finding these answers too easy. Maybe limit it to letters inserted - not appended or prepended - might make it a little trickier but then it's not directly based on your Insertion Ghost game and has less value. $\endgroup$ – Avon Jun 19 '15 at 17:41
  • $\begingroup$ @Joe Z. I am still a little confused about the game rules though. Is this not a winning word because other player has to make a word? Or does the other player not lose if you can then make another word it and they can't from that? This answer fits the "string of letters S that is not a word, and you can insert two different sets of letters to create two words A and B, where A is odd length and B is even length" challenge but does it fit the game rules definition of a non-winning (distinct from losing??) word? (Is that summary of the challenge, in fact, a little wrong?) $\endgroup$ – Avon Jun 19 '15 at 18:47
  • $\begingroup$ No, I'm lamenting the fact that it is a winning word because the strategy to get it hasn't changed at all. $\endgroup$ – Joe Z. Jun 19 '15 at 20:11

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