Score table memorization: Difference between revisions

Revision as of 17:57, 7 April 2024

Memorizing the score table should only be done after learning the basic game procedures and yaku. While the score table is large, it can be memorized over time. At the very least, it is important to know the common point values, due to their importance in game strategy.

Counting Han / Fu

Hand scores can be expressed in terms of han and fu. In order to use the score table, you need to know how much the hand is worth. If you have not memorized the scoring table, you can calculate han/fu, then look at the table.

Han

Main article: List of yaku

Han is determined by the number and value of yaku in your hand. As a reminder, yaku can stack. Then, for each dora, one han is added. The total han is the hand's han value.

Fu

Main article: Fu

Fu starts at 20 fu. It is then determined by:

The type and number of triplets and kan calls.
- Each triplet is worth a base of 4 fu, half if an open triplet, double if a terminal or honor tile.
- Each kan is worth a base of 16 fu, half if an open kan, double if a terminal or honor tile.
- Note: a win by ron opens the triplet, reducing the fu count.
The wait of the hand. Tanki, kanchan, and penchan waits are worth +2 fu. The others are worth +0 fu.
If the hand has a yakuhai pair. A pair of yakuhai (dragons, round wind, seat wind) are worth +2 fu. A pair of a wind that is both round + seat wind is often worth +4 fu, but some rules score it as +2 fu.
Method of winning. Tsumo is +2 fu unless pinfu. A closed hand ron is +10 fu. Open hand ron is 0 fu.
Special cases: Chiitoitsu is always set to 25 fu. An open hand with 20 fu is bumped up to 30 fu.

Finally, fu is rounded up to the next interval of 10 fu, unless it is chiitoitsu. This rounding makes it easier to memorize the hand values.

Common Fu Values

The most common values of fu, by far, are:

30 fu - Most open hands; most closed hand tsumo; pinfu ron
40 fu - Closed hand ron; most open toitoi
20 fu - Pinfu + tsumo
25 fu - Chiitoitsu

Therefore, by learning point values for 1-4 han and each of 20 fu, 25 fu, 30 fu, and 40 fu, you'll cover a large majority of cases.

If a hand has declared kan, has at least 2 closed simple triplets, or 1 closed terminal/honor triplet, it is likely that the hand deviates from these shortcut values.

Mangan

Once a hand reaches 5 han, 4 han 40 fu, or 3 han 70 fu, it reaches mangan, and fu no longer matters for scoring. From mangan onwards, only han determines score. Mangan-or-higher hands are easy to remember - they all have round, convenient numbers and specific names (haneman, baiman, etc.).

Therefore, for any possible hand, it is not needed to learn fu values for 5+ han.

Common Patterns

Point patterns for ron

Overall, the majority of the points in the scoring table pertaining to ron can be learned with these patterned numbers:

1000 -> 2000 -> 3900 -> 7700
1300 -> 2600 -> 5200
1500 -> 2900 -> 5800 -> 11600
1600 -> 3200 -> 6400
2400 -> 4800 -> 9600

The sum of tsumo values are equal or almost equal to these particular numbers.

Tsumo vs ron

The total points gained from a tsumo is identical, or nearly identical, to the points from ron. When a non-dealer wins by tsumo, the dealer pays ~50% of the points, and the other players pay ~25% of the points. When a dealer wins by tsumo, the other players split points equally.

Most differences between tsumo and ron come from rounding. For example:

A 1 han 30 fu ron is worth 1000 points.
If you split that number by 50% dealer/25% non-dealer, then the dealer would pay 500 points and both non-dealers would pay 250 points.
Points in mahjong are always rounded to the hundreds place, so 250 is rounded up to 300.
Thus, a 1 han 30 fu tsumo earns 500/300 (500 + 300 + 300), or 1100 points.

+1 han = doubled fu

When a hand gains +1 han, it is equivalent to doubling the hand's fu. (This does not apply for mangan+ hands.)

1 han 40 fu = 2 han 20 fu
1 han 80 fu = 2 han 40 fu = 3 han 20 fu
2 han 30 fu = 1 han 60 fu
3 han 50 fu = 4 han 25 fu

Therefore, you can multiply fu by 2, then subtract 1 han, and end up with the same score value. You can also add 1 han, then divide fu by 2, and end up with the same score. This means by memorizing the 30 fu values, you will also memorize the 60 fu values. By memorizing the 25 fu values, you will also memorize the 50 fu values.

Mangan and more

Hands at mangan or higher are always worth a set amount.

Mangan or greater		Dealer		Non-Dealer
Name	Han	Ron	Tsumo†	Ron	Tsumo
Mangan	3 (70+ fu) 4 (40+ fu) 5	12000	4000	8000	4000/2000
Haneman	6 or 7	18000	6000	12000	6000/3000
Baiman	8, 9, or 10	24000	8000	16000	8000/4000
Sanbaiman	11 or 12	36000	12000	24000	12000/6000
Yakuman	13+ Any yakuman	48000	16000	32000	16000/8000
† Dealer tsumo applies to all non-dealer players

Common point values

Due to the size of the scoring table, it is important to know the most common values first. Other than the mangan+ hands, knowing the (1-4 han) + (20, 25, 30, 40) fu hands are the more important.

30 and 40 fu

30 and 40 fu are the most common point values, so it is logical to start here. The smallest possible hand is 1 han 30 fu from ron, which is worth 1000 points.

Position	1 han 30 fu	2 han 30 fu	3 han 30 fu	4 han 30 fu
Non-dealer tsumo Non-dealer ron	300/500 1000	500/1000 2000	1000/2000 3900	2000/3900 7700
Dealer tsumo Dealer ron	500 1500	1000 2900	2000 5800	3900 11600

Position	1 han 40 fu	2 han 40 fu	3 han 40 fu
Non-dealer tsumo Non-dealer ron	400/700 1300	700/1300 2600	1300/2600 5200
Dealer tsumo Dealer ron	700 2000	1300 3900	2600 7700

25 fu

Only hands with chiitoitsu can score 25 fu. Unlike all other hands, the fu for chiitoitsu is not rounded - it always remains at 25 fu.

Position	2 han	3 han	4 han
Non-dealer tsumo Non-dealer ron	400/800 1600	800/1600 3200	1600/3200 6400
Dealer tsumo Dealer ron	800 2400	1600 4800	3200 9600

Doubled point values

As mentioned above, adding one han is equivalent to doubling the hand's fu. This rule makes it easier memorize, say, 20 fu, if you already know the 40 fu values.

20 fu and 40 fu

Only hands with pinfu + menzen tsumo can score 20 fu. Pinfu with ron is worth 30 fu (+10 from closed ron). From the 40 fu values, you can add 1 han and divide fu by 2 to reach the 20 fu values. Therefore, you can memorize the 20 fu values by memorizing the 40 fu values.

Position	1 han 40 fu = 2 han 20 fu	2 han 40 fu = 3 han 20 fu	3 han 40 fu = 4 han 20 fu
Non-dealer tsumo Non-dealer ron	400/700 1300	700/1300 2600	1300/2600 5200
Dealer tsumo Dealer ron	700 2000	1300 3900	2600 7700

25 fu and 50 fu

Now, the 25 fu values can be doubled to 50 fu. So, knowing the "chiitoitsu" point values, one would already know the 50 fu column.

Position	2 han 25 fu = 1 han 50 fu	3 han 25 fu = 2 han 50 fu	4 han 25 fu = 3 han 50 fu
Non-dealer tsumo Non-dealer ron	800/400 1600	1600/800 3200	3200/1600 6400
Dealer tsumo Dealer ron	800 2400	1600 4800	3200 9600

Continuing the equivalences place the point values at mangan.

30 fu and 60 fu

Position	2 han 30 fu = 1 han 60 fu	3 han 30 fu = 2 han 60 fu	4 han 30 fu = 3 han 60 fu
Non-dealer tsumo Non-dealer ron	500/1000 2000	1000/2000 3900	2000/3900 7700
Dealer tsumo Dealer ron	1000 2900	2000 5800	3900 11600

70 fu and more

This portion of the scoring table is the least used. Hands scored at 70+ fu rarely occur; but they most certainly do occur. To score 70+ fu, the hand needs the large amount of fu generated by closed kan involving terminal or honor tiles. Otherwise, the hand may also involve any multiple kan calls. Furthermore, the 70+ fu scores only apply to 1 or 2 han hands. With 3 han or more, the value is already set to mangan.

	Dealer					Non-Dealer
	70	80	90	100	110	70	80	90	100	110
1 han	1200 3400	1300 3900	1500 4400	1600 4800	1800 5300	600/1200 2300	700/1300 2600	800/1500 2900	800/1600 3200	900/1800 3600
2 han	2300 6800	2600 7700	2900 8700	3200 9600	3600 10600	1200/2300 4500	1300/2600 5200	1500/2900 5800	1600/3200 6400	1800/3600 7100

Point equivalences continue to apply for the 40 fu and 80 fu column, as well as the 50 fu and 100 fu column. The columns for 70 fu, 90 fu, and 110 fu all produce unique point values not found elsewhere on the scoring table. Therefore, those may have to be memorized on their own. Again, they do not occur frequently; so it is best and practical to learn these values after learning the rest of the scoring table.

40 fu and 80 fu

Position	2 han 40 fu = 1 han 80 fu	3 han 40 fu = 2 han 80 fu
Non-dealer tsumo Non-dealer ron	700/1300 2600	1300/2600 5200
Dealer tsumo Dealer ron	1300 3900	2600 7700

50 fu and 100 fu

Position	2 han 50 fu = 1 han 100 fu	3 han 50 fu = 2 han 100 fu
Non-dealer tsumo Non-dealer ron	800/1600 3200	1600/3200 6400
Dealer tsumo Dealer ron	1600 4800	3200 9600

Once again, these two values are directly linked to the chiitoitsu values. However, these han and fu combinations do not apply to chiitoitsu. As a reminder, the equivalences are (2 han 50 fu = 3 and 25 fu) and (3 han 50 fu = 4 and 25 fu).

Impossible scores

There are no scoring values assigned for 1 han and 20 fu, 1 han and 25 fu, and 2 han and 25 fu (via menzen tsumo).

1 han and 20 fu (tsumo)

To score 20 fu, a hand must be pinfu + menzen tsumo. Pinfu and menzen tsumo are worth 1 han each, so a 20 fu hand needs a minimum of 2 han.

1 han and 25 fu

Chiitoitsu is by default worth 2 han and 25 fu. No other yaku worth 1-han can be set at 25 fu.

2 han and 25 fu (tsumo)

Chiitoitsu with menzen tsumo would be 3 han and 25 fu.

20 fu (ron)

Closed hands score +10 fu. An open hand which would otherwise be at 20 fu gains +2 fu for "open pinfu". Thus, you cannot ron with 20 fu; the lowest possible ron is 1 han 30 fu.

External links

麻雀の得点計算

Score table memorization in Japanese Wikipedia

@@ Line 1: / Line 1: @@
 [[Image:Scoring Table.png|right|350px]]
-Despite the size of the [[scoring table]], it is possible to memorize the table, in a manner similar to memorizing a multiplication table.  However, any attempt to learn the scoring table is fruitless without knowing particular prerequisites, like [[Naki|basic game procedures]] and the [[yaku]] with their han values.  As a recommendation, scoring is among the last of the more basic concepts of the game for any newer player to learn.
+'''Memorizing the [[scoring table|score table]]''' should only be done after learning the [[Naki|basic game procedures]] and [[yaku]]. While the score table is large, it can be memorized over time. At the very least, it is important to know the common point values, due to their importance in game strategy.
-== Overview ==
+==Counting Han / Fu==
+Hand scores can be expressed in terms of [[han]] and [[fu]]. In order to use the score table, you need to know how much the hand is worth. If you have not memorized the scoring table, you can calculate han/fu, then look at the table.
-The scoring table can be subdivided into sections.  Once a section of the scoring table is learned, then a player can move on to the next section and memorize that one.  It is an ongoing process, until the entire table is learned.  As it turns out, some sections share similar point values as other sections.
+===Han===
+{{Main|List of yaku}}
+Han is determined by the number and value of [[yaku]] in your hand. As a reminder, yaku can [[Yaku compatibility|stack]]. Then, for each [[dora]], one han is added. The total han is the hand's han value.
-==Han and fu==
+===Fu===
-Aside from the point values, hand scores can be expressed in terms of '''han''' and '''fu'''.  Players, who do not know point values, may depend on the combination of these two numbers and then rely on an available scoring table.
+{{Main|Fu}}
+Fu starts at 20 fu. It is then determined by:
-===Counting han===
+*The type and number of [[triplet]]s and [[kan]] calls.
-{{main|List of yaku}}
+**Each triplet is worth a base of 4 fu, half if an [[naki|open]] triplet, double if a [[terminal]] or [[honor]] tile.
+**Each kan is worth a base of 16 fu, half if an open kan, double if a terminal or honor tile.
+**Note: a win by [[ron]] opens the triplet, reducing the fu count.
+*The [[Machi|wait]] of the hand. [[Tanki]], [[kanchan]], and [[penchan]] waits are worth +2 fu. The others are worth +0 fu.
+*If the hand has a [[yakuhai]] pair. A pair of yakuhai ([[dragon]]s, round wind, seat wind) are worth +2 fu. A pair of a wind that is both round + seat wind is often worth +4 fu, but some rules score it as +2 fu.
+*Method of winning. Tsumo is +2 fu unless [[pinfu]]. A closed hand ron is +10 fu. Open hand ron is 0 fu.
+*Special cases: [[Chiitoitsu]] is always set to 25 fu. An open hand with 20 fu is bumped up to 30 fu.
-Counting han is simple memorization of the yaku and their han values.  As a reminder, various yaku may [[Yaku compatibility|stack and combine with other yaku]].  For each time a hand is scored, it becomes a matter of counting off the applied han.
+Finally, fu is rounded up to the next interval of 10 fu, unless it is chiitoitsu. This rounding makes it easier to memorize the hand values.
-===Counting fu===
+== Common Fu Values ==
-{{main|Fu}}
+The most common values of fu, by far, are:
-To count fu, a player must understand how fu is generated.  In essence, fu comes from the hand's composition and winning method.  Yaku has no bearing on the fu count, aside from required tile compositions of specific yaku.  The presence of [[koutsu|triplets]], [[kan]] calls, [[machi|closed waits]] (kanchan), and/or [[pair waits]] should be enough to prompt a player to look at a hand more carefully to count fu.
+*30 fu - Most open hands; most closed hand tsumo; pinfu ron
+*40 fu - Closed hand ron; most open [[toitoi]]
+*20 fu - Pinfu + tsumo
+*25 fu - Chiitoitsu
-The convenience of counting fu rests on rounding up.  Even a fu count of 32 fu gets rounded up to 40 fu.  So, when counting fu, it is helpful to note when the count crosses a multiple of 10.
+Therefore, by learning point values for 1-4 han and each of 20 fu, 25 fu, 30 fu, and 40 fu, you'll cover a large majority of cases.
-== Impossible scores ==
+If a hand has declared [[kan]], has at least 2 closed simple triplets, or 1 closed terminal/honor triplet, it is likely that the hand deviates from these shortcut values.
-There are no scoring values assigned for 1 han and 20 fu, 1 han and 25 fu, and 2 han and 25 fu (via [[menzen tsumo]]).
+===Mangan===
+Once a hand reaches 5 han, 4 han 40 fu, or 3 han 70 fu, it reaches [[mangan]], and fu no longer matters for scoring. From mangan onwards, only han determines score. Mangan-or-higher hands are easy to remember - they all have round, convenient numbers and specific names (haneman, baiman, etc.).
-* '''1 han and 20 fu''' (tsumo)
+'''Therefore, for any possible hand, it is not needed to learn fu values for 5+ han.'''
-:The hand must be a closed pinfu hand.  However, it gets paired with menzen tsumo; so it defaults as 2 han and 20 fu.
-* '''1 han and 25 fu'''
-:[[Chiitoitsu]] is by default worth 2 han and 25 fu.  No other yaku worth 1-han can be set at 25 fu.
-* '''2 han and 25 fu''' (tsumo)
-:Chiitoitsu with [[menzen tsumo]] would be 3 han and 25 fu.
-* '''20 fu''' (ron)
-:A notable possibility for this value exists for a hand, that may be considered as an "open pinfu".  In other words, it is an open hand, that takes the shape of pinfu.  Naturally, it is not classed as pinfu, but it still scores 2 fu for an open pinfu. As a result, for "ron" values, 20 fu is impossible; the lowest value possible value is at 1 han and 30 fu.
-==Scoring patterns==
+== Common Patterns ==
-Thankfully, the points arrange themselves into particular patterns.
 ===Point patterns for ron===
@@ Line 47: / Line 53: @@
 The sum of [[tsumo]] values are equal or almost equal to these particular numbers.
-=== Tsumo values ===
+===Tsumo vs ron ===
-Points for tsumo total exactly or closely to that of the ron values.  When a non-dealer wins by tsumo, then the dealer pays about half the total points.  The other half is split among the other two non-dealers equally.  For some ron values, the total is easily divisible by 4; where non-dealers each pay exactly half of what the dealer pays.  However, some values do not.
+The total points gained from a tsumo is identical, or nearly identical, to the points from ron. When a non-dealer wins by tsumo, the dealer pays ~50% of the points, and the other players pay ~25% of the points. When a dealer wins by tsumo, the other players split points equally.
+Most differences between tsumo and ron come from rounding. For example:
+#A 1 han 30 fu ron is worth 1000 points.
+#If you split that number by 50% dealer/25% non-dealer, then the dealer would pay 500 points and both non-dealers would pay 250 points.
+#Points in mahjong are always rounded to the hundreds place, so 250 is rounded up to 300.
+#Thus, a 1 han 30 fu tsumo earns 500/300 (500 + 300 + 300), or 1100 points.
+=== +1 han = doubled fu ===
+When a hand gains +1 han, it is equivalent to doubling the hand's fu. (This does not apply for mangan+ hands.)
+*1 han 40 fu = 2 han 20 fu
+*1 han 80 fu = 2 han 40 fu = 3 han 20 fu
+*2 han 30 fu = 1 han 60 fu
+*3 han 50 fu = 4 han 25 fu
+Therefore, you can multiply fu by 2, then subtract 1 han, and end up with the same score value. You can also add 1 han, then divide fu by 2, and end up with the same score. This means by memorizing the 30 fu values, you will also memorize the 60 fu values. By memorizing the 25 fu values, you will also memorize the 50 fu values.
 === Mangan and more ===
+Hands at mangan or higher are always worth a set amount.
-{| class="wikitable" align=right
+{| class="wikitable"
 |-
 !colspan=2| Mangan or greater
@@ Line 73: / Line 95: @@
 |}
-For '''mangan''' {{kana|満貫}} and beyond, a point cap is applied, such that counting fu may not be necessary.  Fu will still be counted; but for scoring purposes, it is not necessary to count fu, due to the cap on the basic points calculation.  Mangan begins with hands valued at 3 han and 70 fu, 4 han and 40 fu, or 5 han.  For each, if the fu count is greater, they are retained at mangan.
+==Common point values==
+Due to the size of the scoring table, it is important to know the most common values first. Other than the mangan+ hands, knowing the (1-4 han) + (20, 25, 30, 40) fu hands are the more important.
-So, this section of the scoring table easy to remember.  For easier memorization, these higher values possess specific names, namely: haneman, baiman, sanbaiman, and yakuman.  Likewise, they are worth factors more than mangan.
-* '''Haneman''' {{kana|跳満}} = 50% more than mangan
-* '''Baiman''' {{kana|倍満}} = 100% more than mangan (double)
-* '''Sanbaiman''' {{kana|三倍満}} = 200% more than mangan (triple)
-* '''Yakuman''' {{kana|役満}} = 300% more than mangan (quadruple)
-By far, these are the easiest numbers to remember because they are round, convenient numbers.  The names for each makes it even easier.  Plus, their amounts are highly desired.
-==Common values==
-Despite the full range of the entire scoring table, the more frequent score combinations are best to focus on, after the simpler mangan+ scores.  The frequent occurrence of the common scores will end up becoming more routine with each scoring hand.
 ===30 and 40 fu===
-Among the hands valued at 1 han to 4 han, the most common scores involve 30 fu or 40 fu.  So, among the han-fu combinations, this is the most logical section to start.
+and 40 fu are the most common point values, so it is logical to start here. The smallest possible hand is 1 han 30 fu from ron, which is worth 1000 points.
-Naturally, the first score to consider involves 1 han and 30 fu.  Of all the hand values possible, this is the smallest.  While the 20 fu values exist, 1 han and 20 fu does not, as no hand can be valued as such.  For non-dealer ron, the points for 1 han and 30 fu is 1000, or '''senten'''.  For non-dealer tsumo, it is 300/500 or 500/300, which may be referred as '''gomii'''.
 {| class="wikitable" width=70%
@@ Line 111: / Line 120: @@
 ===25 fu===
-The 25 fu column involves the yaku, [[chiitoitsu]].  This yaku is unique enough, such that it has its own fu column dedicated to it. The uniqueness stems from its own hand pattern, as it does not follow the typical "4 tile [[Mentsu|groups]] and a [[Jantou|pair]]" pattern like most hands.  Unlike the general rule to counting fu, the fu for chiitoitsu is not rounded.  Instead, it remains at 25 fu.  This is set by definition.
+Only hands with [[chiitoitsu]] can score 25 fu. Unlike all other hands, the fu for chiitoitsu is not rounded - it always remains at 25 fu.
 {| class="wikitable" width=70%
@@ Line 122: / Line 131: @@
 |}
-Once again, a chiitoitsu valued at 5 han or greater follows the "mangan" scoring pattern.
+==Doubled point values==
+As mentioned above, adding one han is equivalent to doubling the hand's fu. This rule makes it easier memorize, say, 20 fu, if you already know the 40 fu values.
-==Point equivalences==
-Various point values are equivalent among the different han and fu combinations.  By recognizing the equivalences, this eases the task of memorization, when one section or column of the scoring table is learned.
-In general, if a fu count is divisible by 2 and a fu column of that result exists, then the points are equivalent to a han-fu combination of 1+ han.  For example, 3 han and 60 fu is equivalent to 4 han and 30 fu.  Both han and fu combinations score 7700 points for non-dealer ron, 11600 for dealer ron, 2000/3900 for non-dealer tsumo, and finally 3900 from all for dealer tsumo.  Various other similar scoring equivalences exist throughout the scoring table.  In a sense, as long as one learns the 25 fu, 30 fu, and 40 fu score columns, then most of the other fu columns fall on simple equivalency.
 ===20 fu and 40 fu===
+Only hands with [[pinfu]] + [[menzen tsumo]] can score 20 fu. Pinfu with ron is worth 30 fu (+10 from closed ron). From the 40 fu values, you can add 1 han and divide fu by 2 to reach the 20 fu values. Therefore, you can memorize the 20 fu values by memorizing the 40 fu values.
-Hands with 20 fu only applies to [[pinfu]] with [[menzen tsumo]].  This yaku is defined as a hand that does not earn fu.  Although, it still earns the 10 fu with closed ron.  Otherwise, the hand does not produce fu by any other means.
 {| class="wikitable" width=70%
@@ Line 145: / Line 148: @@
 ===25 fu and 50 fu===
-Now, 25 fu can be doubled to 50 fu.  So, knowing the "chiitoitsu" point values, one would already know the 50 fu column.
+Now, the 25 fu values can be doubled to 50 fu.  So, knowing the "chiitoitsu" point values, one would already know the 50 fu column.
 {| class="wikitable" width=70%
@@ Line 210: / Line 213: @@
 Once again, these two values are directly linked to the chiitoitsu values.  However, these han and fu combinations do not apply to chiitoitsu.  As a reminder, the equivalences are (2 han 50 fu = 3 and 25 fu) and (3 han 50 fu = 4 and 25 fu).
+== Impossible scores ==
+There are no scoring values assigned for 1 han and 20 fu, 1 han and 25 fu, and 2 han and 25 fu (via [[menzen tsumo]]).
+* '''1 han and 20 fu''' (tsumo)
+:To score 20 fu, a hand must be pinfu + menzen tsumo. Pinfu and menzen tsumo are worth 1 han each, so a 20 fu hand needs a minimum of 2 han.
+* '''1 han and 25 fu'''
+:[[Chiitoitsu]] is by default worth 2 han and 25 fu. No other yaku worth 1-han can be set at 25 fu.
+* '''2 han and 25 fu''' (tsumo)
+:Chiitoitsu with [[menzen tsumo]] would be 3 han and 25 fu.
+* '''20 fu''' (ron)
+:Closed hands score +10 fu. An open hand which would otherwise be at 20 fu gains +2 fu for "open pinfu". Thus, you cannot ron with 20 fu; the lowest possible ron is 1 han 30 fu.
 ==External links==