Saturday, August 07, 2010

Endgame Penalties and a Problem in Definition

As you readers may know, this blog is devoted to mahjong in Singapore with a focus on Mahjong Competition Rules (MCR), but there is the occasional post on Singapore Style mahjong. The reason why I am so interested in MCR is that MCR is a mahjong variant that is more skill-based, and less affected by luck. However, there are few players who play MCR in Singapore, and I play 'live' MCR with other players rather infrequently. On the other hand, I get to play Singapore Style mahjong somewhat more often, with some regular opponents.

The problem with Singapore Style mahjong is that there are no standardised rules. There is no national association that has codified and promulgated a set of official rules for Singapore Style, and players here just get by with house rules through common agreement. Unfortunately, that has led to a rather messy situation where many players do not really know some common rules, or just play them rather differently. Also, sometimes, some commonly accepted rules are illogical, or inconsistent with some other rules. This may be due to players mixing and matching rules without really understanding how some of the rules came about in the first place, or whether there is any historical precedents for such rules.

One particular situation had arisen recently when I played with my regular Singapore Style mahjong group. This was a disagreement regarding bao (包 bāo) rules in the endgame. So, anyway, before I go into details about the disagreement, I will first have to explain what these bao rules are. It is a little complicated though, due to the various conflicting house rules.

Bao rules in the Endgame
In the endgame, where very few tiles are left for play, bao rules (specifically bao qing/sheng* rules) come into effect. Bao rules refer to rules that make the discarder loser pay for the other losers as a form of penalty for taking risks in discarding dangerous tiles. This is also known as 'insurance penalties' or 'liability'.

After a player takes a tile leaving seven playable tiles (this excludes the 15 tiles that cannot be used at the replacement end of the wall), the bao qing/bao sheng situation occurs. At this point in the game, with so few tiles left, it is particularly risky to discard tiles to opponents to win on. If all the playable tiles have been drawn and there is no winner, a draw is declared, and a new hand begins. For players with no good chance to win, a draw would be a good result. Hence, for someone to win at this stage, there are bao penalties under certain conditions.

So, when a careless or risk-taking player discards a fresh tile (a tile that has not been discarded before), he is discarding what is known as a qing tile (青 qīng). Fresh tiles are the riskiest tiles to discard because they have not been discarded before, and at the endgame, it is most likely that players would want such fresh tiles to win on. In such a danger scenario, a player who discards a fresh tile to let an opponent win has to pay for the other players, that is to say, he 'covers'  (the meaning of bao) for them. The player who takes such a risk, or who makes such a careless mistake, has to take responsibility for the dangerous move of discarding a fresh tile for an opponent to win on.

* Note: Some players refer to fresh tiles as live tiles (the corresponding Chinese character is sheng shēng). The meanings are more or less the same.

Kongs and Wins during the Endgame
The bao qing situation actually covers two separate scenarios: bao gang (包杠 bāogàng), and bao hu (包和 bāohú). Bao gang is a penalty rule for a discarder to pay for all when the discarded tile leads to a kong by an opponent. This rule only operates if the players agree to instant payouts for kongs, which most players would usually do. Bao hu is the penalty rule for letting an opponent win on a fresh tile.

For bao gang, the danger situation begins when there are seven playable tiles left. A player who discards any tile that is taken for a kong will have to pay the bao penalty. For bao hu, the danger situation only begins when there are five playable tiles left (i.e. two tiles after the bao gang situation begins). A player who discards a fresh tile for an opponent to win will have to pay the bao penalty. Both situations will operate through the last five tiles, except the very last tile, since the last tile is never discarded in Singapore Style mahjong.

A slight confusion may arise because there are two competing ways of using the bao rules in the endgame. Some players use the rules in the sequence described above: bao gang when seven tiles are left, and bao hu when five tiles are left. Some other players reverse the sequence of the two bao qing situations: bao hu when seven tiles are left, and bao gang when five tiles are left.

Personally, I prefer the first sequence (bao gang, then bao hu), because it makes more sense to penalise players for discarding tiles for kongs when more tiles are left, because bao gang is a cheaper penalty than bao hu. Players can still afford to take more risks in the initial stages of the endgame (with seven playable tiles left), and less so in the later stages of the endgame (with five or less playable tiles left).

These endgame bao rules are fairly restricted to Singapore Style mahjong. Other variants that have bao rules tend to restrict those only to situations such as Great Three Dragons (大三元), Great Four Winds (大四喜), and Pure Suit (清一色). So, it is not possible to use other variants for comparison when trying to handle these situations. It comes down to mutual agreement on the house rules before playing.

The Disagreement and a Tricky Problem
The whole chunk of text above is merely an explanation of how bao rules work in the endgame. The disagreement I had recently while playing with my regular mahjong group has to do with how fresh tiles are defined.

It was a relatively tough hand, with my friend JN and myself trying for high-scoring hands. JN has a potential five-double hand while my own is a four-double (maybe five-double) hand. So, the hand entered the endgame stage, and I had to make a discard. Out of five tiles left in my hand (the rest had been exposed to make melds), I had three possible tiles to discard, that could keep my hand intact for a win. All three tiles were high-risk tiles, but one less so than the other two. So, I picked the least high-risk (or so I thought) for the discard. To my dismay, it just so happened to be the one tile that JN won on, and that I had to pay for all since it was a bao hu scenario. Of course I argued that it was not really a bao hu, but since JN and another player said it was so (it is a democratic process when it comes to house rule agreements!), I paid up and our game continued.

Later, I discussed this whole issue with JN. Now, JN is a dear friend of mine who has been playing mahjong for as long as I have (and most probably even longer!). We started playing together some eighteen years ago, and are still playing together! Anyway, he has a lot of experience which he honed by playing with his mother, aunts, and neighbours. So, his stance on the issue was based on commonly accepted practice. On my side, I argued that my own commonly accepted practice is different. Of course, I may be wrong, because this particular issue is not commonly encountered. However, I am also partially informed by my knowledge of mahjong theory and practice across various variants.

Back to the disagreement and the issue and problem underlying it. When I was deciding which tile to discard, two of the tiles were totally fresh (no appearance on the table), while the other was less fresh (one of them appeared as part of a chow meld of my hand). To JN, all three tiles are fresh, because they do not appear in the discard pool (牌池 páichí). Tiles are considered fresh even if they have been made use in melded chows and pungs! Of course, this is illogical to me. The very definition of 'fresh' or 'live' tile (青牌, 生牌) is that such a tile had not been discarded (or exposed) before.

Let us look at one such definition (below), from 麻将玩法大全 (Májiang Wánfǎ Dàquán), a compedium and guidebook on mahjong terms, scoring patterns, and rules, published in China in 2007.

生牌:没有亮明, 较生疏的牌。
A rough translation: "Live tile: not previously exposed, unfamiliar tile."

A strict definition of 'fresh' or 'live' tile would thus be: a tile that has not been previously discarded. A less strict definition would be: a tile that was not previously exposed (not necessarily discarded). JN's definition is problematic in that the tile could have been previously discarded, but has been used in a melded chow or pung, and disappears from the discard pool, it is considered fresh during the bao hu scenario. This just goes against any general understanding of 'fresh' or 'live', and the definition also suffers from inconsistency (as used generally, and then particularly for the endgame).

Such a problematic definition and subsequent role in the bao rules can lead to logically inconsistent situations. For example, if Player A discards a 9 Bamboo for Player B to make a pung, then in the endgame, Player C discards a 9 Bamboo for Player D to win, Player C is considered liable for the bao hu penalty, despite there being three 9 Bamboo tiles already exposed (of which one was a previous discard!). Or, if Player B draws a 9 Bamboo late in the game and decides to promote his pung of 9 Bamboos into a kong with his fourth 9 Bamboo during the endgame, and Player D wins the tile by Robbing the Kong, the fourth 9 Bamboo is also considered a fresh discard!

Obviously, the definition of 'fresh'/'live' here is problematic when used for the endgame scenarios in Singapore Style mahjong. JN's approach may work as practice (everyone just has to accept it when playing), but raises general problems of what exactly is 'fresh'/'live', and also leads to somewhat bizarre situations. Consider an extreme example: the endgame is underway (say, six playable tiles left), and Player A discards a 1 Character (it has not been exposed prior to this), and Player B takes it for a pung and discards a tile. Immediately after, Player C draws a tile (leaving five playable tiles, triggering the start of the bao hu scenario), which happens to be 1 Character and discards it, which Player B takes for a win! Despite it being the second 1 Character to be discarded in a row (although interrupted by the pung), this tile is considered a fresh tile by JN's definition, and the player who discarded it is liable for the bao penalty. To me, it makes no sense to treat tiles in such situations as fresh!

Which Approach to Take?
I can understand partly why the exposed tiles in melded sets are not considered to be fresh. This has to do with how tiles are discarded in Singapore Style mahjong. Tiles are discarded haphazardly into the discard pool, not discarded orderly into rows in front of each player (as is the practice for Japanese riichi mahjong and MCR). This also means that players do not mark which tiles they take from other players to make melds. So, it is not easy to tell which tiles had been earlier discarded and are therefore no longer fresh.

JN and other players like him use the approach of only looking at tiles within the discard pool and not from the melded sets to determine if any discarded tile is fresh. This results in 'false positives', players who are penalised when they should not be.

I and other players like me use the opposite approach of looking at all exposed tiles, whether within the discard pool or in melded sets, to determine if any discarded tile is fresh. This can result in 'false negatives', players who are not penalised when they should be, depending how 'live' is defined (exposed or only discarded?).

Either way, there is no one definitive answer. Ultimately, in Singapore Style mahjong, the house rules, including the bao rules, have to be agreed on before the playing commences. I can only advocate a more sensible way of dealing with this issue (which this post attempts to address), and choosing the particular definition of 'fresh/'live' and its role in the bao rules.


Anonymous said...

I am for the definition of fresh tiles to be those found only in the discard pool. For tiles already in melded sets, they are definitely dangerous as no one had discarded them before without any consequences. Hence, towards the endgame, if you want to play such dangerous tiles, you have to pay the penalty.

EP said...

Thank you for your comment. However, your comment is not particularly clear on how some of the problematic scenarios can be resolved.

For example, if a 5 Character had been earlier discarded (therefore no longer 'fresh'), but punged by a player (therefore being removed from the discard pool), is it still considered fresh, since it is no longer in the discard pool? My view is, no, it is no longer fresh because it has been discarded before, but it is also not in the discard pool before it is used in a melded set. So, a second discard of 5 Character (also the last possible tile left) should not be penalisable during the endgame.

I do agree with your notion that the tiles not in the discard pool are dangerous but my main question is: are they fresh? It comes down to how people learn what "fresh tiles" refer to, and how the endgame penalties are applied. Why call the dangerous tiles 'fresh tiles'? Are these dangerous 'fresh tiles' different from normal 'fresh tiles' (tiles that have not been exposed before)?

Since there is no national standard, it is hard to agree on the definitions and practices. But I find it benefiical to reflect on such problems.

Anonymous said...

I guess the only thing unclear here is the definition of what constitutes a fresh card.

Of course, if we were to use a conventional and literal interpretation of "fresh", a card that had been discarded before, regardless of whether it was used in a melded set of not, is definitely not "fresh".

We both agree that tiles not in the discard pool are definitely dangerous, especially towards the endgame. Hence, if we look at the spirit of the rule, which is for the penalisation of playing dangerous tiles, then I believe my definition should be the correct one to use.

There are many variations of house rules, which you had pointed out the lack of a national standard. I am still amazed by some of the new rules that I am discovering every now and then. As long as it is agreed beforehand and applied to all players, I guess there is no advantage lost in playing any variations. A competent player will be able to adapt to any changing conditions.

EP said...

Yes, the whole point about the blog post is about the definition of what a "fresh" tile is. Since the Singapore game is dependent on mutual agreement, most of the other issues with penalty settlement etc. are not a problem.

However, I do see a problem in that many players (especially rather less serious players) not really knowing the rules. Even in my regular group, one of the players does not really know most of the finer details (rules, penalties etc.) of the game, even though we have been playing for close to ten years. If problems arise as a result of unclear rules (because of the lack of prior agreement), it is up to the rest of us to settle.

Now, back to your comment. Again, while I agree with the notion that tiles not in the discard pool are dangerous, I disagree with you that all such tiles should be penalisable. Hence, in my post, I gave a few example scenarios that may give trouble to the concept of what constitutes 'fresh'.

Let us look at what constitutes dangerous tiles. Dangerous tiles are tiles that are highly likely to be the winning tile for a player. The chances of a tile that would be dangerous depends on a few factors, which include prior appearance.

For example, if no Red Dragons (红中) had been discarded earlier, it is more likely than not that a Red Dragon tile discard is dangerous. Let us call such tiles Type I tiles, tiles which had not been discarded before.

Tiles which have been discarded but removed from the discard pool through chows and pungs can also be considered dangerous, because the non-appearance in the discard pool seems to imply that such tiles are desired. However, at the same time, such tiles have been discarded before, meaning that they had not been particularly dangerous (i.e. for someone to win with) at the point of discard. It just so happens that other players made use of such discards to help complete their melds. Let us call these tiles Type II tiles.

Now then, let us consider a tile that had been discarded right at the beginning (perhaps in the first three or four turns), but no other same tile had been discarded since. Such a tile would be dangerous too! This would be a Type III tile. So, why are such tiles considered differently from Type II tiles? Just because they are not in the discard pool? But they are evidently exposed (in the melds), which give players some idea of their distribution and location, as well as a clue to their opponents' hands which these melds are part of.

My point here is: Type I (never exposed tiles) and Type II (previously exposed tiles) are different in their levels of danger. Yes, both are dangerous (as are Type III tiles!), but previously exposed tiles (Types II and III) give clues, whereas never exposed tiles do not.

This is the line of reasoning that informs my post and practice. In my games with my family and family friends, we always take fresh tiles to be only Type I tiles. This practice did lead to the problems with my other regular group (which includes JN). However, I do acceed to the mutual agreements of each playing group. The question is: how extensive do players discuss the various house rules before playing, especially for players who are playing together for the first time?

Anonymous said...

Back in the early 1990s there was this hugely popular mahjong (Singapore style) programme on Rediffusion (if you don't know what this is, you are either very young or not Singaporean) Singapore. In the first half of the programme, the DJ will talk about one topic on Singapore mahjong. In the second half, there is a contest which listeners can call in to guess what the tiles are for a calling combinations (usually it is a 10 tiles suit with 6 calling tiles). On one particular programme, the DJ talked about what a "fresh" tile is. It is defined as one that is in the discarded pool. So those tiles that appear only in melded sets are not considered "fresh".

EP said...

Dear Anonymous,

Thank you for your comment! The information on the Reddifusion programme is very much appreciated. Yes, I am Singaporean and somewhat young, and I have heard of Rediffusion.

Anyway, your comment about the DJ's definition on 'fresh tile' is somewhat unclear. Do you mean is that a fresh tile is one that is not already in the discard pool, rather that one that is in the pool?

YS said...

Sorry, I got my words wrong. The programme said that a fresh tile is one that is NOT in the discard pool (also known as the "sea"). So if it is in a melded set, but not in the discard pool, it is considered fresh. That programme seems quite a definitive guide to Singapore mahjong. However, I do agree that your definition of "fresh" actually makes more sense. The definition of "fresh" is important not just near the end game. It's important when a player already has 5 doubles ("bao" fresh tiles), and someone throws a fresh tile and as a result the player wins. In such a case, a dispute on the definition of "fresh" could arise as well.

EP said...

YS, thank you for your comments and for your clarification here!

I learn something new everyday. In your new comment, you mentioned that fresh tiles are also important when a player has five doubles and there is a 'bao fresh tiles'. Actually, this is the first time I have heard someone use a 'bao fresh tiles' rule (before the endgame). As far as I know, when a player has five doubles, only honour tiles leading to more doubles would dangerous ( it is an extension of the 'bao dapai'/'bao honours' rule). Fresh tiles per se are not liable for bao. My mother (who is my informant for mahjong played in the 70s and 80s) also does not know of anyone who uses a 'bao fresh tiles' rule when not in the endgame.

Is this a common and standard rule that you use with your mahjong group(s)?

YS said...

Actually I have played with different people, and as far as I know, this rule exist.

Basically when a player has 4 doubles exposed, he will bao honour tiles. When someone throws an honour tile (say a dragon) and the player pung, it will become 5 doubles. Now the thrower will have to pay for all if the player were to self draw. Also, because the player has 5 doubles, he now bao fresh tiles as well as bao honour tiles at the same time.

This bao fresh tiles rule for 5 doubles can be quite harsh, especially when a player has 5 doubles very early in the game. It would probably spoils everyone's game. So sometimes we don't observe this rule.

EP said...

YS, I am not doubting that this rule exists, but it is probably very rare, and you youself said that your group sometimes does not observe this rule.

For me, because I teach mahjong, I try my best to present a set of rules common to the majority of players, so that beginners will learn the right things. Of course, many groups have house rules, and I do emphasise to my students that they have to make sure they know all the rules used by any group they play with (of course, they must also already know the basic rules and 'common' rules first). This is to avoid disputes.

So, the version of rules I use does not include the 'bao fresh tiles for five doubles' rule. This is because such a rule is not common, and to me, also not particularly essential. It is, like you said, quite a harsh rule, and can really stifle the game: the situation can deteriorate to the point that no player except the player with five doubles can win (and there is the problematic definition of 'fresh tile' here). In the normal situation where only honour tiles which give doubles are dangerous, players can still try to make those dangerous tiles work for them by incorporating them into their hands; there are round-about ways to prevent being bao'ed, since only limited tiles are dangerous. The cunning player with the four/five doubles can control the game by carefully timed discards. Using the 'bao fresh tiles for five doubles' rule, almost every tile is potentially dangerous, and the dangerous player does not need to do anything to control the game; the rule has already done it for him. Moreover, this form of bao is quite dependent on luck, and not skill, so I feel it does destroy the spirit of the game.

Contrastingly, the 'bao fresh tiles during endgame' rule is important because it encourages defensive play towards the end of a deal to get a draw, and it only affects 7 turns, so it does not destroy the spirit of the game.

Anonymous said...

Hi, not sure if this thread is live but I would like to ask if there is such a thing as 清一色包十二張.. cus i threw out a card and i had to 包九張 but my friend whom i had to 包 dan diao so we were arguing whether or not if another player throws out the winning tile, do i still have to 包..


EP said...

I have not covered the various bao penalties yet, in my ongoing series on Singapore Style rules, but I will answer your question here.

When any player has exposed nine tiles (i.e. three sets) of the same suit, it becomes obvious that he may be playing for a Pure Suit hand (清一色), and therefore all tiles of that suit are dangerous, and anyone who risks discarding such a suit tile for that player to win with Pure Suit has to bao, i.e. pay for everyone else. The condition is that the winning play must have a Pure Suit (which is why there is a bao), and the player must win from any opponent's discard. This is the 包九张 (bao with nine tiles) scenario.

In your case, it is a 包十二张 (bao with twelve tiles) scenario, which is slightly different. Giving the dangerous player a fourth set (therefore becoming 12 tiles exposed) helps the dangerous player towards his goal of winning with a high score. The opponent who does give the dangerous player that fourth set is indeed liable to bao, only if the player self-draws. If any other opponent (other than the opponent who helped the dangerous player) still takes the risk to discard a suit tile for the dangerous player to win with his Pure Suit, it is the liability of the discarding opponent, not the helping opponent.

That means in your case, you had helped creat a 包十二张 (bao with twelve tiles) scenario with your discard, but you did not discard the winning tile to that dangerous player. So, you are not liable to pay, another opponent who discards the winning tile has to. But if the dangerous player self-draws the winning tile himself, then are you liable to bao.

Anonymous said...

hello i just started playing mahjong and i jus wanna ask a situation i just encountered. It will be great if u can answer my question.. Thanks

Situation 1 :
i discarded a tile which appeared in the melded set, because all my other tiles are all "fresh"
is it true that i have to pay the penatly?

Situation 2:
Or what if i have all fresh tiles in my hand? What will u suggest me to do?

EP said...

Situation 1:
The resolution of this situation depends on the house rules governing the definition of fresh tiles.

In my system, I argue for the definition of fresh tiles as only those which have not been exposed in any way, whether as discard or used in melds. Others define fresh tiles as those which do not appear in the discard pool.

If your discard has previously been used in a meld, then under my definition, your discard does not lead to any bao penalties since it is no longer fresh. Under the other definition, if your discard is not in the discard pool at all, it is fresh and you will thus have to pay the bao penalties.

Situtation 2:
This is a more difficult question.

Generally, more expert players will take preventive action to avoid ending in such situations. For example, they may discard potentially dangerous fresh tiles earlier in the game, just so to have non-fresh tiles to discard later.

But sometimes, a player may only find himself with all the fresh tiles at the end of the hand, and the best resort if there was no way to avoid discarding a fresh tile is to: (a) discard one that is least likely to let another player win, based on discards (e.g. look at all the possible tiles adjacent in number to the fresh tiles, and calculate the probability of other players needing such tiles); and/or (b) try to discard the fresh tile to the player with the lowest-value hand (i.e. the player with a 1-double hand instead of the one with the limit hand). The main idea is to reduce losses if avoiding a loss is not possible.