Hello! We'll be travelling to Spain, and will need to catch a train from Madrid to Seville. Because we aren't sure what time exactly we can expect to arrive in Madrid, we're hesitant to pre-book a train ticket. Does anyone know, can you just purchase the cheapest rate train ticket right at the station, the day of?
Thanks so much!

It most certainly won't be the "cheapest" on the date of travel.

But you can purchase tickets at the station for the next train leaving, presuming it is not sold out, of course.

If you allow at least three hours between your expected arrival time at Madrid Barajas airport and the train's departure time from Atocha station, you should be able to make your train without any problem, if you take a taxi from the airport to the station. You only need to be at the station 20 minutes before departure and clearing security at the station is quick and easy, depending on the crowd.

The only discounts, other that for those with a "Tarjeta Dorada", are available online.

if you are 60 and over , you can get a disc. of 25- 40 %.....depending on the train and day
You need to have a Tarjeta Dorada card ( 5 euros )

It also depends on when you will be traveling. One Friday before a holiday weekend, I reached Atocha before 1 p.m. and found that EVERY train for Sevilla that day was already sold out, and most of them for the next day were sold out, too.

The Tarjeta Dorada can only be purchased at a train station, which doesn't do much good if you are just arriving and need to purchase your tickets ahead of time. Besides, the Tarjeta Dorada is only good on certain trains.

FYI, because I was stupid and almost missed the train at Atchoa...the boarding platform is UPstairs, the arrival is downstairs. It looked so uncrowded downstairs that we hung around the garden area until 20 minutes before our train, then sauntered up to board to discover we were in the wrong place. It was fine, but there is a security procedure prior to boarding, and we could have easily missed our train. More adventures than one might have wished for.