Even after immigrating to California at six years old, I have played Taiwanese mahjong on and off for a good majority of my life – mostly with family and friends. No friends and relatives around me were very serious about mahjong, so it wasn’t until a few months ago I was humbled by the skill of strangers. That night I played 4.5 complete, 4-wind games, and lost about $100 playing $3 base/$1 tai bets. Since that night I have researched – from both them and other research – about how opponents think and how they play.
This is the beginning guide to a trilogy of Taiwanese Mahjong, going into statistics and numbers before delving into player behavior and playing scenarios. I don’t think other places in the internet has quite as detailed analyses (in English), and I will continue to add to it for, as I have always mentioned in other of my posts here, personal learning and memorandum.
Table of Contents
Differences With Other Forms of Mahjong
- 16-tile hand instead of 13. Players need an additional set and goes out with 17 tiles.
- A player can win with a “chicken scratch” hand (0 tai).
- A “moving” dead wall in which 16 tiles are maintained at all times (Replacement tiles are taken from this dead wall, in which an equal amount should be added from the end of the live wall). Kongs add an additional 2 tiles to this dead wall.
- The dealer, starting out, gains or loses 1 tai if they win or lose, respectively. On wins or cases where nobody wins, the dealer retains their dealer status and wins/loses 2 additional tai per streak count. For instance, a dealer who won twice but loses afterwards will need to pay 1 + (2*2) = 5 tai to the winner.
- When a player goes out on a self-draw, every loser pays the winner equal to the amount of tai of the winner’s hand. If the dealer is not east, that dealer will need to pay additional tai equal to dealership (1 tai) plus any consecutive streaks they have.
- In cases where a discard results in multiple players going out, the closest person (counter-clockwise from the person who discarded the winning tile) is awarded with the win.
- Concealed Kongs – a player may choose to conceal their kong if they have all four tiles in their hand.
- One cannot meld a Kong from their left player – Pung should be declared and the last tile added to form a Kong on the player’s next draw.
- One may choose not to pick the last tile. The match will still end with nobody winning, and dealer retains their seat and +1 consecutive “streak”.
Probabilities and Statistics
Average number of cycles per round
There are 144 tiles total (136 + 8 flowers) in Taiwanese Mahjong. 16 tiles are reserved for the dead wall at all times. Each player also begins the game with 16 tiles (the dealer begins by drawing the first tile so we consider the dealer having 17 tiles starting out). On average, 4-5 flower tiles are revealed before the dealer makes their first discard.
With all of the above added together (16 dead wall + 65 combined tiles in 4 hands + 4-5 flower tiles revealed), only 58-60 tiles remain to be picked. 4 tiles are picked each cycle which means that there are effectively 14-15 cycles in a single round. This is important when going into detail about strategies in early/mid/end game.
Average rounds per game (4 winds)
A single game (一將/一雀) normally consists of 4 winds, which means that there are a total of 16 dealers (4 per person). Assuming that every player is equivalent in skill, the odds of going out is assumed to be 25%, which means that the amount of times +1 consecutive dealership is achieved is 16 * 0.25 = 4 times. Within those four times there’s another 25% chance that the dealer wins yet again, which brings our average total rounds per game to 21, but is widely known to be 20-22. This means that, statistically, a single player, on average, wins about 5-6 hands per game, with 1-2 hands within that being a self-draw win (everyone pays the winner). Unfortunately, this also means that a single player will be on the losing side of a self-draw 4-6 times.
Why is this important?? Because if a player wins 4 games (with around 1 of which being self-draw to earn more points) to cover up for the times of losing to a self-draw, that player will not lose the game and will finish positive. However, this is valid only if you do not lose by discard. The point is, if ones goal is to finish positive, one can attack to win 4 times (provided their starting hand is quite favorable) while playing more defensively for the remainder of the 16-18 rounds.
There is a method for finding out which starting hands are favorable and which are not, which will be left for a later guide.
Picking tiles
With 3 suits, 4 winds, and 3 honor types in mahjong, the chance of picking a desired tile stands at 1/34 (2.9%). Additionally, although there is not enough evidence to back this claim, it is believed that you will, on average, pick a tile you need to complete a set every two picks. Because there are 4 of the same tile, the probability decreases by -0.75% for each desired tile seen (to 0% if all 4 tiles are accounted for). There’s no need to remember this particular probability, but it does somewhat play into the next point:
Starting hand composition
Taiwanese Mahjong is played using 144 tiles with a 16-tile hand. On average, when a round begins one should expect to see 4.2 tiles of a single suit and 3.4 tiles of wind/honors. This means that an ordinary hand will have roughly 4-5 man tiles, 4-5 bam tiles, 4-5 circle tiles, and 3-4 wind/honor tiles. Likewise, there is a 9/34 (26.47%) chance to pick one of bamboo, circle, or man tiles, and 7/34 (20.58%) chance to pick a word tile.
This is an interesting and important concept to understand when going into detail about play strategy; for instance, a player with many non-pair winds/honor tiles will likely start the first few cycles of the round discarding them, whereas those who start discarding suit tiles very early may have a higher amount of “gates” and be closer to going out.
[Early Game] Discarding Word tiles vs 1, 9 tiles
This part may be controversial and not everybody may agree with the reasoning, but in the discarding phase it is better to discard word tiles over an “orphan” 
or 
. This is because to create a set using , for instance, any of the potential three remaining , four 
, and four 
may be drawn from the live wall. Compared to an orphaned word tile such as 
(only three remaining), the probability of making a meld-able set (any of the following , , or ) is three times higher than picking a second word tile .
This is a controversial concept because some players may take the chance to pick into a paired word tile provided one hadn’t already been discarded, and that the chance another player has a pair of the same word tile you have is minute, and thus if such opponents aim to go out then they will have no choice but to discard it somewhere down the line. That said, however, the following negative possibilities exist which diminishes the chance of one picking and melding word tiles in mid/late game:
- Opponent(s) want to discard the tile but found out they shouldn’t due to fear of discarding the winning tile.
- One or more of the tile resides within the dead wall.
- Another opponent also has a pair of the same word tile.
The above does not include the simple fact that any player can go out with a 0-tai “chicken scratch” hand, so the aim for nearly all ordinary hands is to reach tenpai status as early as possible while waiting for a suitable set of tiles.
Thus, the most optimal discard order for the early game is as follows:
- Wind tiles that are not the prevalent wind nor your position’s wind. This is to account for the chance you may pick a wind or honor tile while still in the early game which has potential to earn you an additional tai.
- Remainder of orphan wind/honor tiles.
- Orphan ‘s and ‘s.
- Other separated tiles depending on situation.
Characteristics of Suit (Number) Tiles
The Principle of Symmetry (對稱性)
The first thing to understand about number tiles is that the set of 1-9 tiles is symmetric. This means that 1 to 5 is the same as 5 – 9 but “flipped” – every characteristic of 1 can be applied to 9, every characteristic of 2 can be applied to 8, and so on. For instance, discussions revolving probabilities of can be exactly applied to .
This principle is very convenient when discussing probabilities and tile logic because one need only look at half (i.e. tile numbers 1 through 5) of the number tiles. From henceforth, barring some side notes, I will use tile numbers 1 through 5 for discussion around number tile logic and probabilities.
The Principle of Suppression (向下壓/向上壓)
The principle of suppression states that, especially in the beginning cycles, a player who discards a numbered tile will likely not want any numbers smaller than it (bigger if talking about 5 through 9). For example, a player who discards a is likely to not want a , and likewise discarding a shows they likely don’t want or . This is true because players want to discard all tiles not suitable for melds in the early game – starting with those numbered tiles furthest away. Of courses, there are cases such as in which a player may discard but normally one chooses to keep it early game in case the left player discards a which can be used complete a meld. One can learn a lot about their opponents’ hands when they discard tiles using this principle.
The “1-4-7” Rule (一路性)
1-4-7:
2-5-8:
3-6-9:
Because mahjong incorporates the Chow mechanic, there is an observation which states that discarding a or is somewhat safe to an opponent who discards a because by discarding the opponent shows they do not have the tiles necessary to meld or to complete a Chow. The same rule can be applied to 2-5-8 and 3-6-9. However, this does not mean that when an opponent discards a that they won’t want a . It is possible the opponent can chow or win with this tile, but the probability that they want this tile is roughly halved. Obviously, throwing a does not have any significant impact on the chances the opponent wants .
The 1-4-7 rule has another interesting characteristic in that it can be leveraged to perform a 3-gated wait. Assuming one already has 3 sets and a pair of eyes (not shown):
One can wait for , , or to win, increasing the amount of wait-able tiles to 11 instead of 8 for a 2-sided wait. Sometimes for higher than 2-gated waits I may choose to not win on a first discard but instead go for a self-draw victory due to the increased chance of success.
D-A-D (Develop – Attack – Defend)
After noting the above sections, we can know go into the philosophy many professionals refer to as the D-A-D strategy. While many online sources go over each section and how it is beneficial to follow the strategy, I haven’t found any which goes into the fine details and reasoning behind why it is so. I will do my best to explain the logics behind this strategy here.
Let’s dive straight into the first “D”, which is:
Cycle 1-6 : Develop (序盤)
The first six cycles is referred to as “D” which stands for Develop, otherwise known in other sources as “Opening” or “Early Game”. Earlier in the “Starting hand composition” section we know that on average a player’s starting hand consists of 4-5 tiles of each suit and 3-4 word tiles. Accounting for the probability of picking an additional 1-2 word (remember there is a roughly 20% chance – 1 in 5 picks – in which a word tile is drawn) tiles plus discarding un-needed orphan tiles, cleaning out your hand to a point where one can begin to attack averages at around 6 rounds. In other words, if one still has orphaned cards after the Develop phase then they may consider giving up for this round, skip the attack phase and go straight into defense.
Cycle 6-12 : Attack (中盤)
The Attack phase (mid-game) can be further split into two:
Cycle 6-9
Players with a good starting hand or has had favorable melds will reach tenpai within the early mid-game. Other opponents who see that they have many melds should watch this player’s discards carefully as it can give clues on what they are waiting on. If one is not tenpai and does not have a safe tile to discard then they can consider folding and playing defense for the rest of the round.
Cycle 9-12
Most players with an ordinary starting hand and luck will likely reach tenpai in this stage. At this point one should weigh the risks of going for the win vs how strong opponents’ hands are. Waiting on a single tile or a blocked 2-gated wait is not ideal at this stage.
Cycle 13-15 : Defend (末盤)
If one is not tenpai at this end-game then give up, because no matter what it is not appetizing to discard a dangerous tile when one is not close to winning. Give that chance to others who are perhaps not as experienced at you are, or believe that the opponent(s) will not win on self-draw due to being stuck or merely waiting on bad tiles.
Good vs Bad Starting Hand
Like with other types of mahjong, the most convenient method is to check how many cards you are away from tenpai. More experienced players are able to adjust the formula to further calculate how easy/hard it is to acquire the remaining tiles necessary – some pointers and advice is left for a future guide on advanced gameplay. For now we will just go over the simple formula, which is how many tiles you are away from tenpai.
- 2-3 to tenpai (Good)
Assuming from above that on average it takes two draws to bring one’s hand a tile closer to tenpai. Thus, 2-3 away from tenpai means one will reach tenpai before mid-game, in which case you should forcibly attack and play to win. - 3-4 to tenpai (Normal)
With this hand you should expect to have either 1 set and 1 pair, or 0 sets and 1 pair but with easy to meld combinations. Expect for everyone to reach tenpai 8-10 cycles into the round. Obviously, because this type of hand is the most often to occur, one should consider the situation and decide whether to continue attacking or to switch to defense during mid-game. - 5+ to tenpai (Bad)
One should seriously consider defending for this round for any hand above five tiles needed to tenpai. Unless the player has amazing luck drawing tiles with their left player feeding them, one would already be at the last three cycles before reaching tenpai, which also means one would need to take 2-3 rounds discarding risky tiles mid-game to get to that point. Withdrawing like this for even a few rounds out of 20-22 rounds is not going to hurt the overall game. There is a saying amongst professional players which goes along the lines of: “Anyone who discards the winning tile (lose) during the end-game (末盤) without tenpai does not know how to play mahjong“.