Every day, Letterly gives everyone the same letter, and you fill each category with something starting with it. The letter used to be picked at random from the date. That sounded fair. It was not.
Random feels broken
A player noticed the same letter twice in one week. Looking back over every round so far, that was not a one-off. There were dozens of repeats within a week of each other. Some letters had come up ten times while others had come up twice, and one letter had not appeared for more than three months.
That is what real randomness looks like. Streaks and gaps are normal. But in a daily game it feels like the game is broken, or lazy, and nobody wants three S days in a fortnight.
A shuffled bag
The fix is an old trick from video games. Put every letter in a bag, shuffle it, and draw one a day until the bag is empty. Then shuffle a fresh bag and start again.
Now every playable letter comes up exactly once in each cycle. A letter can never repeat within a few days, and none can vanish for months. There is one extra rule at the join between two bags, so the end of one cycle and the start of the next cannot land the same letter close together.
The order is still worked out from the date, so it is still the same letter for everyone and nobody can see ahead. Before switching over, I checked the new draw against a separate model of it for three years of future dates to be sure they matched exactly.
It is a small change that most players will never notice. That is the point. The best fairness fixes are the ones that stop people having a reason to complain.