4
$\begingroup$

I like to play a game with my family and friends. It goes like this:

The players take turns to say a letter. The letters taken in order must be the start of some word, and the person who finishes a word without there being a continuation on the word loses. If you are challenged on the letter you say, you lose if you don't have a word, otherwise the challenger loses.

For simplicity, plurals are allowed.

In the two player version of this game, assuming each player plays optimally who has a winning strategy (the player who goes first or the player who goes second)?

Note that by the fundamental theorem of combinatorial games, we are guaranteed that one player has a winning strategy cannot be a draw.

You are welcome to specify your own dictionary that you would use for 'adjudication' in your answer as long as it is reasonably well-known.

$\endgroup$
6
  • $\begingroup$ Isn't this a solved game, or am I thinking of something else? $\endgroup$ Jan 21, 2017 at 22:59
  • $\begingroup$ @greenturtle3141 It may be, I don't know. I couldn't find it online. $\endgroup$
    – boboquack
    Jan 21, 2017 at 23:01
  • $\begingroup$ Nevermind, this is basically the game Ghost with a slight rule change. $\endgroup$ Jan 22, 2017 at 1:13
  • $\begingroup$ I'm guessing that given any first letter, there is a letter which can be added to it so that creates the first two letters of a three-letter word that cannot be extended. Therefore, I'd guess Player 2 would have the winning strategy if both players played optimally. But since this is only a conjecture, I'm not posting it as an answer. $\endgroup$ Jan 22, 2017 at 2:02
  • $\begingroup$ @greenturtle3141 What's ghost? Never heard of it. $\endgroup$
    – boboquack
    Jan 22, 2017 at 7:47

1 Answer 1

3
$\begingroup$

If the players use the Official Tournament and Club Word List as their dictionary, then the first player can always force one of the following words:

jailable
jebels
jiao
jnanas
jodhpurs
juxtaposed
juxtaposes
(I chose j because there's only so many letters it can be continued with.)

I think this strategy also works if they play according to the OSPD5, but I couldn't find a plaintext version for that, so it's hard to verify.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.