Is Game Theory Applicable Here?

A friend of mine and I were discussing a fairly simple game: you are presented the opportunity to take either $240 straight up or to play a game where 25% of the time you will win $1,000. You may only play the game once.

My friend aruged that the expected value for the game is $250 if you take the shot at $1000 and only $240 if you do not, and therefore you should take the chance. I completely understand, but...

Seeing as it is a one time event, I argued that it was not necessarily advantageous to play for the long run. Therefore, it is not unreasonable to sacrifice $10 in expected value in order to play a game you cannot lose rather than one that you are a huge underdog to win.

I understand that one's decision might be influenced by how much money they have to start, or if the game had different values (I feel most people would rather take 240K straight up than take a 1-in-4 on $1 million, even if it is mathematically incorrect), but in general is my logic faulty?