Split the keys in half, and open the vault at 00:00 and 12:00 on a thursday or friday
This is to accomodate a wider range of timezones and give certain people a second chance if they miss, while keeping it on a "first come first served" basis
There's no way to make it fair when it's first come first served.
The only way to make it fair is a lottery system. For example:
A week before the Vault opens, go to the Vault and click a game.
Instead of a "Claim" button, there would be an "Enter lottery" button.
You can enter the lottery for each individual game as long as you have enough ARP. There could also be the possibility of entering a game's lottery multiple times if you have ARP to spare.
When the vault opens, each game has its own separate lottery.
If you win a game, you lose the ARP you spent to enter its lottery. For the games you did not win, you are refunded the ARP.
After the initial lottery, the Vault continues with the current behavior, letting you Claim any remaining games that were not won by lottery.