So I was thinking I might start a series of topics here where I go through a few things I've learned over my 3 years of playing Mahjong, and I saw a situation in a game I was playing in earlier that inspired me to do an explanation of a certain aspect of Mahjong. If you're looking for very beginner-level tips, I'll probably do a post or three about those later on, but this is just a micromanaging tip I've discovered that helps when in doubt. I haven't seen this tip on any other sites, but I've been using it for a while and it works out quite nicely.
Okay, first of all, let's say you have a starting hand like this:
What would you deal first? Anyone who knows the basic rules behind Fanpai should immediately ask what the Round Wind and their Seat Wind are to determine which of the winds will not give them Yaku. The correct move is to pick the two Wind tiles that are not your Seat or Round wind and discard them first. But after that, what do you do?
You're South, and the round wind is East, so you decide to toss Xia and Pei first, drawing two San Gen (dragon) tiles. But then you have to make a decision: which of the Fanpai tiles should you get rid of next? If none of them have been played yet, it might seem that it doesn't matter, as all of them give you one Yaku for collecting three of them. But if you really want to maximize your chances, there is a specific order for disposing of Fanpai tiles that I always use. The correct order, assuming all tiles have an equal amount on the table, is: (Guest Winds) - (Round Wind) - (San Gen Tiles) - (Seat Wind)
Some of you might be thinking that I'm overanalyzing it or that it doesn't really matter if all the tiles are still unseen, but by thinking a bit about how everyone else will manage their tiles, you can infer from there which tiles are likely still in the wall in the above scenario and others like it.
To understand this, let's think about what the East seat of this hand might decide while managing his honor tiles. The Ton will give him Double Fanpai, so it's an obvious keeper for him. So are any San Gen tiles he has, though he'll toss them before the Ton. As for the other three winds, he'll probably be rid of them at the earliest opportunity if he doesn't have a pair of them. That's just logical, after all.
Do you see what we just did there? We just inferred that, if he had a Nan, your Fanpai tile, he would likely play it at the earliest opportunity. And on the contrary, if he has a Ton, he would certainly not play it until the other parts of his hand fill up. The same applies for everyone else but you; Nans go first, Tons go last in terms of single honor tiles. So in the above example, we are 2 turns in and there are no Nans played. Therefore, we can infer that nobody has a Nan, or if someone does, it's in a pair. But I believe you'll find that, most of the time, the case is that nobody has one. Knowing that is huge. We have just inferred that there are likely still nans to be drawn in the wall. Therefore, we will keep the Nan until we have to get rid of it.
But what about the San Gen tiles and the Round Wind tile? Why would you play the Ton before, say, the Haku? For that, we go in a completely different direction: risk management. Which would you hate more, for someone to Pon a San Gen tile, or for the Dealer to Pon his Double Ton? Clearly the latter. So what we're doing by playing the Ton before the San Gen tiles is giving the Dealer as little time as possible to form a pair of Tons. If he pons it anyway, oh well, you did your best. But there's no reason to give him a free turn to pair up his Ton.
Oh, and the San Gen tiles don't have an order.
So to wrap it all up, here's the order you should discard your Honor tiles in, per seat:
East (when East round):
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East (when South round):
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South (when East round):
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South (when South round):
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West (when East round):
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West (when South round):
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North (when East round):
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North (when South round):
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Hope it helps!