Oka and uma
Oka and uma are point modifiers that are applied after the game ends.
- The oka is a bonus to 1st place. All four players pay into the oka at the start of the game, and the sum is paid to 1st at the end.
- The uma is a bonus/penalty applied to each player depending on their placement.
After oka and uma are calculated and a few adjustments are made, each player will have their end game score, also called plus-minus (+/-) score.
Oka and uma
Oka
The oka 「オカ」 can be thought of as an "ante". When oka is used, all players receive the starting score at the start, but pay the target score at the end of the game (the target score is always higher). The difference between the starting and target score is then given to 1st place. The total payment to 1st place is known as the oka.
The oka value is equal to (target score - starting score) x 4. Each player contributes (target score - starting score) points to the oka.
For example, with a starting score of 25,000 and a target score of 30,000, the difference would be 5,000. Each player contributes 5,000 points to the oka. At the end of the game, first place would receive the oka of 5,000 x 4 (20,000) points. Overall, first place has a net gain of 15,000 points and the other have a net loss of 5,000. (The oka value would be stated as 20,000.)
If oka is disabled, then even if a target score is set, no payments are made.
Uma
The uma 「ウマ」 is a set bonus/penalty for ending the game at a certain placement. The typical point spread uses the format of 「+A / +B / -B / -A」, where 1st place receives A, 2nd receives B, 3rd loses B, and 4th loses A. Unlike oka, uma is applied after each player's score is divided by 1000.
The uma does not have to be symmetric. For example, the uma can be set to 「+30 / -5 / -10 / -15」 or 「+15 / -5 / -5 / -5」. Uma usually adds up to 0, but technically does not have to. Modifications may be used to make the conditions easier or harder, namely in tournament settings.
Tie-breaker
When scores are tied, there are two main variations to how it is handled:
- Ties are broken based on the initial wind seating (seats in the first hand). When scores are tied, the initial East player beats South beats West beats North.
- Tied players split oka/uma bonuses evenly. For example, with an uma of 「20 / 10 / -10 / -20」, if two players tie for 3rd, they would pay (-10 + -20) / 2 = -15 each.
Which variation is used will depend on the ruleset.
Procedure
The end game score is calculated as follows:
- Take the raw scores from the end of the game.
- Subtract the target score from the final point values. (If no oka is used, subtract the starting score instead.)
- Find the oka and add it to the winner.
- Divide by 1,000.
- Round to the nearest integer. A result of 0.5 is rounded down, not up.
- Apply the uma spread.
- If, due to rounding, the sum of all four does not equal to zero, then the winner's score is adjusted to produce a zero sum. This adjustment is usually +/- 1 at most. (Note: in some rules, the loser's score may be adjusted instead.)
Formula:
End score = ((Raw points + Oka - Target)/1000) + Uma
Shortcut
For a given value of oka and uma, the overall change between raw score and final score will be the same. Therefore, by finding the net change from oka/uma once, you can skip having to do the entire process over and over.
- Before playing, calculate
Final Score - (raw score / 1000)for each place. Use dummy numbers for raw score. - After finishing the game, find the raw score, round it to the nearest 1,000 (rounding 500 down), then divide by 1,000.
- Use the calculated values from #1 to quickly determine final scores.
For example, if all players ended with 25,000 points, oka = 20k, and uma = 「+20 / +10 / -10 / -20」:
| Raw score conversion | Score comparison: Uma 「20 / 10 / -10 / -20」 | ||||
|---|---|---|---|---|---|
| Raw scores | Rounded to nearest 1000 | Div by 1000 (A) | End score (B) | End score diff (B - A) | |
| 25000 | 25000 | 25 | 35 | 10 | |
| 25000 | 25000 | 25 | 5 | -20 | |
| 25000 | 25000 | 25 | -15 | -40 | |
| 25000 | 25000 | 25 | -25 | -50 | |
This means, for these oka/uma settings, 1st place final score is equal to (rounded raw score/1000) + 10, 2nd place final score is equal to (rounded raw score/1000) - 20, and so on. In other words: instead of having to calculate oka and uma every single time, when you are 1st with these settings, you can divide score by 1000, then add 10.
Using the above picture as another example:
| Raw score conversion | Score comparison: Uma 「20 / 10 / -10 / -20」 | ||||
|---|---|---|---|---|---|
| Raw scores | Rounded to nearest 1000 | Div by 1000 (A) | End score (B) | End score diff (B - A) | |
| 35700 | 36000 | 36 | 46 | 10 | |
| 32400 | 32000 | 32 | 12 | -20 | |
| 22200 | 22000 | 22 | -18 | -40 | |
| 9700 | 10000 | 10 | -40 | -50 | |
First place received 35700 points, so their end score equals (36000) / 1000 + 10 = 46, which is what what first place actually got.
With different oka and uma
Naturally, with different oka and uma settings, the numbers will work themselves out differently than the 「+20 / +10 / -10 / -20」 set up.
With an uma of 「30 / 15 / -15 / -30」:
| Raw score conversion | Score comparison: Uma 「30 / 15 / -15 / -30」 | ||||
|---|---|---|---|---|---|
| Raw scores | Rounded to nearest 1000 | Div by 1000 (A) | End score (B) | End score diff (B - A) | |
| 35700 | 36000 | 36 | 56 | 20 | |
| 32400 | 32000 | 32 | 17 | -15 | |
| 30000 | 25000 | 25 | -20 | -45 | |
| 9700 | 10000 | 10 | -50 | -60 | |
Obviously, the net change is different.
Floating uma
Floating uma, or sliding uma, is an alternate implementation of uma. When floating uma is used, the uma points will vary based on the number of players above/below the target score.
Floating uma is used so that every player above the target score has uma >= 0, while every player below the target has uma <= 0. Afterwards, the uma of 1st is increased / 4th is decreased so that the combined uma still totals 0. This makes end score calculation centered around the target score more so than just simple placement.
| Above | Below | Uma sign |
|---|---|---|
| Two | Two | + / + / - / - |
| Three | One | + / + / 0 / - |
| One | Three | + / 0 / - / - |
For example, when using +15/+5/-5/-15 uma, the numbers would shift as follows:
| Above | Below | Uma sign |
|---|---|---|
| Two | Two | 15 / 5 / -5 / -15 |
| Three | One | 15 / 5 / 0 / -20 |
| One | Three | 20 / 0 / -5 / -15 |
In some rulesets, it is possible for all four players to fall below the target score. Under this setting, there is no extension into the South/West round if the target score is not met; uma is applied as if there were two above and two below the target score (even though nobody hit the target score).
Competition formats
For some competitions, the same four players play out two or more hanchan to settle a score. This is due to one hanchan deemed as inadequate to settle a score between four players due to factors such as luck. Various tournaments and professional organizations use this format.
When multiple hanchan are played, each hanchan applies its own oka and uma. The final scores of each hanchan are summed and players are ranked based on cumulative score.
Strategy
Due to the existence of oka/uma, Japanese mahjong is heavily based on placement, not just raw points. Even a 1000 point hand is valuable if it improves placement in the last hand. Adapting your play based on placement is known as situational analysis. For example, a player comfortably in 1st doesn't need points as much, and can take less risks as a result.
The values of oka/uma will vary by ruleset, so make sure to adjust accordingly.
Online rank points
In online clients, rank points are typically awarded or subtracted based on placement. While their rank systems are technically separate from oka and uma, the concept is the same - placement is crucial for rising rank.
- In tenhou.net and Mahjong Soul (except Celestial rank), last place is penalized, especially in the higher ranks as the last place penalty increases by rank. Therefore, in the higher ranks, going from 4th -> 3rd is a massive gain, and 3rd -> 4th a massive loss, thus encouraging a "4th place avoidance" playstyle.
- In the lower ranks of both clients, the 4th place penalty isn't huge yet, so newer players don't need to obsess over 4th place avoidance.
- In Riichi City, the rank point spread is mostly even between placements; going from 4th <-> 3rd is about identical to 3rd <-> 2nd or 2nd <-> 1st. While there's no special need for 4th place avoidance, it's still good to be conscious of placements when nearing the end of a game.
External links
- Oka and uma in Japanese Wikipedia