I bought the London Pass for my trip in just over a month. I added on their Oyster Travelcard option (how they word it) for a credit of 25 pounds.
As I understand - I will be billed against that credit for the first 3 trips of the day and then no additional charges will apply that day no matter how many times you ride. I will take the train in from Heathrow on arrival so that looks like about 13 pounds as it will be off-peak on the Piccadilly line (blue). I believe all my other travel will be in zone 1 for about 2.5 pounds as I'm staying at Earl's Court station which looks to be the edge of the zone.
I tend to take a few trains the wrong way - a few too many stops - and a little confusion along the way in a new city so want to be sure I understand the rules of the card.