Tuesday, August 16, 2011

Becoming a Better Technical Player, Part 2

In the previous post (Becoming a Better Technical Player, Part 1), I had listed what I think are qualities and skills that lead to better technical play in mahjong (recapitulated below).

List of skills/qualities for technical success in Singapore Style mahjong:
1. a good knowledge and understanding of rules and scoring elements;
2. quick decision-making;
3. ability to create and manage flexible hands for optimum tile-matching;
4. a good memory (to recall opponents' tile discards and discard order);
5. knowledge and judgement of when to build high-scoring hands and when to run off with low-scoring hands;
6. ability and willingness to give up hands;
7. knowledge and judgement of which tiles are dangerous to discard.

I had also elaborated on the first three points, which I consider to be rather basic skills that should be developed right from the beginning. Of course, I do not mean only beginners should develop such skills, advanced players should too! Advanced players can re-evaluate themselves to see if they have deficiencies in their game, and start developing skills that they lack.

For this post, which continues from the previous, I will elaborate on the other four points in the list. These four skills are a little more advanced, and generally defence-oriented, and so are not skills beginners would normally be concerned about when they start learning the game. These skills would need to build on more fundamental skills that beginners are still trying to master.

4. A good memory to recall opponents' tile discards and discard order

In some variants of mahjong, such as MCR and riichi majan, players have to discard their tiles by placing them neatly in front of them in rows. This allows their opponents to see clearly which tiles the players did not want, and in the order these unwanted tiles were discarded. For such mahjong variants, there is a clear element of defence, and for riichi majan, there are strict rules about defensive play and players with good defensive play are not penalised unnecessarily. In variants of mahjong that do not mandate orderly discards, Singapore Style mahjong being one of these variants, players simply discard their tiles all over the space in the centre of the table, often mixing the tiles as play goes on, to disguise their tracks as they go about building their high-scoring hands. Players would then have to keep track of the discards of their opponents by memorising the tiles and the order they were discarded, and using their deductive skills in tandem with this memorising of the tiles hope to fathom the intentions of their opponents.

So, a good memory is required for good play in terms of defence. In fact, a good memory would be useful for keeping track of what tiles each player discards himself! Very often, I have observed beginners discard some tiles, only to draw them again just a turn or two later, and inexplicably start to ponder about the usefulness of the newly drawn tile, even though this same tile was just discarded! Without major, obvious changes in the hands of the opponents, such discarded-and-redrawn tiles do not deserve so much (re)consideration!

I do not think it is necessary to really memorise exactly all the tiles discarded by the different opponents and the order in which they were discarded. Rather, it would be enough to have a general idea of the discard patterns, especially if such discard patterns are notable. For example, a player systematically discarding all his Character tiles then discarding all his Dot tiles would appear to be trying for a Pure or Mixed Suit. Or, a player may suddenly discard three identical tiles from one of the suits, which is rather unusual, and such a player's moves would have to be scrutinised more.

In Singapore Style mahjong, it is difficult to defend against opponents with low-scoring hands, since these hands are usually multi-suited and are usually chow-based, so their discards often do not give many clues. Additionally, low-scoring hands are not very damaging, so players may ignore defence to focus on completing their hands. High-scoring hands, however, require more effort from players. If players are working on high-scoring hands without the benefit of many bonus tiles, their options tend to be limited (it is usually Pure Suit, or Mixed Suit with various pungs of honour tiles) and their melds and discards would be rather telling. Careful players can then make good use of their memory and deductive skills to choose safe discards and not discard winning tiles for these high-scoring hands.

Memorising opponents' discards for the sake of defence is generally considered a more advanced skill, and beginners tend not to develop this skill. To become better at defence, I do think that beginners should learn to at least notice what other opponents are doing, in terms of their discard patterns.

5. Knowledge and judgement of when to build high-scoring hands and when to run off with low-scoring hands
How do mahjong players win against their opponents? If all players are equally matched, and the goal is to make a complete hand as fast as possible (as is the case for a game of basic mahjong without any scoring, known as 推倒和麻将 tuīdǎohú májiàng), it is most likely that every player will win roughly the same number of games, or around 25% of the time. A variant without scoring does not give higher scores to particular ways of winning, and any win is the same, so players would just go for the fastest and most efficient way of winning. But all major variants of mahjong assign different values to different ways of winning, giving different scoring elements different number of points or doubles or fan/han/tai, so players can choose how they want to win their hands. Usually, the more difficult it is to get a scoring element, the higher the score, so it is usually a balance between speed (to complete the hand) and value. Good mahjong players would try to get high-scoring hands and yet try to complete them as fast as possible too.

I have observed some experienced players when they play (Singapore Style mahjong), and I notice they tend to just go for a speedy win, regardless of what kind of tiles they get in the beginning. This is why such players lose in the long run. These players may be experienced and who have played mahjong for a long time. They know the proceedings of the game very well, and play fast and easily. Yet, they lose. Why? They always ignore good starting hands, and just play for a quick win, which is usually low-scoring.

Let me use a scenario to explain and illustrate this. We assume that these players are playing with other equally skilled players, so the winning rate can be assumed to be roughly 25% of the time. In 16 hands, a player only aiming for speedy wins (let us call him Player A) may win 4 hands, and since these speedy wins are low-scoring, Player A may win 16 points (for four 1-double hands on discards, on a 0.5 point base). Compare this to a player who plays shrewdly and capitalises on good starting hands whenever they appear (let us call this player Player B). For the sake of the example, we postulate that Player B may win one 1-double hand and one 5-double hand, on discards. So, Player B would win 76 points, which is much higher than Player A. Player A would in fact be losing over the 16 hands: if every player wins an equal number of time on the same kind of scores, no player actually wins many points; but Player A has to lose at least 16 points to Player B for that 5-double hand, so Player A does lose in the end.

Mahjong is a game with an element of chance: tiles are dealt randomly, and sometimes, a player would get a good starting hand, which has potential to score highly. No player is guaranteed a high-scoring win though (unless it is a Heavenly Hand, 天和 tiānhú), and the player has to be deliberate decisions to work towards a high-scoring hand or complete the hand in a different way but for a lower score. If a player does not develop the judgement of when a high-scoring hand should be aimed for and when it should not, it is unlikely that such a player will become a successful player, since this player will only keep losing to other players who obtain high-scoring wins.

The converse is also necessary: a player must know when to just aim for a low-scoring but quick win. He must be able to assess his hand and determine whether it has a chance to become a higher-scoring hand which may take a while to develop, or to just complete it as soon as possible with a low score, keeping in mind the actions and intentions of his opponents and their potentially high-scoring hands.

6. Ability and willingness to give up hands
This skill is a crucial part of defence. Defence in mahjong is about not letting the opponent win easily, especially for high-scoring hands. For low-scoring hands, it is usually inconsequential if a player does let his opponents win on his discards once in a while. If a player is working on a high-scoring hand, the returns are high if he does succeed with such a hand, and it would be worth the various dangerous discards to opponents who seem to be only working for low-scoring hands. If the player is only working on a low-scoring hand, but his opponent is perceived to be working on a high-scoring hand, then defence is needed instead of obstinate offence.

The start of defence is the ability to perceive danger, and this is carried out in two basic ways: observation of bonus tiles and melds by opponents; and observation and memorising of opponents' discards and tile discard order. The combination of these kinds of information should lead to the player judging whether it would be prudent to continue playing for a win, or to play for a draw instead. The player would need to judge the situation. Sometimes, it would be possible to continue playing for a win, as the player's hand may not contain any dangerous tile. At other times, the player have freshly drawn a dangerous tile that the opponent with the high-scoring hand may want or the player's hand may already contain dangerous tiles which are difficult to get rid of. So, the possible solutions are: to brave the danger and discard the dangerous tile for the opponent, hoping that the tile (and the ones after it) are not wanted for a win; or to give up trying to make a winning hand and keep all the dangerous tiles to prevent the opponent from winning, and hope for a draw.

What the player does in the end really depend on many factors: the potential winning value of his own hand, the potential winning value of his opponent's hand, the cost he would have to pay on discarding the winning tile to the opponent (for example, bao penalties affect the amount of points/money losers have to pay to winners in Singapore Style mahjong), the stage the game is in (it could be early in the game, or close to the endgame, where a draw is in sight), the amount of points the player has (he could be in the lead with a lot of points as buffer, so risky discards are affordable) etc. It would also depends on the player's mentality and playing approach: some players are naturally more prone to risk-taking, others are greedy and ambitious, yet others are cautious and disciplined. All these things would affect the decision-making, and consequently, the kind of defence a player has. For merely good technical skill, it is about the recognition of danger and the acknowledgement that defence through giving up the hand is a good direction to take.

7. Knowledge and judgement of which tiles are dangerous to discard
Besides knowing when an opponent is building a high-scoring hand, and that some tiles are now dangerous to discard, a good player would have to develop a sense of which specific tiles are dangerous. This skill ties in with good knowledge of rules and scoring elements, good memory and good deduction, and knowing when to give up.

High-scoring hands can come about in two basic ways: there are a lot of bonus tiles giving many doubles to the opponent; or the opponent is working very hard with his starting hand to build a high-scoring hand. For the first kind of high-scoring hands (found only in more luck-based variants, like Singapore Style, and not in variants like MCR), it is less easy to know or predict the dangerous tiles. All tiles can be considered dangerous, except tiles discarded by the opponent himself. Therefore, defensive play against such hands are to follow the opponent and discard the same tiles or similar tiles judged to be safe (for example, by using the '1-4-7' rule). Tiles discarded by other players and not taken by the opponent for a win are also considered safe for the turn before the opponent drawns a tile. So, good observation and memory of the tiles discarded are crucial for defence here.

For the second kind of high-scoring hands, where the opponent must work hard to make the high-scoring hand, it is usually more obvious, with the opponent making melds and discarding tiles in identifiable patterns. For Singapore Style mahjong, the number of scoring elements that lead to high scores are is small, so it is easy to predict the direction the opponent is going, so dangerous tiles are easier to identify.

So there, I have taken seven qualities/skills that I think good mahjong players possess (perhaps not all to the same degree), and explained them as best as I could. They are not the be-all and end-all of good mahjong play; I am sure there are many more specific qualities and skills that make players better.

Related Posts
Becoming a Better Technical Player, Part 1

Updated at 01:15, 21st August 2011


daas said...

Hi. I was the one who emailed u a few months back. Your blog post is really helpful and informative. I feel that those players who ran off with low scoring hands, it is because of the ease of doing so and perhaps may increase their winning percentage from 25%? Since it is more difficult to do high scoring hands. Also, how did u get the percentages of drawing useful bonus tiles (5.6% and 8.1%)? Some places also play ping hu and qing yi se together as a limit hand or 10 tai.

EP said...

Hi daas, thanks for following my blog!

While players who run with low-scoring hands do so because it may be easier to win with such hands, but the winning percentage may not change very much. In my example, the assumption is that such players are playing against other equally skilled players, so such opponents will also run with low-scoring hands whenever possible. Therefore, all winning percentages will be forced into some kind of equilibrium around 25%.

In real life, this is unlikely to be so, because we hardly really get 4 equally skilled players, and even so, with randomness of the tiles, and illogical moves by the players, the results are usually not optimal. Some players will do better than others, even if they are all equally skilled; it may be down to pure luck, sometimes. So, my example is really just for illustrative purposes.

EP said...

As for the percentages of 5.6% and 8.1% (mentioned in the post Rules of Singapore Style Mahjong: Bonus Tiles), these are actually the percentages of actual bonus tiles within the playable set.

So, for Singapore Style mahjong, we play with 148 tiles, and we have 12 bonus tiles, so the percentage is 12/148 = 8.1%. Since 50% of all bonus tiles are useful for any player in Singapore Style, the percentage of useful bonus tiles is then actually about 4.1%.

Hong Kong Old Style is played with 144 tiles (it does not need the 4 extra animal tiles we use in Singapore Style), and has 8 bonus tiles, so the percentage of bonus tiles is 8/144 = 5.6%. As only 25% of bonus tiles are useful for any player, this means the percentage of useful bonus tiles is then down to just 1.4%.

So, basically, it is slightly harder to get a useful bonus tile in Hong Kong Old Style mahjong, so wins in HKOS is slightly less dependent on luck (i.e. if depending on bonus tiles to score doubles for winning), compared to Singapore Style mahjong.

EP said...

Last, on your comment about the 10-double pinghu–qingyise combination, I can only say this is more of a house rule. With a 5-double limit, a pinghu–qingyise hand will always be a limit hand, but if the limit is not observed or if the limit is set higher by some groups, then an agreement has to be made on how it is valued.

Personally, I think 8 doubles (4 for the pinghu and 4 for the qingyise) is actually already quite high. To be set at 10 doubles is overvaluing it, compared to some other difficult limit-type hands.

Also, in general, I think it would be best to avoid complications by not adding extra doubles to combinations. For example, it can be argued that a qingyise–pengpenghu should be valued higher than the current 6 doubles, just because it is more difficult to do than just any qingyise. Well, if any group wants to agree on that, I think that is fine. But I doubt this will have a standardising effect across groups in Singapore.