According to the historians on Reddit, Romans couldn’t just go to Ticketmaster to purchase tickets to watch events at the Coliseum. Here’s what they did do:

• The tickets were free. They were given out in bulk by the organizer, and those who received them would further distribute them to those they wanted to show favour to.
• There was tiered seating. The richer and more powerful you were the closer you got to sit to the action.
• The tickets themselves were etched into broken shards of pottery called ostraca and had information on the section, row, and seat.
• To prevent counterfeit tickets, shards from the same pot were used for each group of seats so that the tickets could be put together to re-form the pot.

Read the wider discussion about Coliseum events over here.

Source: Reddit