Why the rules differ between sanma and yonma
Sanma does not have one universal ruleset used at every table. The tiles used, starting points, settlement reference points, uma, treatment of north tiles, tsumo loss, chips, bankruptcy, and end conditions vary by table and service.
Therefore, simply substituting your numbers into an example from another table may not produce the correct profit or loss. Keeping the following rules table as an input for each calculation lets you verify later which rules were used to obtain the result.
Rules table used for calculations
To calculate the base score, compare each participant’s final point total with the return points (kaeshiten), the baseline used for settlement.
The difference between the final point total and return points, converted into units of 1,000 points, is the base score (soten). When the starting points and return points differ, all players’ base scores will not total zero. Oka makes up this difference, and the table rules determine which placement receives it. Add uma and, if used, oka to the base score to calculate the final game points.
| Category | Settings to decide before play | Purpose |
|---|---|---|
| Number of players and format | 3-player or 4-player, east-only or hanchan | Separate records |
| Tiles and north | Tiles used, red fives, whether chii is allowed, and whether north is treated as a value tile, nuki dora, or a regular tile | Standardize game conditions |
| Point sticks | Starting points and return points | Calculate base scores and oka |
| Placement | Uma for 1st through 3rd, whether oka is used, and which placement receives it | Calculate final game points |
| Tsumo | Whether tsumo loss applies and how dealer and non-dealers pay | Determine point-stick transfers for each hand |
| Chips | Eligible yaku or tiles, the value per chip, and how payments are exchanged | Add to the actual net result |
| End conditions | Busting, ending with 0 points, extensions, and handling of riichi deposits and honba | Confirm final point totals |
| Ties and fractions | Placement for tied scores, rounding methods, and allocation of fractions | Confirm placements and the total |
| Conversion | Unit per point, total table fee, and how it is shared | Convert the final game points into actual net results |
The rules sheet is not merely a note for naming a game setting. Use the final point totals and return points to calculate the base scores, then use uma and oka to calculate the final game points. Apply the conversion unit, chips, and table fees only when calculating actual net results. Include the ruleset name with the result, and save the figures together with their assumptions.
Briefly note the main differences in the ruleset name. For example, “3-player, 35,000 starting points, 40,000 return points, tsumo loss, north extraction” helps prevent confusion with other rulesets. When conditions change, do not overwrite the previous ruleset; save a new one.
Named tournaments in SEGA NET MAHJONG MJ ARCADE, Tenhou, and Mahjong Soul also provide examples with different starting points, settlement base points, north-tile rules, and tsumo payments. These examples show that rulesets can vary; none should be treated as the universal rules for 3-player mahjong.
How to set uma for three players
Uma are placement adjustments applied to the final game points. In this example, 1st receives +20, 2nd +10, and 3rd −30, for a total of 0 across all three players.
+20 + 10 − 30 = 0
Record 3-player uma as a set of three values. A label such as “uma 20, 10” may not be enough to reconstruct the value for 3rd, so list every placement: “1st +20, 2nd +10, 3rd −30.”
Some tables use other distributions totaling 0, such as +20, 0, −20. The +20, +10, −30 shown here is one example used in the calculations below, not a ruleset that applies to every table.
Final game-point calculation example
From here, we use an example whose rules sheet records “3-player, 35,000 starting points, 40,000 return points, uma of +20, +10, −30, and oka of +15 to 1st.” Assume there are no riichi deposits, fractions, or external prizes, and all point-stick transfers have already been reflected in the final point totals. Those totals are 50,000 points for 1st, 35,000 for 2nd, and 20,000 for 3rd, matching the 105,000 points distributed at the start.
| Placement | Final point total | Base score | Uma | Oka | Final game points |
|---|---|---|---|---|---|
| 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 base score for 1st is
(50,000 − 40,000) ÷ 1,000 = +10. - Adding the +20 uma to the first-place base score gives +30.
- Adding the +15 oka under the adopted rules gives first place +45.
- Calculating in the same order gives second place +5 and third place −50.
The oka generated under these conditions is (40,000 − 35,000) × 3 ÷ 1,000 = 15 points. The three base scores total +10 − 5 − 20 = −15, so awarding the +15 oka to first place according to the table offsets the difference in their total base scores. The uma also totals 0, so in this settlement example, the final game points total +45 + 5 − 50 = 0.
When deposits or remainders remain
This example assumes that no deposits remain on the table and that there are no fractional points. If deposits remain at the end, add together all players’ final point totals and the deposits left on the table once, then compare that sum with the points distributed at the start. Record, according to the table rules, which player ultimately receives the deposits or whether they remain separate. Any remainders caused by rounding are also handled separately according to the rules table.
Settling rates, chips, and table fees
Under rules where all players’ final game points total 0, as in this example, first confirm that the total is 0, then apply the conversion unit, chips, and table fee. If the table has different rules for oka, uma, or rounding, compare the result with the total specified by those rules. Keeping in-game point calculations separate from actual profit-and-loss calculations helps identify where a discrepancy arose.
The conversion rate is the value of one final game point. Below, P is the conversion unit used in the calculation examples.
Conversion conditions using P
- Final game points: first place +45, second place +5, third place −50
- 1 point = 100P
- 1 chip = 100P
- Chips: first place +2, second place −1, third place −1
- The total table fee of 1,200P is split equally among the three players, at 400P each
Final result = final game points × conversion unit + number of chips × chip value − share of the table fee
| Placement | Point conversion | Chips | Table fee | Final net result |
|---|---|---|---|---|
| 1st place | +4,500P | +200P | −400P | +4,300P |
| 2nd place | +500P | −100P | −400P | 0P |
| 3rd place | −5,000P | −100P | −400P | −5,500P |
The converted final game points total 0P, and the chip transfers also total +200 − 100 − 100 = 0P. After applying the table fee, the final results total +4,300 + 0 − 5,500 = −1,200P, matching the table’s total fee.
If bonuses such as a bust bonus are used, record them in a separate column rather than grouping them under “adjustments.” If you can see how many P moved from whom to whom, you can recalculate the total actual result. Settlement items, including those for four-player mahjong, can also be checked in Mahjong Results Calculation Guide.
Recordkeeping and verification checklist
- Selected the number of players and game format, and kept three-player and four-player records separate
- Recorded the tiles used, north tiles, tsumo loss, chips, bankruptcy, and end conditions
- Recorded the starting points, return points, uma, oka, and handling of ties and fractions
- Confirmed that all players’ final point totals + riichi deposits left on the table = the total starting points
- Recorded who receives the riichi deposits left on the table, or whether they are tracked separately
- Under rules where all players’ final game points must total 0, the three players’ total was 0
- Confirmed that the total chips received matched the total chips paid
- Confirmed that the players’ table-fee shares totaled the table’s overall fee
Order of confirmation when the totals do not match
- Add all players’ final point totals and the riichi deposits left on the table, then compare the result with the total starting points
- Check the relationship between the three players’ total base scores and the oka
- Check that the three players’ uma total is correct
- Check chip and prize transfers
- Check the total table fee and each player’s share
Performance metrics such as average placement
Assuming all three placements are equally likely, the mathematical midpoint of average placement is (1 + 2 + 3) ÷ 3 = 2.0. 2.0 is only the mathematical midpoint, not a universal benchmark of skill for every table.
| Metric | Calculation | Conditions to check |
|---|---|---|
| Average placement | Sum of placements ÷ number of games | Same number of players and same key rules |
| First-place rate | Number of 1st-place finishes ÷ number of games | Same reporting period |
| Last-place rate | Number of 3rd-place finishes ÷ number of games | Same reporting period |
| Average final game points | Total final game points ÷ number of games | Same uma and oka |
| Average net result | Total actual net result ÷ number of games | Same conversion unit, chip rules, and table fees |
If games with different player counts or conditions are combined, rule differences cannot be separated from performance differences. Compare only games in the same format with matching key conditions, such as tsumo loss and uma. The Mahjong Performance Metrics Guide explains how to interpret average placement and related figures.
Frequently asked questions about three-player mahjong results
How do you decide the uma for three-player mahjong?
Prioritize the rules of the table where you actually play, and record all values from 1st to 3rd place. If using uma that sum to 0, also confirm that the three values add up to 0. +20, +10, and −30 are one example used in this guide.
Does the settlement formula change depending on whether tsumo loss applies?
Even when only the treatment of tsumo loss differs, the formula for the base score, (final point total − return points) ÷ 1,000, remains the same. However, because tsumo payments differ, point transfers during the game and final point totals also differ. Apply the table's uma, oka, and rounding rules to the base score to calculate the final game points. Record games with different tsumo loss conditions as separate settings.
Can three-player and four-player mahjong results be aggregated together?
No. The placement range differs with the number of players, and the tiles used and settlement conditions may also differ. Separate three-player from four-player mahjong, then compare results with matching key rules and periods within each format.
Three-player mahjong rules referenced
- SEGA NET MAHJONG MJ ARCADE: Three-Player Rules: Official rules specifying the tiles used, North tiles, chii, tsumo payments, starting points, and settlement baseline
- Mahjong Soul 3rd Anniversary Appreciation Cup: A named official three-player tournament whose rules explicitly state that tsumo loss applies
- Tenhou Manual: Official rules for starting points, settlement baseline, tiles used, North tiles, and chii in ranked three-player games
Each source describes the rules of a specific service or tournament. The Mahjong Soul source covers a named tournament held in 2022 and should not be generalized to all current modes. The Tenhou source is not used as evidence for tsumo loss and is cited only as an example of configuration differences. The uma, oka, and P-based settlement in this guide is an illustrative example with explicitly stated conditions. Sources checked: July 28, 2026.
Summary
Record three-player mahjong results together with the rules used. Calculate the final game points from the final point totals and verify the total, then apply the conversion unit, chips, and table fee. When comparing results, separate three-player and four-player mahjong and use the same key rules and time period for each.