When deciding between which lone guest wind or which lone dragon to discard, the choice may seem arbitrary, but there are tiny advantages you can gain based on your decisions. Let's take a look.
In general, the philosophy is that you discard the tile you would least like to be called first, and the tile you would most like to be called last.
Each turn that passes gives your opponents another chance to pair up their tile, and so, increases the chances that they can call what you're discarding. In the first six discards, each turn that passes increases the call chance by about 2%, if they want to call the tile. Starting at ~9%, then going to 11%, 13%, 15%, 17%, 19%.
But, which tiles do we want to be called the least / most?
Three Lone Dragons
We'll start with the easiest case, having one of each dragon, with none of them being dora and no visible dragons anywhere. Totally equivalent. In this case, which one do you want to be called the least? They're all yakuhai, right?
Well, the green dragon can also be used in Ryuuiisou, All Green. Therefore, you should discard the Green dragon first if you have one of each. Of course, given the rarity of ryuuiisou, this is incredibly minor, but it is something. If you're playing in a ruleset that uses beni kujaku, then the Red would be next to go.
Two Lone Dragons
So, what if you instead have two lone dragons? We'll assume the conditions are the same as before. The dora is not a dragon, and you can't see any dragons anywhere. To further equalize them, let's say the dragons are the Red and the White, so we don't have the ryuuiisou consideration.
What do we do here? Since the Red dragon would make the White dragon be the dora, and you have one in your hand, that means that the White dragon is slightly less likely to become a kandora or uradora. If we imagine someone calling our tile, then calling kan, then it's slightly less likely to be dangerous if that call was the White dragon.
Thus, in this case, we want the Red to be called less than the White, so we should cut the Red for a very minor safety bonus. Or you could cut the White instead, if you really need points. You can add discards into this calculation. For example, if you could see two Green dragons discarded, then the Red would now be less likely to be kandora compared to the White.
For some data relating to when one of the dragons is a dora, check out my Analysis - Lone Dora Dragons post.
Guest Winds
Of all of these, this is the one that actually matters to a reasonable degree. Let's say it's East 1-0. Completely flat points, and you're the dealer, with one of each guest wind. In what order should you cut them?
If your shimocha calls their wind, no turns get skipped. If your toimen calls, shimocha's turn gets skipped. If your kamicha calls, toimen and shimocha's turns get skipped. This slows their hands down by a turn, giving you an advantage. In a flat situation, that's the order you should discard them, counter-clockwise. In this case, that means cutting South, then West, then North.
The point situation can change this order. For example, you might not want to give fourth place the chance to come back, so you'd cut their wind first even if they were your toimen or kamicha. Or maybe if you were in a comfortable first, you'd want to cut third place's wind last to tempt them into speeding up and helping you close out the game. There's lots of small decisions you could make here, so try thinking about it a bit next time you're reviewing a game.
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