EDIT: THEY CHANGED THE MENU THE DAY AFTER I MADE THIS GUIDE. IT LOOKS DIFFERENT BUT ITS ALL STILL THERE.
The Subordinate City Searching Event is one that tends to confuse a lot of new players and that's OK. The event isn't very clearly laid out which leads to much confusion. But let's go ahead and fix that!
The Sub City Searching Event is a raffle. Like any other raffle, the more tickets you put in, the higher your chance at winning the prize.
First off, the event can be accessed in your Event Menu here:
Upon opening the menu you can see that there are three ways to get Clues (Tickets) for the raffles: Gathering from tiles, killing monsters, and by buying the current Event Packs.
The second page in the Event is all the individual rounds of the raffle. Every round has different subs and the winners are drawn and announced. The rounds are spaced 4 hours apart.
Each Sub raffle displays information about the current state of the raffle including: your number of Tickets, the total number of Tickets in that raffle, your chance of winning that raffle, and how many Clues counts as a Ticket.
What subs should I put my tickets towards?
The most sought after subs like Japans, Russians, and Koreans will likely have hundred of thousands if not millions of total tickets entered. If you aren't able to spend heavily to give yourself a fighting chance at the purple or golds, you should probably put your tickets towards the blues of the culture you are after as they will have smaller ticket pools.
WHAT DO I DO IF I WIN A SUB?
First, congrats! Now remain calm, you will have received a Key for the sub in your Mail and it will show up in your items. You have 24 hours to use the key and open the sub. Once you've opened the sub, you need to take the sub. But here's the catch. Once you take the sub, there is a 10 minute timer before you can bubble again. If your server is not in NAP at the time, this can be very dangerous and you and your alliance need to develop a way to sneakily do it as it will be announced in World Chat when you use the key. If you do not use they Key within 24 hours, the sub opens automatically and can be taken by anyone who finds it. They still have to remain unbubbled for the first 10 minutes though.