Oka and uma

At the end of the game, the raw scores are converted into an "end game score". This is most commonly referred as the plus-minus (+/-) score. The four end game scores are always set up to sum with zero. However, due to rounding errors, it is possible for the scores to equal to 1 or -1. In this case, the leader's or that of last place end game score is adjusted to ensure a zero sum.

Oka and uma

The oka 「オカ」 is the point difference between the start score and the target score; and then it is multiplied by the number of players. In general, this can be viewed as the "ante". Typically, the start score and target score are 25,000 pts and 30,000 pts respectively. So, in this case the oka is 5,000 x 4. At the end of the game, the oka is awarded to the winning player.

The uma 「ウマ」 is the set point spread applied to the players at the end of the game. The typical point spread uses the format of (+A/+B/-B/-A), where A > B. Of course, the point spread does not necessarily have to follow that pattern, by which the spread does not have to be symmetric. In general, the point spread can be set to any value as long as the four numbers add up to zero. Point modifications may be used either to ease the conditions or increase the difficulty, particularly for tournament settings.

Procedure

The end game score is calculated as follows:

Raw are taken at the end of the game, naturally ordered by the final point values.
Note the start score and target score point difference, find the oka.
Subtract the target score from the final point values.
Add the oka to the winner.
Divide by 1,000.
Round to the nearest integer. If the division result produces a digit of 0.5, then the number is rounded down.
Apply the uma spread, if any.
If the sum of all four does not equal to zero, then the winner's score is adjusted to produce a zero sum.

Due to rounding, the final values may not add up to zero. Therefore, it may become necessary to alter the winner's score. Usually, the difference is only +/- 1.

End score = (((Raw points + Oka - (Target - Start))/1000) + Uma

Shortcut

End game results with raw scores and uma scores

This short cut only applies to the distribution of (+20/+10/-10/-20). Using the procedure above, suppose all players unrealistically finish with 25,000 points each. The target points is 30,000 as standard.

End points	Oka	Minus target	Add oka	Div 1000	Rounded	+/-	End score	Diff. from 2nd column
25000	20000	-5000	15000	15	15	+20	35	+10
25000	0	-5000	-5000	-5	-5	+10	5	-20
25000	0	-5000	-5000	-5	-5	-10	-15	-40
25000	0	-5000	-5000	-5	-5	-20	-25	-50

As a shortcut, the adjustment can use the scores in the first column. Then the scores can be divided by 1000 and rounded. Finally, the values in the last column can be used to adjust for the final scores. Once again, this only works with the regular (+20/+10/-10/-20) uma.

Just to show, the values in the image to the right are used:

End points	Oka	Minus target	Add oka	Div 1000	Rounded	+/-	End score	Diff. from 2nd column
35700	20000	5700	25700	25.7	26	+20	+46	+10
32400	0	2400	2400	2.4	2	+10	+12	-20
22200	0	-7800	-7800	-7.8	-8	-10	-18	-40
9700	0	-20300	-20300	-20.3	-20	-20	-40	-50

If the original scores of (35700, 32400, 22200, 9700) were rounded and divided by 1000, the original scores would be converted to (36, 32, 22, 10). If (+10, -20, -40, -50) were added to the converted numbers, they would produce (46, 12, -18, -40).

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.

Tie-breaker

End game results with two players with the same raw scores.

In the event of tied scores at the end of a game, then the tie-breaker based on the initial wind seating (or the first hand) is applied. The player closest to the dealer position takes the higher position. Afterwards, the final score procedure takes into effect. Even with tied scores, the player in the lower position will receive a lower uma score.

External links

ウマ_(麻雀)

Oka and uma in Japanese Wikipedia

Barticle's guide