There is no official answer that I have found, but I asked the same question on BGG about Betrayal Legacy, which has the same rule for starting the haunt, without ever getting an answer.

However, this is in all likelihood only a theoretical question, and not a practical one, because the odds of it coming up are pretty tiny. On the 12th role, you have just about a 1% chance of not getting 6 or higher. And that's after having failed the other roles. The total probability:

Chance of not starting haunt on role #:

• #1: 1
• #2: 1
• #3: .96
• #4: .81
• #5: .60
• #6: .40
• #7: .25
• #8: .14
• #9: .08
• #10: .04
• #11: .02
• #12: .01

The odds of all of these events happening in a real game?

0.000000385464%, or 1 out of every 259,427,843 games.

Now if you're limiting yourself to only using 8 dice, since the rules aren't clear about what to do if you don't start the haunt after drawing your 8th omen, then the odds are a better, but still unlikely.

There is no official answer that I have found, but I asked the same question on BGG about Betrayal Legacy, which has the same rule for starting the haunt, without ever getting an answer.

However, this is in all likelihood only a theoretical question, and not a practical one, because the odds of it coming up are pretty tiny. On the 13th role, you have just about a 0.45% chance of not getting 6 or higher. And that's after having failed the other roles. The total probability:

Chance of not starting haunt on role #:

• #1: 1
• #2: 1
• #3: .96
• #4: .81
• #5: .60
• #6: .40
• #7: .25
• #8: .14
• #9: .08
• #10: .0397
• #11: .0198
• #12: .0096
• #13: .0045

The odds of all of these events happening in a real game?

0.00000000174149%, or 1 out of every 57,422,154,217 games.

Now if you're limiting yourself to only using 8 dice, since the rules aren't clear about what to do if you don't start the haunt after drawing your 8th omen, then the odds are a better, but still unlikely.