Conclusion: First, lower the number of Shanten, and if it is the same, compare the "number of valid tiles in the pile"!
The basic procedure for tile efficiency is two steps. First, leave the tile with the highest Shanten number after discard. Second, if the number of Shanten is the same, choose the one with the largest number of effective tiles and the number of remaining tiles to proceed to next. However, just because there is one more effective tile does not always mean it is the correct answer. I decide on a shot by comprehensively considering the points scored by dora and yaku, the retention of safety tiles, the ease of calling, the number of rounds, and the point situation.
If you are unsure about the basic structure of hand such as meld, pair, sequence etc.Introduction to mahjong rules for beginnersIt will be easier to understand if you check the shape.
What is shanten number and effective tiles?
Shanten numberis a number that represents how many steps away the current hand is from the hearing tile. In the general counting method, a hearing tile is treated as 0shanten, if there is one more hearing tile, it is treated as 1shanten, and a win type is treated as minus 1. In addition to the normal form of "four melds and one pair", there is another shanten calculation for Seven Pairs and Kokushi Musou, so if you evaluate a tile arrangement with an extremely large number of pairs or nine tiles based only on the normal form, you will overlook it.
Valid tilesbasically refers to a tile that lowers the Shanten number when drawn.Effective number of tilesis the total number of valid tiles remaining. You can concretely compare candidates with the same number of Shanten by counting not only the types such as ``Sanman and Rokuman are valid'' but also the number of cards such as ``Sanman is expected to have 4 cards and Rokuman is expected to have 3 cards, so a total of 7 cards.''
"Tiles that stick together" and "tiles that lower the number of Shanten" are not necessarily the same.
Even if the shape of only a part of the hand improves, the number of completed melds and pairs remains the same, and the number of Shanten for the entire hand may not decrease. Effective tiles are always determined based on the entire 13 tiles after discard. In order to make the counting method clearer, the hand examples in this article clearly state the premise as a listening tile shape with a fixed completed meld, or a comparison of single blocks.
In the research field, the Shanten number is also a central concept that deals with the distance between hand and win forms. While there is research to formalize the calculation method, actual AI combines not only the number of valid tiles but also the subsequent position evaluation. In other words, the number of Shanten and effective tiles are important yardsticks, but they are not the purpose of match itself.
Effective tiles are counted as "4 tiles - hand - visible tiles"
In riichi mahjong, if you count red five as the same type as regular five, each tile has four tiles. To count the number of tiles remaining, subtract the number of tiles in your hand and the number of tiles that you can see, such as the river, subroute, and dora display tiles, from the four tiles. If you have one Niman in your hand and two Niman in the river, there is a maximum of one Niman in your hand.
Remaining number of valid tiles = 4 - Similar tiles in your hand - Revealed tiles of the same type
"Not visible" does not mean "it is always on the mountain." It may be in someone else's hand. Therefore, the effective number of tiles is the maximum number of candidates from your point of view, and is not a number that determines the probability of drawing in the next round. Nevertheless, it provides a common basis for comparing discard candidates under the same information conditions.
The order of counting is to first count the valid tiles.Enumerate types without duplicationThen, add the rest of each type. In compound forms, the same tile may affect multiple blocks. For example, even if Sanman improves two tarts at the same time, adding Sanman's 4 cards twice will not count as 8 cards.
See suji on the way to "four melds and one pair" in 5 blocks
A normal win consists of four melds, each consisting of a sequence, triplet, and quad, and a pair of two identical tiles. Therefore, the hand is divided into a completed meld, a meld candidate tart, and a pair candidate pair, and the final5 blocksIt will be easier to organize if you look at it as
For example, for "123 tubes / 456 tubes / 789 lines / East East / 45 million", there are 3 completed melds, 1 pair candidate, and 1 double-sided tart, making a total of 5 blocks. If you add 30,000 or 60,000 to 450,000, the fourth meld will be completed, and you can win by pairing East and East. In this way, the shape in which the yaku percentage for each block is determined makes it easy to find unnecessary tiles.
On the other hand, in a hand with 6 blocks, you must organize one of the blocks. Rather than simply dropping the lowest number of tarts, we compare whether they are double-sided or inlaid, whether they contain dora, whether they are necessary for yaku, and whether they are worth having as a safety tile. In a hand with only 4 blocks, you need to leave room for new tarts to form from isolated tiles.
A pair can be a pair candidate or a triplet candidate, but please note that counting all pairs as independent completed blocks can easily result in too many blocks. Also, the structure of moves aimed at Shichitaiko and Kokushi Musou is different, so you can't forcefully apply the 5-block method. The 5-block is a tool to make normal forms easier to read, and is not an absolute rule to exclude special forms.
Ikko listening can even be seen in the form of ``complete ikko listening, headless, and stick-on''
Even with the same 1 shanten, the type of valid tiles changes depending on the combination of meld, tarts, and pair. The terminology differs depending on the teaching material, but in the normal form, it is easier to count effective tiles by dividing them into ``whether there is a pair,'' ``how many tarts there are,'' and ``waiting for it to stick to an isolated tile.''
Complete listening: 2 meld + both sides + both sides + pair
45 tubes are melded with 3 tubes and 6 tubes, and 56 ropes are melded with 4 ropes and 7 ropes. Furthermore, if you draw seven tubes, you can create a pair of seven tubes and a five-line triplet, and if you pull five lines, you can create a five-line triplet and a seven-line pair, so there are also effective tiles in the champon direction. The total is 20 pieces, including 16 pieces of 4 types on both sides, and the remaining 2 pieces of each of the seven tubes and five lines, which I already have. If there is a tile that looks like a river or sidero, subtract it from that type.
Headless listening: 3 meld + 2 tarts, no pair
If you draw Ichiman or Shiman, 230,000 will be melded, and you can cut one side of the 67 ropes and wait for a single rider. If you draw 20,000 or 30,000, you will make a pair, and if you cut the other one, you will have 67 lines waiting on both sides. The 67 rope side is also the same, so not only the tiles that complete the tarts, but also the tiles that create pairs by stacking the tiles in the tarts are valid. This is why the effective tiles can be wider than a complete ikkobi with a pair.
Cut together sticks, compound tarts, and quintuple shapes without fixing them.
If there are 3 melds and a pair, and the remaining two are isolated tiles, draw an adjacent tile or similar tile to one of them to make tarts.Listen closelyIt is. The isolated tiles in the center change frequently, and their value changes depending on the number of tiles already visible and their relationship with dora and yaku.
composite tartsis a tart with a follow tile that can be used as a companion or as another tart. The 556 cables in the complete Ikkocho above serve as both the ``pair of the 55 cables'' and ``both sides of the 56 cables.''double-sided pairIt is. For this reason, there are holders that make sequences with four or seven strands, and holders that make triplets by stacking five strands. There are other types such as mebari taiko, hebari taiko, and ryogan, which list valid tiles without counting the same tiles twice.
34567 million like5 seriesis a compound form that can be distinguished not only from tarts but also from meld. It can also be seen as "345 million + 67 million" or "34 million + 567 million." If you fix the completed meld to 345 million, you will overlook the changes on the 20,000 and 50,000 sides, and if you fix it to 567 million, you will overlook the changes on the 50,000 and 80,000 sides. Return each discard candidate to 13 and check which tiles reduce the number of shanten.
Compare the number of remaining sheets for both sides, inlays, hembari, and pairs.
The following four examples all have 13 pieces of playing tiles. The common conditions are 3 completed melds, a pair, and the last unfinished block. It is assumed that no tiles other than those in your hand are visible unless otherwise specified. This allows you to calculate how differences in shape affect the effective number of tiles.
Double-sided 450,000: 4 30,000 + 4 6000 = 8
Continuous middle tile tarts, such as 45, are a sequence of two types on the outside. The reason why both sides are said to be strong is because there are two types of waiting tiles, and if the number of visible tiles is the same, there are more effective tiles than Mebari or Henbari.
Ganbari 46-man: Go-man sees 1 piece, remaining 3 pieces
46 inlays can be completed with just 50,000. In this example, one Goman card is visible, so there are only 3 cards left at most. Red Goman is also counted as one of Goman. Because it's red, we're not adding four pieces as a different type.
Benbari 120,000: 30,000 4 pieces
12 can only be a sequence in 30,000. 23 has both 10,000 and 40,000, but 12 has no 0,000, so it is one way. 89 is also Benbari who is waiting for Seven. Even though it is the same type of waiting as Ganbari, the changes when surrounding tiles are drawn and the relationship with Yaku are different.
Two pairs of pairs: East 2 pieces + Goman 2 pieces = 4 pieces
If there are two pairs, one can be a triplet and the other can be a pair. Even though there are two types of tiles in this double selection, two of each type have already been used, so there are a total of four tiles. You can see why you shouldn't just look at the same number of types as ``up to 8 pieces of two types'' on both sides. Furthermore, if the east is the own wind or the field wind, it can be a yaku at the time of win, so the value other than the number of cards will also change.
The closer the isolated tile is to the center, the more types of changes there are.
In the early stages, when 5 blocks have not yet been assembled, compare the possibilities of forming tarts or pairs from isolated tiles. For a single 50,000, you can make 35 inlays with 30,000, 45 on both sides with 40,000, pairs with 50,000, 56 on both sides with 60,000, and 57 with 70,000. If you have 1 Goman in your hand and no public tiles, you have 4 each of 3, 4, 6, and 70, and 3 Goman remaining, for a total of 19 changing tiles.
For a single 10,000 pieces, 10,000 pieces can be paired, 20,000 pieces can make 12 hembari, and 30,000 pieces can make 13 mebari. If you have 1 10,000 tiles in your hand and no public tiles, you have 3 10,000, 4 20,000, and 4 30,000 tiles for a total of 11 cards. The center tile has more adjacent numbers, so the range of variation is generally wider.
The 19 and 11 pieces counted here are two sets of isolated tiles.change tilesIt is. This is not to be confused with strict effective tiles, as the overall Shanten count of the hand does not necessarily decrease. If you already have enough 5 blocks, the tiles that make new tarts will not advance your move, and you may end up with 6 blocks instead.
Discard checklist for use in practice
It is difficult to completely list all candidates every time you cut one card out of 14. You can reduce oversights by following the following order at first.
- Check the win shape candidates:We will look at whether the normal form is the main focus, or whether Shichitaiko and Kokushi Musou are also realistic. If the possibility of a special form is low, proceed to block 5.
- Divide the completed meld into blocks without making it too rigid:There are multiple ways to divide the continuous form. For example, 34567 can also be seen as 345+67 or 34+567.
- Compare the shanten numbers after discard:Candidates that will increase the number of Shanten will be postponed unless there is a clear reason such as Yaku or defense.
- Enumerate valid tiles if they have the same number of shanten:Write down the tile type first to avoid counting the same tile twice.
- Draw the number of cards visible in your hand and in play:Draw each type from the 4 cards and add them up. Red five is included in normal five.
- See the quality after effective tiles:Even if you play the winning tiles, we will compare whether it will be a single horse or a mebari, whether both sides will remain, and whether there will be a yaku or a dot.
- Make final adjustments based on situational conditions:Check the safety tiles, rounds, other players' tricks, score status, parent and child, and choose.
How to write to avoid counting mistakes
Leave the type and number of remaining cards in one line, such as "Sanman 4, Rokuman 3, East 2, total 9". If you only use the three types, Sanman, Rokuman, and East, you will lose track of how many cards are used in the hand and river. In the compound form, it is easier to compare by arranging the number of shanten, tile type, and remaining number of tiles horizontally for each candidate.
Do not maximize only the number of effective tiles
Tile efficiency is a tool to consider the speed at which you approach winning, but the purpose of mahjong is not to "make the widest hand every time." In order to compete for results, including the value of the station and the risk of losing points, even if the candidate with the highest effective tiles is the most likely candidate with the same number of Shanten, the conclusion will change depending on the following conditions.
RBI and yaku
In situations where cutting dora increases the number of effective tiles by 2, but leaving it on allows you to see Mankan-level moves, you will be trading speed for hitting points. The yaku that is likely to be established will change depending on the tiles you leave, such as tanyao, peace, three-color same order, one-shot through, mixed one-color, etc. If you are unsure about the conditions of yakuriichi mahjong's yaku listYou can check closed hand only and calling possible separately.
Safety and aspects
At the end of the game or after the opponent's riichi, the value of avoiding a deal-in becomes greater, not just the proximity to victory. While early processing of honor tiles and marginal tiles can improve efficiency in the early stages, you may run out of safe tiles later on. To determine how far to push, look at your number of chants, wait times, RBIs, rounds, parent and child, and point difference. The defensive material ismahjong defense and push-foldIt is organized by.
Confirmation of calling ease and hand yaku
Even if yakuhai's pair has only two cards left, you can pon the other family's discarded tiles to meld and confirm yaku. Even if the effective tiles of closed hand double-sided tarts are wide, the yaku may disappear if you chime in. We will consider separately the number of candidates drawn from the pile, the candidates who can be called from other houses, and the yaku after they have been called.
Shape after effective tiles
After drawing a valid tile, it is important to know whether it will be a good waiting tile or if you need to change hands. Even if the current effective tiles are the same, 8 tiles, if one is all double-sided tiles and the other is single-sided or has many tiles, the quality will be different. Check not only the current number of pieces, but also the shape that will remain in the next move.
Therefore, using tile efficiency as a "rule for selecting the maximum number of tiles" is insufficient in actual combat. An easy-to-use procedure is to narrow down the candidates based on the number of Shanten and effective tiles, and then reselect based on value, safety, and situation. Make decisions based on public information and the tiles you can see, without relying on baseless fixed thresholds.
How to practice tile efficiency
The first exercise is to count the number of waiting tiles. The basic rule is two types for double-sided cards, one type for Ibari and Henbari, and two or less cards each for two types for Sojoku, and subtracted from the hand and river each time. Once you can quickly count the waiting tiles, spread them out to 1shanten discard candidates.
Next, save only one discard that got lost during the match, and rearrange the 14 cards after the match. For each candidate, write down the number of shanten after discard, the type of effective tiles, the number of remaining tiles, the wait after effective tiles, and the yaku or dora lost. Rather than determining a single correct answer, it is important to be able to explain which conditions changed the conclusion.
In tile score analysis and mahjongAI research, we handle a large number of situations and combine different evaluation axes such as hand distance, effective tiles, wins and points conceded. The same goes for people when learning; it is effective to first make the elements that can be calculated accurate, and then add information about the opponent and the score situation. After recording the number of effective tiles, you can look back not only on whether you actually won, but also on the quality of your wait and the reason why you had dangerous tiles.
common counting mistakes
- Do not draw your own tiles:The maximum number of tiles that can be turned into a triplet from a pair is two, since two have already been used.
- Not seeing rivers or dew:Even if there are two types of valid tiles, if a total of four tiles are visible, the maximum number is not eight.
- Add red five as another 5th piece:Red Five is one of the four pieces of Five.
- Add the same tile twice in compound form:Sanman, which works on two blocks, has a maximum of 4 tiles.
- All changing tiles are called valid tiles:Tiles whose overall shanten count does not decrease even if their shape becomes flexible are classified as effective tiles in a narrower sense.
- Fix 5 blocks too much:In the continuous form, the division changes, and the pair can be either a pair or a triplet candidate.
- Determine the discard by the number of cards only:If you eliminate yaku, RBI, safety, and aspect, you may end up with a choice that does not suit your purpose.
Summary: Think in the order of distance, number, quality, and situation.
The starting point for tile efficiency is to lower the number of Shanten after discard. If the number of Shanten is the same, list the types of effective tiles, subtract the number of tiles visible as hand from each of the four tiles, and compare the effective tiles. If you organize the normal form as 5 blocks of four melds and one pair, you can find extra blocks or missing blocks.
A double-sided 45 million has a maximum of 8 of the 30,000 and 60,000 pieces, a 460,000-sided piece has a maximum of 4 of the 50,000, a 120,000 hembar has a maximum of 4 of the 30,000, and a double-sided pair has a maximum of 4 because each pair uses 2. However, if there is a tile that is visible, you must draw that tile. Finally, select the shape after the effective tiles, RBI, Yaku, safety tile, calling, round, and score situation.
Reference material
- What is Ishanten? (Kinma web)(Confirmation of terminology for Ikko-cho and complete Ikko-cho with two sets of double-sided champon receivers)
- Performance evaluation of mahjong AI that increases tile efficiency by counting valid tiles (CiNii Research)(Research information on hand evaluation using valid tiles)
- A Fast Algorithm for Computing the Deficiency Number of a Mahjong Hand(Research on calculating the distance between hand and win shapes)
- Waiting tile estimation considering riichi player's hand in mahjong (J-STAGE)(Research that deals with waiting based on public information.Referenced as a different aspect of evaluation from tile efficiency)
- Analysis of mahjong by analyzing tiles (Journal of the Society for Artificial Intelligence)(Research on mahjong analysis using tile data)
This article refers to the ideas of each study and reconstructs it as a procedure for beginners to count real tiles. There is no fixed tactical push-fold threshold or probability that an invisible tile will be in the pile.