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Information gain from discarded tiles in Mahjong

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Information gain from discarded tiles

What information do you gain when another player discards a tile apart from seeing which tile it is? In particular from the position from which the tile is discarded. I neglect the timing side-channel in this context.

You can sort your tiles, but no good player will do that, since it increases the information your opponents gain while giving you no advantage.

As I understand the rules at http://mahjong-europe.org you can't regularly shuffle the tiles. In particular not between taking and discarding a tile.

From this I conclude you can find out in which turn the discarded tile was drawn(all initial tiles count as a single turn), but nothing more.

Is that correct, or did I miss a way to gain additional information, or hide information about when the discarded tile was drawn?