Betrayal at House on the Hill: How Many Rooms Until Haunt Occurs?

Simulate the number of room tiles until a haunt occurs

Talking with my friends the other day and we started having questions like "how many turns is average for the haunt to start?" or "what are the odds of having the haunt on the first room reveal?". We quickly decided it would be very easy to get a rough estimate based on some Monte Carlo simulations.
Assumptions
ignore the floor required for the room tile
no dice-rerolls or other things affecting the haunt or haunt rolls
Method
1) Set the number of room reveals to 0, and the omen card count to 0. Start with a pool of the room tiles [13 omen cards, 34 non-omen cards]
2) Add 1 to the number of room reveals
3) Remove a tile from the room tile pile
4) IF this tile would draw an omen card, then add 1 to the omen card count and do a haunt roll [step (6), see below].
5) If it is not an omen card, go back to step (2)
6) Roll the 6 dice and sum the result (i.e. generate 6 uniformly distributed pseudorandom numbers, in the range of 0-2 and sum those 6 numbers)
7) If the sum of these dice is less than the number of omen cards drawn to this point, the haunt begins. Record the number of turns that have passed and restart the whole simulation [i.e. go to step (1)]
8) If the sum of the dice are greater than or equal to the omen card count, go back to step (2)