HONG KONG OLD STYLE HANDS
All Pungs and Seven Pairs
All Pungs and Seven Pairs are very similar hands in a lot of ways, and it's hard to say whether one is better than the other or not. Generally, Seven Pairs is considered a more 'advanced' or 'skilled' yaku to aim for (All Pungs is treated as a very simple, novice yaku), but both have their advantages or disadvantages. Generally, you'll go for one of these two hands if your opening hand has at least four pairs, or a couple of concealed pungs.
Now, you'll have to decide which way to take that hand the first time someone discards a tile to turn one of your pairs into a pung. If you take the call, your hand is entirely forced to be All Pungs, and that's probably all your hand will score (except maybe if you're lucky enough to have a pung of dragons or valuable winds, or your own bonus tile). If you ignore the discard, your hand has a bit more versatility, but is slowed down if you go for All Pungs later. However, one huge benefit of a Seven Pairs hand is that it always inherently gets an extra faan for having a Concealed Hand.
Seven Pairs is also generally faster than All Pungs. If you open with five pairs, you only need to draw one of nine tiles from the wall (pairing up one of the three unpaired tiles in your hand) and you'll be waiting. If you open with two concealed pungs, you still need to create two more pungs and another pair. Even being able to call on tiles for pungs generally doesn't make up for the inherent slowness of an All Pungs hand.
Half Flush and Full Flush
Half Flush and Full Flush are the most common hands to aim for in Hong Kong Old Style mahjong, because of how simple and intuitive they are. If your opening hand seems biased towards one suit (at least five or six, plus a few honor tiles), it's could be a good idea to go for one of these hands. Within the first few turns, you should have an idea of who's going for one of these hands by paying attention to their discards: Anyone who discards honor tiles early on is likely going for a different hand (or far less likely, putting all their hopes on a Full Flush), and anyone who discards two different suits over the first few turns is likely making a hand based on the third suit.
Unfortunately, since there are four players but only three different suits, it's incredibly common for two or even three players to be trying to make a hand based on the same suit. If the player to your left seems to be going for the same suit as you, your hand will be much more slow to develop: Since you can't expect her to discard any tiles in that suit until her hand is almost complete, it'll be almost impossible for you to make any open chows. On the other hand, if the player to her left is going for a different suit, he'll naturally end up feeding her all of his spare tiles. In cases like this, it might pay to go for a different hand or to just focus on playing defensively, hoping someone else discards her winning tile in the end.
The other main downside of these hands are how easy it is to defend against them. Once you see a player make two or three open melds of a suit, it's best to stop discarding tiles in that suit (even at the cost of completing your hand), and the other player will have to rely on a self-picked win. In addition, since the Full Flush hand is liable for the responsibility penalty, you should always be cautious about discarding tiles if a player has three open melds in that suit, or else you might have to pay for the entire value of her hand.
Of course, Half Flush is much easier to get than a Full Flush, but the Full Flush is worth twice as much (neglecting any dragon or valuable wind pungs in the Half Flush), so it's sometimes worth slowing your hand down a bit if you can spare it.
Other Common Hands
Sometimes, your opening hand won't have lots of pairs, and won't be biased towards one suit. In these cases, you just have to try to mix multiple cheap yaku together and scrape together a 3 faan win.
The most common, easy yaku to get is an All Chows hand. Chows are much easier to make than Pungs since instead of waiting on one of two tiles to complete the pung, open-ended chows can be completed with one of eight tiles.
Another really common yaku for these cheap hands is having a Concealed Hand. As long as you get a waiting hand without making any open melds, you're guaranteed one faan for that. Though it might be tempting to try to make pungs of dragons or valuable winds, keep in mind that by doing that, you're losing any opportunity to get All Chows, or to get Fully Concealed if you make an open pung, so it's a net loss of one faan overall.
Your third faan can come from any number of sources. Usually, you'll be hoping that you don't draw any bonus tiles before you make a quick win, but sometimes the odds will be against you. If you can't get a faan for no bonus tiles (or for getting one of your own bonus tiles), you'll have to hope on winning by Self-Pick, All Chows, Concealed Hand for a 3 faan win.
On the other hand, if you're lucky enough to get both copies of your bonus tiles, you can either make a Concealed Hand with pungs or an open All Chows hand. Get even more bonus tiles, and you might not even have to worry about those qualifiers.
JAPANESE RIICHI STYLE HANDS
Riichi
Riichi is by far one of the easiest yaku to get in Japanese Style mahjong, and it can combine with virtually any other yaku. Though there are some risks in declaring riichi (defense becomes impossible and a chance at losing your 1000 points bet), the fact that you get access to the under dora and a chance at One-Shot generally makes up for these risks. Riichi is essentially identical to a Concealed Hand in Hong Kong Old Style mahjong, so just try to get your hand to a waiting position as fast as possible without calling on any tiles. Before you do declare riichi though, double check all of your discards to make sure you're not in furiten! If any of your discards could possibly be your winning tile (even ones the other players called on for an open meld), you won't be permitted to win off of any discards, and you can't change your hand to fix that once riichi is declared.
As a note, beginners should never expect their only yaku to be Fully Concealed: If you can declare riichi, you probably should unless someone else at the table has an obviously valuable hand. More advanced players will know when to declare riichi and when not to (and those that don't still will almost always have some yaku beyond just Fully Concealed).
Pon of Dragons, Seat Wind, or Round Wind
If your opening hand comes with a pair of any of these tiles, you're guaranteed a yaku to make a cheap win if you want one. Of course, this would be an incredibly cheap hand, so unless you have some other yaku or a couple dora tiles to combine with it, it's often better to keep your hand closed and go for riichi than to open it to take the honor tile pon.
All Simples
This yaku is so fast and cheap that some house rules don't even allow it to be earned if you have any open melds (The McGill Students' Mahjong Club is NOT one of these groups, feel free to make an open All Simples hand here). It's incredibly easy to make since you can call any chiis or pons you want, as long as you don't use any honor tiles, 1's or 9's. Conversely, the All With Orphans hand (which is basically the opposite of All Simples) is an incredibly bad hand for new players to go for, with a high-risk/low-return play style.
On the other hand, it can sometimes pull your hand into furiten (if your final meld is a 2-3 dots and you draw a 1-dots, you can't win with it since your hand will no longer be All Simples, and once you discard it you can no longer win with another player's discarded tile). Pay attention to your 2-3 and 7-8 potential melds for this reason.
In any case, this hand is also incredibly cheap, so you're often better keeping it closed and going for riichi unless you can score some other yaku with it or need a cheap, quick win.
Peace
Peace is a complicated hand for beginners to understand, but it can combine really easily with many, many different hands (commonly All Simples; Riichi; Large Straight; Three Colors, One Chii; Pure Double Chii...). It's important not to think of it as identical to Hong Kong Old Style mahjong's All Chows hand, but it does play very similarly to a cheap All Chows and Concealed Hand.
- Keep your hand concealed. You can't score Peace if you have any open melds.
- Your pair can't be dragon tiles, your seat wind, or the round wind. Change them out for anything else.
- Your final hand must be waiting on at least two tiles, and it must be to complete the chii. For this reason, it's more important to have a pair early than a chii, so sacrifice sets like 4-6 earlier than pairs (especially since closed waits like that invalidate Peace).
- You must keep your winning tile separate if your self-pick it. This is always a good idea in Japanese Riichi mahjong, but if you mix the tile in with your hand before revealing it, you will lose your chance at Peace (since it can't be proven that you were waiting to complete the chii with one of two tiles).
Large Straight and Three Colors, One Chii
These yaku are rather similar in Japanese Riichi mahjong. Both of them are simple to make easily, but become cheap enough to be almost worthless on their own if your hand has any open melds. Large Straight has the benefit of being fairly easy to combine with a Half Flush or Full Flush, whereas Three Colors, One Chii can easily combine with All Simples, All With Orphans, or All With Terminals. If your opening hand has a few almost-chiis to make either of these hands, consider working towards them. However, be aware that these hands have to risk playing around furiten for the same reason as All Simples, so closed waits are far safer for these hands if you open them (A 1-3 bamboo is guaranteed to win with a 2-bamboo, but you might lose your chance at Large Straight if you draw a 4-bamboo with a 2-3 bamboo already in your hand)
All Pons and Seven Pairs
Unlike in Hong Kong Old Style mahjong, Seven Pairs is generally seen as objectively superior in Japanese Riichi mahjong. Since the game is more defensive and the dead wall limits the tiles available, it becomes much easier to make a Seven Pairs hand than an All Pons hand, and the former also is easier to take apart and defend with if you need to. But there are still some hands that can easily go for All Pons, and if you can get Three Concealed Pons with one as well, you can easily get a big hand. Concealed pons are also good for fu, while a Seven Pairs hand's biggest weakness is the heavily limited amount of fu it has, meaning it's hard to make it valuable without declaring riichi.
Half Flush and Full Flush
Just like in Hong Kong Old Style, these are always valid hands to go for, but a Half Flush is generally considered too slow and not subtle enough to compare against most other hands in Japanese Riichi mahjong. By the time you open your second meld, any other player might have finished her All Simples hand, or might have an open pon of dragon tiles to run away with a cheap win. And since it's as easy to defend against as it is in Hong Kong Old Style, you usually have to pray for a self-picked win (or someone in riichi being forced to discard your winning tile).
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