Sanma net results: calculating uma, oka, chips and final settlement

Separate table scores, game points and net balances

To avoid confusion, calculate three stages separately: table scores, game points and net balances. Return points (kaeshiten) are the settlement baseline. Raw result points (soten) are the difference between the final score and return points, divided by 1,000. Return points differ from the starting score.

Finishing with 50,000 does not directly mean +50 raw result points. With a 40,000 return baseline, it is (50,000 − 40,000) ÷ 1,000 = +10.

For remainders below 1,000, one common convention is rounding 500 or less down and 600 or more up. A ±1 game-point mismatch caused by rounding all three players is normally adjusted in first place's raw result points.

Uma: fixed placement bonuses and floating/sinking uma

Uma transfers placement points between players. Sanma commonly distinguishes fixed placement uma from floating/sinking uma (ukishizumi uma).

1. Fixed placement uma

Allocation depends only on first, second and third place, regardless of the final table scores. Positive and negative values sum to zero.

• +20 / 0 / −20: a common zero-sum allocation with no uma transfer for second place.
• +30 / 0 / −30: increases the gap between first and last, giving placement greater weight.
• +20 / +10 / −30: the worked example rewards second place and increases third place's penalty.

2. Floating/sinking uma

Used notably in Kansai-style sanma, this method changes the allocation according to how many players finish above the return-point baseline.

• One player above the baseline (only first at or above it): first receives the full positive allocation, for example +30 / −10 / −20.
• Two players above the baseline (first and second at or above it): both receive a share, for example +20 / +10 / −30.
• All three below the baseline: follow the placement allocation specified by the table rules.

With floating/sinking uma, whether second place stays above the baseline can substantially change net results. Final-round push-or-fold decisions and score requirements become especially important.

Oka: calculate the difference for three players

Oka is the first-place bonus arising from the gap between starting and return points. Four-player mahjong with 25,000 starting and 30,000 return points uses four players' gaps: 5,000 × 4 = 20,000, or +20 game points. Sanma uses three players' gaps.

The worked table awards all 15 points to first place. Raw points total −15, oka adds +15, and uma totals zero, so final game points sum to +45 + 5 − 50 = 0.

Common starting/return-point examples follow. Check your table's rules instead of assuming oka is 20 points as in a familiar four-player setup.

Convert all three players' game points into net balances

Convert the table's game points at 1 game point = 100P. Let one chip = 100P, and suppose first place wins a chip-eligible hand by tsumo, collecting one chip from each opponent. Chip changes are +2 (+200P), −1 (−100P) and −1 (−100P). Split the total 1,200P table fee equally, at 400P each.

First place's calculation is 50,000 table points → +10 raw points → +30 with uma → +45 with oka → +4,500P after conversion + 200P chips − 400P fee = +4,300P net.

Converted game points sum to 0P, and chip balances also sum to 0P. Net balances total +4,300 + 0 − 5,500 = −1,200P, exactly the negative of total table fees. For settlement items including four-player games, see how to calculate mahjong net results.

Chip settlement: two payers on tsumo

Sanma chips are an important settlement item separate from table scores and game points. Common triggers include red dora, gold tiles, ippatsu, ura-dora, North extraction and yakuman.

1. Chip transfers differ between ron and tsumo

The key distinction is who pays after ron and tsumo.

• Ron: Receive the eligible number of chips from the single discarder: winner +1 share, discarder −1 share.
• Tsumo: Receive the eligible number from each of the two opponents: winner +2 shares, each opponent −1 share.

Four-player tsumo collects from three opponents for three shares; sanma has two payers, so it collects two shares.

2. Settle chips at the end of the game

These three steps help prevent chip-settlement errors.

1. Count chips: Total each player's final chip holdings or net change during the game.
2. Check the total: Add all three net changes and confirm they sum to zero chips.
3. Convert to net balance: Use net chip balance = chip change × value per chip (for example, 100P), then add it to or subtract it from the converted game-point result.

With many red tiles and North extractions, chip transfers can be substantial. A player can finish first with positive game points yet have a negative net balance after chip losses. Always retain the breakdown, such as “game +4,500P, chips −1,000P, fees −400P.”

Tsumo loss and North extraction

Tsumo loss affects final table scores

With tsumo loss, the winner receives the specified payments from two opponents without replacing the absent North player's share. A method that compensates for that share to match the ron total is called no tsumo loss.

This changes transfers during each hand. The post-game formulas for raw points, uma and oka are unchanged; do not adjust settlement points a second time for tsumo loss.

North extraction affects hand value and chips

If North is extraction dora, extracting it adds dora and can greatly increase hand value. Some rules also award one chip per extracted North. Confirm whether North is extracted or instead treated as a value honor for all three players.

Handle negative scores, deposits and special bonuses

Negative-score settlement and bankruptcy bonuses

High-value sanma hands can frequently push a player's score below zero and end the game under bankruptcy rules. Settlement at that point differs substantially by table.

• Negative scores included: Use the actual negative score in raw-point calculation. Finishing at −8,000 with 40,000 return points gives (−8,000 − 40,000) ÷ 1,000 = −48 game points, including the full negative amount.
• Negative scores excluded: Cap the score at zero, or −40 raw result points in this example, and waive the further negative amount.
• Bankruptcy bonus: The bankrupt player, or all other players, pays a fixed award to the player who caused bankruptcy—for example +10 game points or 1–2 chips.

Including or excluding negative scores can greatly change both the losing player's payment and the winning player's result. It is a key rule to confirm before playing.

Deposits, rounding and tied placements

• Riichi deposits: Remaining deposits at game end are commonly awarded to first place. If added to the final score, do not count them again when reconciling against total starting points.
• Rounding: Adjust any total mismatch from rounding sub-1,000-point remainders in first place's raw result.
• Ties: Some rules prioritize players by proximity to the original East seat; others divide the relevant uma equally among tied players.

Check in order, from table scores to net balances

Working downward pinpoints the stage where the mismatch arose. This checklist assumes zero-sum transfers among the players.

If negative scores are waived and only a bankruptcy bonus is paid, or if external awards exist, reconcile against the total required by those rules.

Save settings before play and results afterward

Sanma rules vary widely, so save a rule profile and label each result with it—for example, “three players, 35,000 start/40,000 return, tsumo loss, North extraction, negative scores included.” When rules change, create a new profile instead of overwriting the old one.

For online games, record the service and mode

Label Mahjong Soul, Tenhou and MJ results with service, mode, rules and date range. For example, MJ ARCADE sanma treats North as a value honor for everyone; keep those results separate from North-extraction rules such as Mahjong Soul's.

Compare matching rules and periods

Aggregate results by saved rule profile. When only the conversion rate differs, compare game points. For net-balance comparisons, align chip and fee conditions too. If rules cannot be matched, note the differences.

Look at per-game results and placement alongside total balance

A +10,000P total over 100 games averages +100P per game; the same total over 1,000 games averages +10P. Analyze these measures with game counts, rather than total balance alone.

If first, second and third occur equally often, sanma's mathematical average-placement baseline is (1 + 2 + 3) ÷ 3 = 2.00. Lower is better: below 2.00 indicates a positive placement record relative to that baseline, while above 2.00 indicates a negative one.

Sanma's high hand values and substantial chip component mean a good average placement can still produce a negative net balance after chip losses and fees. Compare placements, game points and net balances to locate the difference. See sanma rules for North and tsumo payments, and understanding average placement for deeper performance analysis.