1) The first thing to do is to find the Playing Card Mission in the lobby. The quest will disappear when the countdown ends, and it will reappear after about 10 minutes. So if you can't find this mission, please wait about 5 minutes and come back to the slots lobby. You can see what this mission looks like in the screenshot below:
2) Enter the slot machine with this mission, you will see it if it exists:
3) Click the mission icon to check requirement:
4) Play this slot machine to complete the mission before the countdown ends. If you succeed, you will get a new playing card:
5) The mission will reset after completion, you can try again to collect more cards.