When you are the active player, you'll need to carefully choose where to play (and where not to play) to convey information about your remaining fate to your allies.
Your play will help them narrow down the possible values of your fate until they are able to confidently predict it (which may take more than one turn).
Pay attention not only to where you can play, but where the other players may assume you could not play.
For example, if another player plays a fate with a value of 1 onto the Midnight arcana card ("If one of your fates is lower than the other, play the lower one here"), that player has not conveyed much information (they could still have a 2, 3, 4, 5, 6, or 7).
You might conclude that they made this (uninformative) play because they couldn't play elsewhere.
So, if The Deep arcana card ("If the sum of your fates is 5 or less, play one of them here") is also in play, you can conclude that their fates did not sum to 5 or less.
Since you know they played a 1, you can conclude that they did not have a second 1, a 2, a 3, or a 4, because any of those values paired with the 1 would have allowed them to play on The Deep and give more information. Now you're making progress - you've narrowed the possibilities down to 5, 6, or 7!