To complete this quest, the Courier needs to play the games that the casino has to offer (Blackjack, Slots and Roulette) until they are banned from gambling in the casino. They can be banned by winning too many games and getting too much money from the casino. During this process, three different prizes will be received from the casino, after the Courier wins 2500, 5000 and 7500 caps. These prizes are usually given by the floor manager of the Tops.
After winning 10,000+ chips, the Courier will be banned from playing games in The Tops. They can still use its other functions like the bar, but cannot gamble on its tables anymore. This ban is permanent.
If the player character breaks the house limit before getting any comp gifts (by getting a large win) they will not receive any comps they have missed.
The quest is shown as completed when the Courier enters The Tops High Roller suite, so being banned from the casino is optional; however, being banned is required if one wants the "The Courier Who Broke the Bank" achievement/trophy.