4 cards are shuffled and placed face down. Hidden faces display 4 elements: earth, wind, fire, water. You turn over cards until win or lose. Question: 4 cards are shuffled and placed face down in front of you. Their hidden faces display 4 elements: water, earth, wind, fire. You turn over cards until win or lose. You win if you turn over water and earth. You lose if you turn over fire. What is the probability that you win?

I understand that wind is effectively absent from the sample space. Does not affect your chances of winning or losing. I also know that 1/3 (because we removed wind), you can pick fire where you lose the game.
Since there are 4 cards, there are 4! = 24 possible orderings of the cards.

You lose in the following cases:  

1) Fire is the first card. There are 3! = 6 ways for this to occur. 
2) Wind is the first card and Fire is the second. There are 2! = 2 ways for this to occur.  

Hence, the probablity of losing = $\frac{6+2}{24}=\frac{1}{3}$
So your answer is correct.
Probablity of losing is not 1/3. It should be 2/3.

As Below,
He wins if,


First three cards are Water/Earth/Wind = 3!
First two cards are Water/Earth and third is Fire = 2


so the total = 6 + 2 = 6

Probability of winning  = 8/24 = 1/3 , so loosing 2/3.