three-player mahjong is a game with larger rules differences between tables than four-player mahjong. Not only starting score and return score, but also the handling of the north and the targets of tsumo loss and chips are different, so it is not possible to decide on one formula, ``sanma must be this formula.''
However, the order of calculation is the same. If you convert final score to game points and then reflect conversion rate, chips, and table fee, you can organize even the seemingly complicated settlement. In this article, we will explain how to record and verify calculations, along with specific examples using rules for explanation.
1. [Conclusion] Calculate results of sanma in this order
Check the table rules first and calculate in the following order:
- Check rules such as starting score, return score, uma, oka
- Check 3 people final score
- Output raw points from the difference with return score
- Add uma according to rank
- If adopted, add oka
- Reflect other ranking settlements and issue final game points.
- Convert game points to conversion rate
- Adjust chips and special prizes
- Finally, subtract table fee to get the actual balance.
raw points= (final score−return score)÷1,000
final game point=raw points+uma+oka+Other payments
final balance= Final game points x conversion unit + chips balance + other balances - table fee
Points, game points, and actual balance are different numbers. For example, even if final score has 50,000 points, it will not be a "50 point win". If return score is 40,000 points, raw points is +10, and adding uma and oka is the game point. Furthermore, the actual balance will be determined only after reflecting conversion rate, chips, and table fee.
2. What is the difference between the results calculations of sanma and four-player mahjong?
sanma rules vary greatly depending on the table and service. The tiles used, starting score, the reference point for settlement, uma, the handling of the north, tsumo loss, chips, and the closing and ending conditions must be confirmed before the game.
Even if you apply the numbers to another table's example calculations, it does not guarantee that you will get the correct balance. If you leave a rule table in advance, you can tgame back which conditions were used to calculate the results.
| Item | four-player mahjong | sanma |
|---|---|---|
| Number of people/rank | 4 people, 1st to 4th place | 3 people, 1st to 3rd place |
| average placement criteria | 2.50 | 2.00 |
| starting score example | 25,000 points etc. | 35,000 points etc. |
| uma | 4 places | 3 places |
| North extraction | usually not adopted | There is a table to adopt |
| tsumo loss | usually does not occur | Check for presence |
| Chi | Yes | None is common |
Although the basic calculation order is the same as four-player mahjong, the numbers to be input and the movement of dots during the game are different. In particular, if you record uma of sanma only by calling four-player mahjong like "10-20", you may not be able to identify the 2nd and 3rd place values later.
3. In sanma, check the "table rules" before calculating results.
To convert points into game points, compare each participant's final score to the checkout reference points. This reference pointreturn score (Kaeshiten)It is.
The difference between final score and return score is converted into game points in units of 1,000 points.raw points (Soten)It is. If starting score and return score are different, adding up everyone's raw points will not add up to 0. oka fills in the gap, and the order in which it is distributed is determined by the rules of the table. The final game point is the sum of raw points, uma, and oka if adopted.
| classification | Things to decide before the game | Situation to use |
|---|---|---|
| Number of people and format | Will it be a 3-man or 4-man game, a match against Dongfeng or a match against Hanzhuang? | separate records |
| tiles and north | Which tiles to use, red tiles, whether to play Qi, whether to treat the north as yakuhai, dora without, or as a normal tile. | Match the game conditions |
| point stick | starting score and return score | Calculate raw points and oka |
| rank | Presence or absence of uma and oka from 1st to 3rd place and where to add them | Calculate game points |
| tsumo | Presence of tsumo loss, how to pay for dealer and non-dealer | Determine score sticks movement for each station |
| chips | Target yaku, tiles, unit of 1 piece, and delivery method | add to actual income and expenses |
| Termination condition | Tobi, if you have 0 points, extend, riichi deposits and stacking stick handling | Confirm final score |
| Ties and fractions | Ranking in the event of a tie, rounding methods such as rounding, and passing of fractions | Confirm rank and total |
| Conversion | Unit of 1 point, total amount and payment method of table fee | After determining game points, convert to actual balance. |
In the rule table, not only the game name but also the conditions used for calculation are recorded. starting score and return score are required to calculate points, uma and oka are required to calculate game points, and conversion units, chips and table fee are required to calculate actual balance. Add the setting name to the calculation results and save the numerical values and assumptions together.
The setting name should include a short description of the main criteria. For example, if you write something like "3 players, 35,000 points, 40,000 points returned, tsumo loss, North extraction", it will be difficult to confuse it with another setting. On the day you change the conditions, the previous settings will not be overwritten and will be saved as new settings.
Settings are different for Mahjongso, online mahjong, tournaments, and friend sets. It is important to consider the calculation example as just one example and not to assume that there are "sanma common rules".
4. What is uma of sanma?
uma is a game point that is added or subtracted depending on the ranking. In this calculation example, we will distribute +20 to 1st place, +10 to 2nd place, and -30 to 3rd place, making the total for 3 people 0.
+20＋10−30＝0
The three-person uma records three values as a set. Since you may not be able to tell the value of 3rd place just by calling it "uma20, 10", write the entire ranking as "1st + 20, 2nd + 10, 3rd - 30".
Some tables have different distributions, such as +20, 0, and -20. The +20, +10, and -30 used below are settings for calculation examples, and are not uma, which is common to sanma.
5. What is oka of sanma?
oka is the point resulting from the difference between starting score and return score. If you have 35,000 points and return 40,000 points, the starting score sticks is 35,000 points x 3 people = 105,000 points, but the total for return score is 40,000 points x 3 people = 120,000 points. If you convert the difference of 15,000 points to 1,000 points = 1 point, oka will be 15 points.
(40,000−35,000)×3÷1,000=15 points
If the rule is to add all 15 points to the top, we would put oka+15 in 1st place. Even if you have 30,000 points and return 35,000 points, the difference is the same 15 points. On the other hand, if starting score and return score are the same, oka will not occur based on this idea.
However, the presence or absence of oka and how it is distributed also depends on the table. There are also payment methods other than adding to the top and rules that do not provide oka. Don't decide on the processing based only on starting score and return score, but write something like "Add oka15 to the top" in the rule table.
6. Actually calculate the balance of sanma
Below, we will use an example in which the rules are recorded as "3 players, 35,000 points, 40,000 points returned, uma is +20, +10, -30, oka is +15 for 1st place". riichi deposits, there are no fractions or external awards, and all movements of the score sticks have been reflected in final score. final score has 50,000 points for 1st place, 35,000 points for 2nd place, and 20,000 points for 3rd place, and the total is 105,000 points, the same as at the start.
| rank | final score | raw points | uma | oka | final game point |
|---|---|---|---|---|---|
| 1st place | 50,000 points | +10 | +20 | +15 | +45 |
| 2nd place | 35,000 points | −5 | +10 | 0 | +5 |
| 3rd place | 20,000 points | −20 | −30 | 0 | −50 |
- The 1st place raw points is
(50,000−40,000)÷1,000＝+10It is. - Adding uma+20 to 1st place raw points gives +30.
- According to the recruitment rules, if you add oka+15, the 1st place is +45.
- If you calculate in the same order, 2nd place is +5 and 3rd place is -50.
oka generated under this condition is(40,000−35,000)×3÷1,000=15 pointsIt is. The raw points of the three people is +10−5−20=−15, so if you distribute oka+15 to the first place according to the rules in the table, you can make up for the total difference in raw points. The total of uma is also 0, so in this settlement example where the total of 3 players is 0, the final game point will be +45 + 5 - 50 = 0.
riichi deposits or if fractions remain
In this example, no riichi deposits remains on the table and there are no fractions on the score sticks. If riichi deposits remains at the end, add everyone's final score and the riichi deposits on the table and compare it with the total number of points at the start. After that, follow the table rules to record who's points should be added to their points or kept in a separate slot. Fractions due to rounding are also handled in a separate field according to the rule table.
7. Follow the number one results from beginning to end.
In the previous example, let's follow the progress until the top score of 50,000 points reaches the actual balance. First, if you divide the difference between return score and 40,000 points by 1,000, raw points is +10. If you add uma+20 to +30, and then add oka+15 to be distributed to the top, the final game point will be +45.
50,000 points → raw points+10 → +30 points including uma → +45 points including oka
If 1 point = 100P, +45 points is +4,500P. If you add +200P for 2 chips and subtract table fee400P, the final balance will be +4,300P.
+4,500P＋200P−400P＝+4,300P
The trick is not to skip any numbers in the middle, and to keep the ``point stick'', ``game points'', and ``actual balance'' separately. This makes it easier to find the cause when calculations don't add up, rather than just recording the final result.
8. Calculate conversion rate, chips, and table fee of sanma
If the rule is to set everyone's total game points to 0, first check to see if the total is 0, and then reflect the conversion units, chips and table fee. oka, uma, for tables with different rules for rounding, please check against the specified total. By calculating the score sticks and the actual balance separately, you can identify the stage of deviation.
Conversion conversion rate is the conversion value per 1 game point. In the following, P is used as the conversion unit for calculation examples.
Conversion conditions using P
- Final game points are 1st place +45, 2nd place +5, 3rd place -50
- 1 point = 100P
- chips1 piece = 100P
- chips is 1st place + 2 pieces, 2nd place - 1 piece, 3rd place - 1 piece
- table feeTotal of 1,200P will be shared equally among 3 people, 400P for each person
Final balance = Game points x conversion unit + chips number x chips unit - table fee share
| rank | Point conversion | chips | table fee | final balance |
|---|---|---|---|---|
| 1st place | +4,500P | +200P | −400P | +4,300P |
| 2nd place | +500P | −100P | −400P | 0P |
| 3rd place | −5,000P | −100P | −400P | −5,500P |
The total converted game points is 0P, and the delivery of chips is +200−100−100=0P. The final balance reflecting table fee is +4,300+0-5,500=-1,200P, which matches table fee for the entire table.
When adopting Tobi awards, etc., record them in a separate column rather than grouping them together in one item under "Adjustment." Once you know how many P moved from who to whom, you can recalculate the total actual balance. Settlement items that include four-person play are:mahjong balance calculation methodBut you can check it.
9. What is “tsumo loss” specific to sanma?
sanma has one fewer person participating in payment than four-player mahjong, so there are multiple ways to pay when tsumo is available. "With tsumo loss" is a method that receives payment for only two people for dealer and non-dealer, which is the same as four-player mahjong, and does not compensate for the one person who does not exist. The method of adjusting the lack of Agari points in some way is generally called "No tsumo loss".
The presence or absence of tsumo loss changes the score sticks movement for each station. As a result, final score and game points may change even if the content is the same. However, the formula for issuing raw points after the end of Hansho is the same for both.
raw points=(final score−return score)÷1,000
What is different is not the formula, but the final score that enters the formula. If you tally up games with and without tsumo loss, the difference in playing style and the difference in rules will be mixed together, so record them as separate settings.
10. How does North extraction affect the results of sanma?
In sanma, there is a rule to remove North from the hand and treat it as dora. The further north you go, the easier the score will be, and in a table where North extraction itself is the target of chips, it will directly affect not only the score bar but also the balance of chips.
On the other hand, there are rules that do not use North extraction, such as making the north yakuhai for everyone or treating it as a normal tile. "The north of sanma is not necessarily dora". If North is treated differently, his batting points and defensive decisions will also change, so when comparing results, it is better not to lump them together under the same conditions.
11. sanma may have a greater influence on chips results.
For tables that use chips, check what to target, such as red tiles, one shot, ura-dora, north, yakuman. It depends on the rules whether you receive ron from the gunman or tsumo from the other two people.
Even if the game points are positive, if the payment of chips is large, the actual balance will be small. On the other hand, even if you don't finish well, you may be able to make up for it with chips income. When analyzing, do not mix chips into game points, but separate them as "Game +4,500P, chips+200P, table fee−400P".
12. If there is Tobi Award, Yakitori, riichi deposits, etc.
Depending on the table, there are special payments such as Tobi Award, Yakitori, yakuman Congratulations, etc. riichi bars may be marked riichi deposits at the end, or the handling of stacked bars may be determined separately. After completing the basic calculations for raw points, uma, and oka, it will be easier to organize them if you add or subtract them as independent items.
You cannot check the contents later if you only select "Other adjustments +500P". Please record how much you moved from who to whom, for what reason, and how much you moved, such as "Tobi Award 500P from 3rd place to 1st place". If the prize is transferred between players, you can also check that the sum of the received amount and the paid amount is 0.
13. How to troubleshoot a sanma result that does not balance
- Selected the number of players and game format, and divided the records of sanma and four-player mahjong
- The tiles used, North, tsumo loss, chips, Tobi and the end condition were left.
- starting score, return score, uma, oka, left tie and fraction handling
- Checked everyone's final score + remaining riichi deposits on the table = total number of point sticks at the start.
- I recorded who the riichi deposits left on the table should be distributed to and whether it should be allocated to a separate slot.
- In a rule that sets everyone's total game points to 0, the final game point total for 3 players is 0.
- Confirmed the total number of chips received and paid.
- The total burden of table fee matched the table fee of the entire table.
Order of confirmation when the totals do not match
- Add everyone's final score and the remaining riichi deposits on the table and compare it with the total number of points at the start.
- Check the relationship between the total of three people's raw points and oka
- Check the total uma of 3 people
- Check chips and award delivery
- Check the total amount of table fee and each person's burden
| symptoms | Where to check | Main cause |
|---|---|---|
| The total number of dots does not match. | final score・riichi deposits | Input omission, oversight of riichi deposits |
| Game points don't match | raw points・oka | Setting error of return score or oka |
| It shifts when adding uma | 3rd place uma | Input error in 2nd and 3rd place values |
| chips included and shifted | Number of tickets received/paid | Mismatch in number or units |
| Only the actual balance shifts | Conversion unit/table fee | conversion rate conversion or contribution amount error |
14. Items that must be recorded when managing results of sanma
To properly tally data later, leave not only the results but also the conditions. At a minimum, record the following items for each game or rule setting used.
| Recorded items | Reason for leaving |
|---|---|
| Date/game format | Separate period, sanma/four-player mahjong, Dongfeng/Hanzhuang |
| starting score・return score | Recalculate raw points and oka |
| uma・oka | Recreate game points |
| North・tsumo loss | Distinguish between sanma-specific conditions |
| Ranking/final score | Calculate average placement and raw points |
| game points | See results not affected by conversion rate |
| conversion rate・chips・table fee | Recalculate the actual balance |
| Game memo | Break ties and leave special prizes |
15. Be sure to manage the results of sanma and four-player mahjong separately.
sanma ranks 1st to 3rd, and four-player mahjong ranks 1st to 4th, so they differ from the standard of average placement. Since the conditions such as uma, oka, tiles used, North extraction, tsumo loss are different, it is not possible to accurately judge the ability and key non-dealer just by looking at the total balance of both.
First, separate sanma and four-player mahjong, and if possible, aggregate them by major conditions such as Dongfeng/Hanshuang, tsumo loss, North, and uma within sanma. Even if the amount of plus is the same, the meaning will change if the number of games and conversion rate are different. The more conditions you have, the more fair you can compare your performance.
16. sanma not only shows results but also average placement
Assuming that the three ranks occur with equal probability, the mathematical center of average placement is(1＋2＋3)÷3＝2.0It is. 2.0 is just a calculation center and is not a passing score that can be used at any table.
| indicators | Calculation method | Conditions to check |
|---|---|---|
| average placement | Total rank ÷ number of games | Same number of people and same main rules |
| first-place rate | Number of times in 1st place ÷ Number of games | Same aggregation period |
| last-place rate | Number of 3rd place ÷ Number of games | Same aggregation period |
| average game points | Total game points ÷ Number of games | Same uma and oka |
| average balance | Total actual balance / number of games | Same conversion unit, chips, table fee |
As a guideline, a score of 2.00 to 2.09 is considered to be around average, 1.95 to 1.99 is above average, and 1.90 to 1.94 is considered a strong score. 1.85 to 1.89 is quite strong, 1.80 to 1.84 is very good, and 1.70 is a top class number. However, with a small number of games, the results can fluctuate greatly, so you must also consider your opponent, table level, and rules.
Income and expenditure and average placement do not necessarily match. If raw points or chips at the top is large, it may be positive even if average placement is slightly bad, and the actual balance may be negative even if average placement is good due to the influence of losing table fee or chips. North extraction and tsumo payments aresanma rule list, detailed criteria areGuideline and how to read average placement of mahjongYou can check it here.
17. If you want to see the results of sanma, also check "1 game average"
You can't tell how many games you played to get the results just by looking at the total balance. If you get +10,000P for 100 games and +10,000P for 1,000 games, the results per game are very different even though they have the same total.
Average balance = total balance ÷ number of games
Average game points = total game points ÷ number of games
Average balance is suitable for understanding actual profit and loss, and average game points are suitable for understanding game results excluding conversion rate and table fee. By arranging average placement, average game points, and average balance, you can check the "placement order", "points/ranking points", and "final profit and loss" separately.
18. Compare sanma results by rule
With and without North extraction, with and without tsumo loss, with different uma and oka, and against Dongfeng and Hanzhuang, we will tally them separately as much as possible. Online and real games are also different in terms of game environment and the presence or absence of table fee, so it will be easier to analyze if you keep separate tallies.
When comparing games with different conversion rate, use game points rather than money. If you want to compare the actual balance, please also check whether chips and table fee are included. If you can't match the conditions perfectly, at least note what's different.
19. sanma such as Jakukon, Tenho, MJ etc. are not the same rules
Even for online mahjong, starting score, payment standards, handling of north, payment at tsumo, ranking points, etc. differ depending on the service and mode. For example, in MJ's official three-man rules, North is treated as everyone's yakuhai, and the ranking points and starting score and return score are also clearly specified. The conditions are not the same as another sanma which removes the north and becomes dora.
Settings may change depending on tournaments or special modes even within the same service. Rather than simply arranging the results of Jakukon, Tenho, and MJ, record them as a set, including the service name, mode, rules, and aggregation period.
20. Common mistakes in sanma results management
- Use uma of four-player mahjong as is and do not record the 3rd place value
- Confuse starting score with return score and forget or double add oka
- Aggregating different rules together without recording the treatment of north or the presence or absence of tsumo loss
- chips is mixed into game points, making it impossible to understand pure game results
- Mix table fee into mahjong grade itself
- sanma and four-player mahjong, summarize the match against Dongfeng and Hanzhuang
- Just look at the total balance and do not check the number of games played or the average per game.
The way to prevent this is to leave the numbers and rule settings that are still being calculated. It is not possible to determine whether the cause of the ups and downs lies in the order of arrival, raw points, chips, or table fee just by looking at the final balance.
21. Frequently asked questions about sanma results calculation and management
How do I calculate the balance of sanma?
Subtract return score from final score to get raw points, add uma, oka, and special settlement to determine game points. After that, convert conversion rate, add or subtract chips, and finally subtract table fee.
How do you decide uma for sanma?
Record all values from 1st to 3rd place according to the rules of the actual table. If uma has a total of 0, please also make sure that the sum of 3 people's numbers becomes 0. +20, +10, -30 are examples of calculations.
Is there a general uma for sanma?
There is no one standard. There are multiple settings such as +20, +10, -30, +20, 0, -20, etc., so check the three rankings of the playing table.
What is oka in sanma?
This point arises from the difference between starting score and return score. Generally, it is added all at once to the top, but there are some tables that do not use oka or that handle it differently.
How many oka have 35,000 points and return 40,000 points?
The difference between the three people is (40,000-35,000) x 3 = 15,000 points, so if 1,000 points = 1 point, it is 15 points.
Will the balance of sanma be 0 in total?
Game points and chips, which only move between players, will total 0 in a zero-sum setting. Please check the prescribed total depending on the rules for fractions and special settlement.
Why doesn't the total become 0 when I include table fee?
table fee is not a transfer between players, but an expense that goes out from the results of all three players. If it is 400P per person, the total final balance will be -1,200P of the total amount of table fee.
What is tsumo loss?
The idea is that the tsumo agari of sanma will not compensate for the payment of the non-existent 4th person, and the total received points will be less than the equivalent of four-player mahjong. Please check the table rules for specific payments.
Does the payment formula change depending on the presence or absence of tsumo loss?
Even if only the handling of tsumo loss is different, issue raw points(final score−return score)÷1,000The formula is the same. However, since the payment at tsumo will change, the point stick movement during the game and final score will change. For the final game points, apply uma, oka, and rounding for that table. Games with different tsumo loss conditions will be recorded as separate settings.
Will North extraction affect the balance?
Yes. In addition to raising the score by punching dora, it also affects chips results in tables where the north is targeted for chips. There is also a rule that treats the north as yakuhai or a normal tile.
How do you calculate chips?
Subtract the number of pieces paid from the number of pieces received and multiply by the unit of 1 piece. After converting game points to conversion rate, it will be easier to understand if you add or subtract as a separate item.
Can I aggregate the results of sanma and four-player mahjong together?
They are not aggregated together, but separated into sanma and four-player mahjong. This is because not only the range of rankings but also the tiles used and settlement conditions may differ. Compare each with the same main rules and time period.
Can the sanma results of Jakukon and Tenho be compared?
You can use it as a reference, but you cannot make a simple comparison. Since the North, tsumo payment, starting score, ranking points, etc. are different for each service and mode, we prioritize and compare results within the same conditions.
Is average placement2.00 of sanma strong?
2.00 is the mathematical standard when 1st, 2nd, and 3rd place are evenly distributed. We haven't lost much, but we can't judge them as ``strong'' just by looking at the numbers.
Is average placement1.90 of sanma strong?
If you can maintain around 1.90 over a sufficient number of games under the same rules and competitive environment, it can be considered a strong performance.
Should I look at the balance or average placement for sanma?
Both. Balance represents the actual profit and loss, and average placement represents the stability of the order of arrival. If you also include game points, first-place rate, and last-place rate, you can analyze the content in detail.
sanma's results can be used as a reference at what game?
If the number of games is small, it will fluctuate greatly. You can start to see trends after about 100 matches, and it becomes easier to compare after a few hundred matches, but you need to match the opponents and rule conditions.
How do you compare the results of games with different conversion rate?
Compare the average game points and average placement instead of the actual balance amount. When comparing prices, please match not only conversion rate but also chips and table fee.
sanma rule reference material
- SEGA NETmahjong MJ ARCADE "Three-person hit": Examples of official rules that define the tiles used, north, Qi, tsumo payment, starting score, and the reference point for settlement.
- Jakutama “Jakutama 3rd Anniversary Appreciation Cup”: Example of an official tournament that clearly states "tsumo loss" for three-man play
- Online match mahjong Tenho "Manual":Official regulations regarding starting score, settlement reference point, tiles used, north, and chi for Dan match three-man hit
Each document is the rules for a particular service or competition. The materials for Sparrow Soul are from a tournament held in 2022, and may not apply to all current modes. Tenho's materials are not used as the basis for tsumo loss, but are referenced as an example with different rules. The settlements using uma, oka, and P in this article are illustrative examples that clearly state the conditions. Document confirmation date: August 27, 2026.
22. Summary｜sanma records not only the results but also “which rules were used to play the game”
The balance of sanma is raw points from final score, uma and okaAfter adding XZ and confirming the game points, conversion rate, chips, special payment, and table fee will be reflected in order. If you separate the numbers that are being calculated, it will be easier to find where the balance is not in line.
sanma does not have settings for uma, oka, North, and tsumo loss that are common to all desks. Before the game, please check starting score, return score, and uma and oka for 3 positions, and also record the conditions for North, tsumo loss, and chips.
Results will be calculated separately for sanma and four-player mahjong, and if the main rules are different between sanma, they will be calculated separately. It will be easier to judge your long-term ability by looking at not only the total balance but also the number of games played, average balance per game, average game points, average placement, first-place rate, last-place rate.