Mahjong Balance Calculation: Uma, Oka, Rates, and Chips

A worked four-player balance calculation

Check final table points

Assume final table points of 40,000, 30,000, 20,000, and 10,000. Calculate each base score from the difference against return points, then apply uma and oka to determine the final game scores.

Calculate the base scores

For each player, subtract the 30,000 return points from their final table points, then divide by 1,000. Final points of 40,000, 30,000, 20,000, and 10,000 give base scores of +10, 0, −10, and −20.

Add uma

Apply +20 for first, +10 for second, −10 for third, and −20 for fourth according to the confirmed standings. Uma alone sums to 0.

Add oka

Add oka +20 to first place. Everyone else receives 0 oka. This +20 offsets the −20 total of the players' base scores.

Calculate final game scores

The final game scores are +50 for first, +10 for second, −20 for third, and −40 for fourth. They sum to 0, confirming the calculation through uma and oka.

Apply the rate

At 100P per score point, multiply each final game score by 100. +50 becomes +5,000P; +10 becomes +1,000P; −20 becomes −2,000P; and −40 becomes −4,000P.

Add or subtract chips

Assume net chips of +5 for first, −1 for second, −2 for third, and −2 for fourth. Table fees are 400P per player.

At 100P per chip, these become +500P, −100P, −200P, and −200P. Check that chips received and paid sum to 0.

Deduct table fees

Each player pays an equal 400P share. Because table fees are separate from wins and losses, deduct 400P from everyone after calculating score points and chips.

Calculate the final balance

Follow the first-place player's balance from start to finish

STEP 1. Calculate the base score from final table points

First place finishes with 40,000 table points. With 30,000 return points, (40,000 − 30,000) ÷ 1,000 = +10.

STEP 2. Add uma

Add the first-place uma of +20 to reach +30 score points.

STEP 3. Add oka

Add the first-place oka award of +20 to reach +50 score points.

STEP 4. Confirm the final game score

The base score of +10, uma of +20, and oka of +20 give a final game score of +50.

STEP 5. Apply the rate

At 100P per score point, +50 × 100 = +5,000P.

STEP 6. Add chips

With five chips received, add 5 chips × 100P = +500P.

STEP 7. Deduct table fees

Finally, subtract the 400P table fee for a final balance of +5,000 + 500 − 400 = +5,100P.

1. Base score: (40,000 table points − 30,000 table points) ÷ 1,000 = +10 score points
2. Uma and oka: +10 + 20 + 20 = +50 score points
3. Rate conversion: +50 × 100P = +5,000P
4. Chips: +5 chips × 100P = +500P
5. Table fees: +5,000P + 500P − 400P = +5,100P

The calculation progresses from 40,000 table points to a base score of +10, a final game score of +50, a converted value of +5,000P, and a final balance of +5,100P. Keeping units separate and calculating one stage at a time is the foundation of avoiding mistakes.

Why do mahjong balances sum to 0?

Scoring sticks usually just move around the table

Scoring sticks change hands through wins and deal-ins, but the table's total normally does not increase or decrease on its own. Final table points plus any deposits should equal the total distributed at the start.

Uma sums to 0

The example's uma values are +20, +10, −10, and −20, totaling 0. Uma transfers placement points between players, so the amounts received and paid balance.

Oka fills the shortfall in the base scores

With 25,000 starting points and 30,000 return points, the four base scores total −20. Adding oka +20 to first place fills this gap, making the final game scores sum to 0.

Chips also sum to 0 when transferred between players

If one player receives five chips, the other players should collectively pay five chips. If all net chip counts do not sum to 0, check for missing entries or incorrect signs.

Including table fees makes the total negative

In this example, final game scores of +50, +10, −20, and −40 sum to 0. Uma and oka account for the table-point shortfall, so all settlement remains within the table. Net chip counts of +5, −1, −2, and −2 also total 0, leaving the combined balance before fees at 0P.

After fees, final balances are +5,100P, +500P, −2,600P, and −4,600P, totaling −1,600P. This negative amount matches the 1,600P in total fees, confirming that the calculation is correct.

How do you handle fractional scores?

What is the base score for 35,700 points?

Rounding depends on the table's rules. With 35,700 final points and 30,000 return points, the difference is +5,700 table points, giving a base score of +5.7. Whether to keep +5.7 or round to an integer—and whether to round up, down, or to the nearest integer—depends on the agreed rules.

Rounding to nearest, up, or down depends on the rules

There is no universal rounding rule. Some tables round +5.7 up to +6, some retain decimals, and others use different rounding methods depending on placement. Always follow the rules in use at your table.

Do not round repeatedly during the calculation

If rounding is required, apply it once after entering the final table points. Rounding the same fraction again during P conversion compounds the error. If the chosen rounding method does not produce a zero total, an additional step such as assigning the remainder to first place may be specified. Record the agreed method instead of adjusting one player's result arbitrarily.

Some rules assign the rounding remainder to first place

If individual rounding causes the total game score to differ from 0, some rules add the remaining difference to first place. Keep rounding adjustments in their own column so it is clear who received how many score points.

How do tied placements affect uma?

Confirm placements first

When players finish tied, the rules may prioritize the seat closest to the starting dealer or split the placement bonuses equally. Identical final table points can therefore lead to different uma. Confirm the tie rule before calculating, and record both final table points and the confirmed placements.

Tiebreaks based on proximity to the starting dealer

One method resolves ties by the original seating order relative to the starting dealer. This assigns each player a distinct placement and the normal uma for that place.

Splitting uma for tied places

Another method adds the uma for the two tied places and divides it between the two players. For example, splitting second-place +10 and third-place −10 gives each player 0 placement points.

Tie handling varies by table

Final game scores change depending on whether ties are resolved by seating order or by splitting uma. Since this can cause settlement disputes, follow the method agreed before the game.

Confirm rules before playing

Ties are uncommon enough that their treatment may first become an issue at settlement. Stating the tie-breaking method on the rule sheet in advance helps avoid disputes afterward.

Bankruptcy bonuses, yakitori, and deposits

Bankruptcy bonus

A bankruptcy bonus transfers additional score points from a player whose points fall below a specified threshold to the player who bankrupted them or another designated recipient. Confirm who receives and pays it, and whether bankruptcy ends the game.

Yakitori

Yakitori penalizes a player who does not win a single hand during the game. The conditions for removing the penalty and the recipients of payment vary by table.

Riichi sticks and deposits

A 1,000-point stick left on the table after a riichi declaration is a deposit. Rules may award remaining deposits to first place or carry them into the next game. Avoid counting them twice in final table points.

Other special adjustments

Rather than lumping extra awards into “other adjustments,” record who paid whom and how many points changed hands. For a five-point bankruptcy bonus, enter +5 for the recipient and −5 for the payer together. An externally funded bonus will not sum to 0, so record its purpose and source.

Keep special rules separate from the basic calculation

First establish the base result using base scores, uma, and oka, then add special adjustments.

Decide who receives leftover riichi sticks

Scoring sticks left on the table after riichi declarations are called deposits (kyotaku). Rules determine who receives any deposits remaining at the end or whether they carry into the next game. Record when they are settled so they are not counted in both table-point totals and final game scores.

How does sanma balance calculation differ from four-player mahjong?

The calculation follows the same basic sequence

In sanma, you still derive base scores from final table points, apply placement bonuses and oka, then add or subtract the rate conversion, chips, and fees as needed. The settings—such as starting points and placement bonuses—change, not the basic calculation sequence.

Starting and return points often differ

Sanma often starts at 30,000 or 35,000 points, unlike common four-player settings. Return points also vary by table. Do not automatically apply a four-player 25,000-start / 30,000-return setup.

Uma settings differ

Sanma has only first through third place, so uma must be set for three players. Distributions vary: some reward and penalize only first and third, leaving second at 0. Check how the three values are intended to total.

Oka also depends on the rules

Some rules calculate oka from the gap between the starting total and three return amounts; others define a separate first-place award. There is no universal fixed oka value for sanma.

Watch for sanma-specific chip rules

Some rules award chips for North extraction, red tiles, yakuman, tsumo wins, or other conditions. Record point settlement separately from chips and keep the main rules, including whether tsumo-loss payments apply.

Do not directly compare sanma and four-player balances

The number of players, point movement, placement bonuses, and chip conditions differ, so the same +30 score points can mean different things. Keep long-term sanma and four-player statistics separate. See how to manage sanma balances for more details.

How are M.League and competitive mahjong scores calculated?

Competitive mahjong also uses placement bonuses

Some competitive formats add placement bonuses to the result derived from final table points. Their purpose is to aggregate league performance, which differs from calculating actual balances at a regular table.

M.League score calculation

Under the official M.League rules, each player starts with 25,000 points. Points above 30,000 count positively, and the shortfall below 30,000 counts negatively. Placement adjustments are +50,000 for first, +10,000 for second, −10,000 for third, and −30,000 for fourth. Table points and placement adjustments are converted at 1,000 table points per score point.

For example, second place with 35,800 table points receives a base score of +5.8 plus a +10 placement bonus, totaling +15.8. This distribution differs from ordinary uma 10–20, so do not substitute that setting.

The purpose differs from ordinary uma and oka

At a regular table, game scores may be converted further into actual balances using a rate. M.League points accumulate as competitive results; they are not a system for calculating player-to-player balances with chips and table fees.

Professional organizations use different rules

Starting points, placement bonuses, ties, and rounding differ by organization and tournament. Use the published official regulations when calculating professional results.

Do not automatically apply ordinary uma 10–20

Assuming all mahjong placement bonuses are the same will produce results that differ from official scores. Check the specific allocation for first through fourth rather than relying on a rule name.

How to troubleshoot a balance calculation

It is more efficient to check final table points, base scores, uma and oka, rate conversion, chips, and fees in order than to work backward from the final balance. Finding the first stage where a discrepancy appears avoids rechecking every later step.

Common balance calculation mistakes

Confusing table points with score points

40,000 table points and +50 score points are different values. Subtract return points from table points and convert the result into units of 1,000 before applying uma and oka.

Confusing starting points with return points

With 25,000 starting points and 30,000 return points, 25,000 is the starting score and 30,000 is the baseline for calculating the base score. The difference funds oka.

Adding uma twice

A tool or app's final game score may already include uma. Decide whether you are calculating from final table points or recording a previously calculated score, and avoid adding the same uma twice.

Adding oka twice

If the first-place score already includes oka and you add another first-place award, the combined total becomes incorrectly positive. Check that oka matches the shortfall in the total base scores.

Adding chips to table points

Chips are exchanged separately from scoring sticks. Do not turn 40,000 table points into 40,500 or combine +50 score points and five chips into +55. After rate conversion, use a separate chip-count × chip-value column. This also lets you calculate performance without chips from the same records.

Treating table fees as part of playing performance

Table fees are the cost of using the table. Saving them separately from wins and losses lets you assess both playing results and actual costs. With a fixed fee per game, the total after fees also falls further as the number of games increases.

Combining sanma and four-player statistics

The number of players and range of placements differ, so identical score points can mean different things. Keep sanma and four-player statistics separate, combining only their actual balances when you need an overall total.

Directly comparing results under different rules

Different uma, oka, rates, chips, and fees can produce very different balances for the same placement. Analyze performance by comparing games played under the same main rules.

Rounding repeatedly

Rounding at the base-score, rate-conversion, and final-balance stages compounds errors. Round once at the stage required by the rules and keep the original unrounded values.

Items to keep when recording mahjong balances

If you save only the final balance, you cannot recalculate it later or investigate why it changed. Record at least the following items for each game.

Record starting points, return points, uma, oka, and rounding in the rules field too. You can use the mahjong rule sheet template for pre-game checks.

Keep statistics separate for sanma and four-player games, East-only games and hanchan, and games with different uma or rates.

Can a good average placement still produce a poor balance?

Average placement and balance do not always move together

Your actual balance can be negative even with a good average placement. The metrics describe different things and respond differently to rule settings.

Small base scores when finishing first

Many narrow first-place finishes improve average placement but produce small positive base scores. Conversely, a few large first-place finishes can substantially increase your balance.

Large losses when finishing last

Even with a low last-place rate, a single very large last-place loss can have a major effect on your balance. Check the average score for each placement as well as the placement distribution.

Poor chip results

Good placement results do not prevent your actual balance from falling if you pay more chips than you receive. Comparing balances with and without chips helps identify the cause.

The effect of table fees

Table fees apply each game, so their total grows with game count. A small positive balance from play can become negative after fees.

Mixing games with different rules

Combining games with different rates or uma makes the relationship between average placement and balance harder to understand. Analyze results separately by format and main rules.

Read several metrics together

Place average placement, balance, first-place rate, last-place rate, and game count side by side to see whether placements or point gains and losses changed. Avoid judging performance by a single number.