I feel a bit silly posting this and maybe it's been mentioned before but I see people complaining that 3P variant has too much randomness as 1/4 of the tiles are removed. What we do is to simply display those removed tiles for all to see hence that aspect of randomness is removed.
That sounds like a good idea if you're looking for a variant with the least amount of change to the actual rules. However, we prefer to not remove any tiles from the game. Instead we lay out 4 tiles each turn instead of 3 and whichever one doesn't get picked gets discarded. (There's a thread on the forums here where that was suggested. Thanks to whoever came up with it.)