I feel like the bet has been clearly described a number of times, but I'll describe it again for you.
For each trial, we roll 2 dice.
If neither of the dice show a 2, then there is no action.
If at least one of the dice show a 2, then the bet has action: The bet will win and pay odds if the dice are showing 2-2. The bet will lose 1 unit if the dice are showing a 2 and any other number.
The only thing left is to determine what the proper odds for the payout should be. You believe the answer is 1/6, and so from your perspective, the fair odds would be 5 to 1. I believe the answer is 1/11, and so from my perspective, the fair odds would be 10 to 1. Let's set the payout odds exactly between those two, at 7.5 to 1 (or 15 to 2, if you prefer).