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 生 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.