2 fo 1

No, it does not. You need to get a paper travelcard at a National Rail station. If you are using an Oyster card pay-as-you-go, you can get a 1-day paper travelcard just on the days you plan to use the 2-4-1 deals. IOW, the travel card will take the place of the Oyster card on the days you will be using the 2-4-1 deals. (You can use this paper card on the tube, buses, and DLR) You could also get a 3-day or 7-day paper travelcard at the rail station. Don't know what airport you are using, but if you are taking the train to and from Gatwick, Stansted, or Luton and have r/t tickets, then your rail tickets will qualify you for the 2-4-1 deals during your stay, and you don't have to bother with getting the 1-day paper travelcards from a rail station.

as long as the ticket is valid on the day you are at the attraction

If you buy round-trip rail tickets (called "return" tickets in the UK), the 2-4-1 deals are good for the entirety of your stay in London. If you buy 1-day passes, as I stated in my original post, you need to buy them on the day you plan to use the 2-4-1 vouchers. (Actually, you can buy them the day before, but be sure they are dated for the next day, i.e., the day you are using the vouchers) From the daysoutguide.co.uk website: If for example you buy Return tickets to London, outbound on a Monday and returning on a Friday, you will be able to use the vouchers throughout the Monday-Friday period, provided you show both outward and return portions of your tickets (remember to tell the train company staffs that you need to keep your outward tickets!).

I understand now, thank you.