Test Run: Makushita Game

[Itachi 396]

Makushita Game: Standings Nagoya 2005

Position

Sum Top 3 Shikona Top 3 wins Top 2 wins Top 1 wins Sum

1 1 Susanoo 11 9 5 25

2 2 Doitsuyama 11 7 5 23

3 10 Yubiquitoyama 8 7 6 21

4 5 Hamanoyama 9 8 4 21

5 4 Itachi 10 7 4 21

6 9 Kaihayaiha 9 6 5 20

7 12 sashimaru 8 6 5 19

8 8 Zenjimoto 9 7 3 19

9 7 Torideyama 9 6 3 18

10 3 sekihiryu 11 6 1 18

11 15 Asashosakari 7 5 4 16

12 6 Oshirokita 9 4 3 16

13 16 Kintamayama 7 5 3 15

14 18 Gusoyama 7 5 3 15

15 20 Feginowaka 7 5 3 15

16 21 Takamueda 6 4 4 14

17 19 Flohru 7 4 3 14

18 13 Senpai 7 5 1 13

19 11 Randomitsuki 8 4 1 13

20 23 Holleshoryu 6 3 3 12

21 17 Sakana 7 4 1 12

22 14 Tamanaogijima 7 5 0 12

23 22 Hakanonami 6 4 1 11

24 24 Gernobono 5 3 1 9

Here is my attempt at posting an excel file.

The columns aren't lining up regardless of how I arrange them on my own speadsheet in excel so I'd appreciate tips on how to fix it up.

Anyway, the columns after the shikona are the number of wins under top 3, 2, and 1. The last column is the sum as I suggested.

The first column is obvious, the second is the rankings under top 3 as presented by Randomitsuki.

Though I lost a spot under this, I think it better reflects the original stated object of the game which was to pick the winners of each bracket. We all get consolation points for picking top 2 and 3 but the biggest reward goes to top 1 picks. Oshirokita sits just above the median and so he would be the last 8-7 when the scores are translated to records of 15.

What do you think? I'm sure Yubi-zeki likes it better.

Itachi

Edited July 24, 2005 by Itachi

[Asashosakari 19,627]

I think if we're going to go with some kind of points-based scoring it's easier to just use Doitsuyama's suggestion and add up the wins of the 15 picks. Serves the same purpose and would probably be much easier to score than having to assign Top 1/2/3 status to all picked rikishi. (I scored my own guess after Day 12 and it was rather time-consuming; I can only imagine how long it took Randomitsuki to do the same thing for 24 players, even with repeating picks.)

[Doitsuyama 1,192]

Yes, right. Itachi's scoring method just fails to provide a handy 0-15 to 15-0 score. If this is not a given, just sum the wins and don't make such complicated second-hand-derived methods.

We might look slightly dull to just take the top three out of eight. But fact is that this isn't an easy game, so you can't expect great results. The top three of eight is a line of 62.5% which would for example be a hugely satisfying quote in Sekitoto, so it isn't really too easy.

Edit: The line is lower than .625 due to ties for third which also qualify for a full shiroboshi, I think. The number of rikishi per bracket are 4, 4, 3, 3, 4, 3, 6, 5, 3, 5, 3, 3, 4, 6, 6. In fact, this is less than .500, which indeed a bit unsettling. The groups of 6 rikishi even include all 3-4 rikishi. I must say that the scoring indeed is looking too generous this way.

Maybe it would be wise, NOT to give a shiroboshi for make-koshi rikishi, be they in the top three or not. And maybe we could give half a shiroboshi for rikishi who are only tied third (@Randomitsuki: Did you give shiroboshi for these?). Those halves could be rounded up in the end. The scoring of the beta test would go down a bit with these suggestions, but I think there should be some competition to get a kachi-koshi with such a method...

Edited July 24, 2005 by Doitsuyama

[Doitsuyama 1,192]

When I think a bit about it, I just like the sum of the wins most. Top three of eight isn't that great a method to start with to have a great visual appeal, especially if this in fact means more than half with all the tied third places. And sum of the wins just is the fairest method, I guess.

[Asashosakari 19,627]

In case anyone's wondering why the scoring is so bad, here's how the top picks in each bracket did. ;-)

Top 1:

ms5-8: Baruto

ms25-28: Takanoyama

ms37-40: Koryu

Top 2:

ms13-16: Dewaotori

ms45-48: Saita

ms49-52: Wakakirin

Top 3:

ms1-4: Shiraishi

ms53-56: Kotonomine

ms57-60: Shibuya

less:

ms9-12: Bushuyama

ms17-20: Kotokanyu

ms21-24: Tamarikido

ms29-32: Nakanokuni

ms33-36: Gokenzan

ms41-44: Kasugakuni

I must admit that's worse than even I expected, and I didn't have particularly high hopes for the scores in this game to begin with. ;-)

[Randomitsuki 2,843]

I tend to agree with an earlier post by Zenjimoto and stick with the 15-brackets / 15 bouts analogy. That's what makes this game tick. If I had opted for a Gunga-style or Fantasy Sumo-style or Hoshitori-style game I wouldn't even have started with 15 rikishi.

However, I agree that being among the top 3 sounds awful, especially if you consider the number of ties involved. Just to count kachi-koshi is an idea that I do not like so much. If a bracket is crappy and has only make-koshi rikishi, it shouldn't be the fault of the players.

When I have more time, I will check the results for alternative scoring methods that involve the 15-bracket / 15 bouts idea. For instance by counting all rikishi above the bracket median, or by exploiting (standard) deviations.

A question to the experts (hey, that's you). I have never followed Makushita before, so I don't know if this basho was somehow exceptional in terms of surprises. There were quite a lot of successful rikishi that none of us had been picking (Takamifuji 6-1, Kitataiki 5-2, Nodera 5-2, Yotsuguruma 5-2, Kotohikari 5-2, Aogifuji 5-2). Considering that we had only 27 unpicked rikishi in this game, the number of unpicked guys finishing 5-2 or better seems very high to me. Is this "normal"? In other words, is Makushita known for so many surprise effects? Or was it just a highly unusual basho? This would of course affect the choice of scoring methods.

Anyway, please do not hesitate to suggest other scoring methods although I guess it can be difficult to convince me of a method that is not relying on 15 brackets with a 15-0 score system.

[Randomitsuki 2,843]

Oh, and here are the results (who picked whom). May include errors made by transferring your picks or with respect to the rikishi records or errors of any other kind.

To make this table at least somewhat readable I have taken the liberty to shorten your shikonas. Sorry for that.

Ugly table below.

Makushita Game: Rikishi Records Nagoya 2005

Bracket #1st place2nd place3rd place1Masatsukasa 6-1 (Hama)Raiko 5-2 (Toride)Shiraishi 4-3 (Itachi, Susanoo, Mueda, Doit, Senpai, Tamana, Oshiro); Dairaido 4-32Ryuho 5-2 (Holle, Haka); Baruto 5-2 (Kaiha, Kinta, Itachi, Rando, Toride, Guso, Sakana, Susanoo, Fegi, Mueda, Doit, Senpai, seki, Zenji, Oshiro, Asasho, Hama, Yubi)[/td]Kakuryu 4-3; Homasho 4-33Hochiyama 6-1 (Doit, Asasho, Yubi)Daishoma 5-2 (Susanoo, Senpai, seki, Zenji); Wakainami 5-24Takamifuji 5-2Dewaotori 4-3 (Kintama, Itachi, Susanoo, Doit, Haka, seki, Tamana, Zenji); Surugatsukasa 4-3 (Senpai, Oshiro, Hama)5Mokonami 6-1 (Itachi, Susanoo, Yubi)Oga 5-2 (Toride, Tamana, Hama)Hokutoiwa 4-3 (seki); Dewanofuji 4-3 (Guso, , Sakana, Holle)6Kitataiki 5-2; Satoyama 5-2 (Kaiha, Itachi, Sakana, Susanoo, Doit, Zenji); Nodera 5-27Takanoyama 4-3 (Kaiha, Itachi, Guso, Fegi, Mueda, Holle); Kakureizan 4-3Kirinowaka 3-4 (sashi, Asasho); Asahibenten 3-4 (Gerno); Ichinotani 3-4 (Kinta, Rando, Sakana, Doit, Oshiro, Floh); Ryugi 3-48Nishikikaze 5-2 (Kinta, Gerno, Toride, Guso, sashi); Tochitenko 5-2 (Susanoo)Kaonishiki 4-3 (Rando); Yutakamaru 4-3 (seki); Kotokuni 4-3 (Floh)9Nakao 7-0 (Kaiha, sashi, Zenji, Oshiro, Floh)Fukuzono 5-2 (Senpai); Matsumidori 5-2 (seki, Tamana)10Yotsuguruma 5-2; Koryu 5-2 (Kinta, Rando, Fegi, Doit, sashi, Asasho, Hama, Yubi, Floh)Musashifuji 4-3 (Toride, Holle, Haka, Oshiro); Terukaze 4-3 (Kaiha, seki); Daisogen 4-311Tenichi 6-1 (Kaiha, Toride, Mueda, Hama)Kirinoumi 4-3 (Itachi, Sakana); Rikiryuyama 4-3 (Susanoo, Haka)12Kimurayama 6-1 (Susanoo, Mueda, Doit, Senpai, sashi, Asasho, Yubi, Floh)Saita 5-2 (Gerno, Itachi, Rando, Guso, Sakana, Fegi, seki, Tamana, Zenji, Hama)Tatsuyutaka 4-3 (Toride)13Hoshihikari 5-2 (Holle)Wakakirin 4-3 (Kaiha, Kintama, Gerno, Rando, Guso, Susanoo, Asasho, Hama, Yubi); Wakatenro 4-3 (Toride, Fegi, Doit, seki, sashi, Tamana, Zenji, Floh); Omusashi 4-314Kotohikari 5-2; Munakata 5-2 (Haka, Oshiro, Yubi)Chokozan 3-4 (Hama); Kimenryu 3-4 (Gerno, Rando, Fegi, Tamana, Asasho); Tachigami 3-4; Kotonomine 3-4 (Kaiha, Kinta, Itachi, Doit, seki, sashi, Zenji, Floh)15Aogifuji 5-2; Enatsukasa 5-2 (sashi)

[Itachi 396]

Makushita Game: Standings Nagoya 2005

Position

Sum Top 3 Shikona Top 3 wins Top 2 wins Top 1 wins Sum

1 (12-3) 1 Susanoo 11 9 5 25

2 (11-4) 2 Doitsuyama 11 7 5 23

3 (10-5) 10 Yubiquitoyama 8 7 6 21

4 (10-5) 5 Hamanoyama 9 8 4 21

5 (10-5) 4 Itachi 10 7 4 21

6 (9-6) 9 Kaihayaiha 9 6 5 20

7 (9-6) 12 sashimaru 8 6 5 19

8 (9-6) 8 Zenjimoto 9 7 3 19

9 (9-6) 7 Torideyama 9 6 3 18

10 (9-6) 3 sekihiryu 11 6 1 18

11 (8-7) 15 Asashosakari 7 5 4 16

12 (8-7) 6 Oshirokita 9 4 3 16

13 (7-8) 16 Kintamayama 7 5 3 15

14 (7-8) 18 Gusoyama 7 5 3 15

15 (7-8) 20 Feginowaka 7 5 3 15

16 (7-8) 21 Takamueda 6 4 4 14

17 (7-8) 19 Flohru 7 4 3 14

18 (6-9) 13 Senpai 7 5 1 13

19 (6-9) 11 Randomitsuki 8 4 1 13

20 (6-9) 23 Holleshoryu 6 3 3 12

21 (6-9) 17 Sakana 7 4 1 12

22 (6-9) 14 Tamanaogijima 7 5 0 12

23 (5-10) 22 Hakanonami 6 4 1 11

24 (4-11) 24 Gernobono 5 3 1 9

Ok, there are a few ways of converting the raw sum to a score out of 15 and I chose one that would give the players above the median kk and those below mk. Also, it is possible to get 15 wins in this system without having a perfect record but since no one was even close, it wasn't necessary to do anything too fancy.

I just found a ratio that would make the median score of 15.5 into a score of 7.5/15, applied the ratio to all the scores and rounded to an integer. I assume we don't want to automatically give a 15/15 record to our top scorer and this method won't do that unless they score 30 or more. If lots of us scored so well, the median would be higher and the score to earn 15/15 would rise so I think this will give reasonable /15 scores but I could fit them to a normal curve if requested.

Doitsuyama and others have suggested merely using total wins as a score but I agree with Randomitsuki that the 15 brackets concept would be weakened and that (I think) is one of the interesting features of this game.

If the main complaint about my summing idea is that it doesn't convert to a score out of 15 easily then that is easily overcome. Many other games have raw scores not out of 15 and then convert them later. The Juryo game for example. Even Oshirokita's GTYW game has a raw score different from the eventual /15 score used for banzuke movement.

The sum of top1,2, and 3 rewards bracket winners and punishes those who fail to select rikishi that are even competitive in their brackets. No one will win only by fishing out on the top 3 but it is possible to do well with a few top1 and a majority of picks in the top2 and 3.

I don't want to give up on bracket by bracket scoring. Adjusting to /15 score is not that big a deal. Now if I could just get my Excel file lined up nicer in the post window...

Itachi

[Asashosakari 19,627]

Is this "normal"? In other words, is Makushita known for so many surprise effects?

<{POST_SNAPBACK}>

My somewhat speculative answer would be: yes. A couple of things that I think can result in surprising results in Makushita:

1) Nobody has any idea which rikishi might be entering the basho with injuries.

2) The schedule strength can be very different for rikishi who are ranked in the same area. To give a simplified example: Everybody in high Makushita who got an early bout against Kaido or Hakiai this basho was pretty lucky. Everybody who got an early bout against Baruto or Masatsukasa, not so much.

3) One simple case of luck on the dohyo (opponent slipping, mis-call by the gyoji or shimpan etc.) can be the difference between 3-4 and 4-3, which is a much bigger difference than between a sekitori's 7-8 and 8-7. Combine this factor with some luck of the schedule in another bout and somebody's 3-4 just turned into a 5-2 through basically no action of his own.

4) Sooner or later, every rikishi can be expected to have a 5-2 or 6-1 basho. Imagine an idealized Makushita division with 128 (not 120) rikishi. Because of the way the torikumi are made, this division would finish with one 7-0, one 0-7, seven 6-1 and 1-6, twenty-one 5-2 and 2-5, and thirty-five 4-3 and 3-4. In other words, almost one quarter of the division will go 5-2 or better, simply because there's no way they cannot. Real Makushita is of course just an approximation of that, but the logic still holds.

Now, an average career Makushita rikishi can be expected to have results that roughly follow the same distribution. In other words, the average Makushita guy should have one or two basho each year with at least 5 wins, and likewise one or two basho with 2 or fewer wins. Some of the time those results will be "logical", e.g. because he's ranked too high/too low for his abilities, but other times it will be a function of luck. Now consider that there are 120 rikishi in Makushita, so there's a lot of room for surprising results, in both directions. And since a quarter of the division has to end up 5-2 or better/2-5 or worse, it's pretty much guaranteed that some of those results will be caused by luck, rather than ability.

Edited July 24, 2005 by Asashosakari

[Itachi 396]

OH, I feel bad for not taking my long time adoptee Nishikikaze. The problem is I've been following him long enough to know he doesn't tend to do well at that level. Well, congratulations to him and to those who supported him.

Also, who did I take in the Hoshihikari bracket? I thought I was going to go for him... maybe it's just 20/20 hindsight kicking in... is that the Nakanokuni bracket?

[Randomitsuki 2,843]

OH, I feel bad for not taking my long time adoptee Nishikikaze. The problem is I've been following him long enough to know he doesn't tend to do well at that level. Well, congratulations to him and to those who supported him.

Also, who did I take in the Hoshihikari bracket? I thought I was going to go for him... maybe it's just 20/20 hindsight kicking in... is that the Nakanokuni bracket?

<{POST_SNAPBACK}>

In the Nishikikaze bracket you picked Nakanokuni (3-4).

In the Hoshihikari bracket you picked Tamawashi (3-4).

[Randomitsuki 2,843]

Thank you, Asashosakari, for sharing your insights. So I guess there is little hope that we perform much better next time.

Hm, I see a problem here. I just did a very quick and dirty check of results where you only get a win in a bracket if your picked rikishi was ABOVE the median. The results are shattering. Except for Susanoo (10-5), Doitsuyama (8-7), Itachi (8-7), and Hamanoyama (8-7) we all would get a make-koshi.

Let's admit it: we suck at this game! We can experiment with the numbers as much as we want. The fact of the matter is that the Top 3 method, while easy to calculate for everyone, was giving quite balanced results. Should we abandon this method just because our pride tells us that we should be sooo much better than chance, when in fact we hardly aren't?

[Asashosakari 19,627]

Let's admit it: we suck at this game! We can experiment with the numbers as much as we want. The fact of the matter is that the Top 3 method, while easy to calculate for everyone, was giving quite balanced results. Should we abandon this method just because our pride tells us that we should be sooo much better than chance, when in fact we hardly aren't?

<{POST_SNAPBACK}>

But, is it still an interesting game if a random number generator plays as well as experienced (or so we think) sumo gamers?

Since nothing beats real-life data, I just did simulate 5 runs of random picks. The randomizer's scores according to Top 3 scoring:

7-8

11-4

9-6

6-9

9-6

(I am not worthy...) That looks pretty much as well as we all did.

Maybe we'll need to reconsider one of Doitsuyama's ideas from earlier in the thread...perhaps scores would improve if players were allowed to pick 15 rikishi from all over the banzuke, instead of being locked into brackets? That would require a different scoring base of course...I'm tempted to say "one point for each rikishi that scores 5-2 or better", but I suspect that correctly picking 8 (for a kachi-koshi) of the about 30 possible rikishi could still prove difficult...

Edit: Well, this could be augmented by another of Doitsuyama's ideas (I feel I'm repeating myself here for some reason (Clapping wildly...)) by giving half-wins for each 4-3. Random picking of 15 rikishi should result in getting about three or four 5-2 or better, and four 4-3, which would mean a 5-10 to 6-9 record. That might provide a good baseline that human players should be able to beat....

Edited July 24, 2005 by Asashosakari

[Doitsuyama 1,192]

Edit: Well, this could be augmented by another of Doitsuyama's ideas (I feel I'm repeating myself here for some reason :-)) by giving half-wins for each 4-3. Random picking of 15 rikishi should result in getting about three or four 5-2 or better, and four 4-3, which would mean a 5-10 to 6-9 record. That might provide a good baseline that human players should be able to beat....

<{POST_SNAPBACK}>

I don't know. Maybe you could do another random test with that and tell us how this fares? (Enjoying a beer...)

[Asashosakari 19,627]

Random picking of 15 rikishi (...) would mean a 5-10 to 6-9 record.

I don't know. Maybe you could do another random test with that and tell us how this fares? (Enjoying a beer...)

<{POST_SNAPBACK}>

Sure enough, let's do that right now.

Well, 10 runs later, this is how the number generator would have done this basho (in brackets: picks at 5-2 or better + 4-3 picks):

2.5 wins (1 + 3)
7.0 wins (4 + 6)
4.0 wins (3 + 2)
6.0 wins (3 + 6)
7.5 wins (6 + 3)
3.0 wins (1 + 4)
6.5 wins (3 + 7)
4.5 wins (2 + 5)
8.0 wins (6 + 4)
4.5 wins (4 + 1)

In other words, all over the place from 3-12 to 8-7. The average was 5.35 wins on 3.3 "full" picks and 4.1 "half" picks. (Expected: 3.56 and 3.94 picks, for 5.53 wins.)

That does look like a decent enough baseline to me; the question is just if we're able to exceed that. :-)

Edited July 25, 2005 by Asashosakari

[Randomitsuki 2,843]

I have fiddled a little bit with the numbers (again), and upon some reflections I would like to try out a mixture of Doitsuyama's and Asashosakari's suggestions (why didn't you tell me beforehand that your scoring method is superior? (Applauding...)

I was looking at how we would have scored by adopting Doitsuyama's suggestion of giving one win for 5-2 or better, and half a win for a 4-3 score. If I am not mistaken, the chance number of wins with this method would be 5.46. Using the bracket method we already had an average value of 5.77 wins. In other words, we were slightly better than random, but definitely not good enough to use the bracket system.

Therefore I suggest to use the rule of picking 15 Makushita rikishi at your discretion. This might give the necessary boost to allow for a good KK-MK distribution.

The only problem is that you can finish with a score like 7,5-7,5 or other half-wins. Maybe these half-wins should be rounded up or down depending what gives a better KK-MK distribution.

This model keeps the original idea of 15 single rikishi that can bring you 15 wins while being a little easier than the bracket system.

Edit: Wasn't aware of the intricacies of Poisson distributions, and had to change the number of expected wins by chance from 5.16 to 5.46.

Edited July 26, 2005 by Randomitsuki

[Itachi 396]

I guess I'm out voted.

I still like my simple solution better. It aheres to the original concept of winners in the 15 brackets being the most important and merely gives bonuses to those whose picks finish 2nd or 3rd.

The conversion to a score out of 15 is not difficult and many other games use scoring systems that must be converted to scores out of 15. I think the scores I posted are a reasonable measure of everyones relative success at this game.

That having been said, I'll be happy to participate in the Makushita game even without the brackets and with a different scoring system. It will be a little more difficult for me to make selections when I have to consider all 120 rikishi at once and not just 8 at a time though.

Oh, and it was a boy. Born yesterday. We just got home. The little fellow was good enough to wait until the tournament ended.

[Doitsuyama 1,192]

Oh, and it was a boy. Born yesterday. We just got home. The little fellow was good enough to wait until the tournament ended.

Congratulations!

(Applauding...) (I was stupid...) (Blowing horn...) (Blushing...)

[Manekineko 200]

Oh, and it was a boy.

<{POST_SNAPBACK}>

(Applauding...) (Blushing...) (I was stupid...)

Congratulations to happy parents!

[Torideyama 32]

Oh, and it was a boy. Born yesterday. We just got home. The little fellow was good enough to wait until the tournament ended.

<{POST_SNAPBACK}>

(I was stupid...) (Blushing...) (Applauding...) (Whistling...) (Whistling...)

Congratulations! Glad all are doing well.

Torideyama

(Clapping wildly...) (Clapping wildly...) (Clapping wildly...) (Clapping wildly...) (Clapping wildly...)

[Sakana 46]

Congratulations. (I was stupid...)

About Makushita Game : another beta-test in september ?

[Randomitsuki 2,843]

I guess I'm out voted.

I still like my simple solution better. It aheres to the original concept of winners in the 15 brackets being the most important and merely gives bonuses to those whose picks finish 2nd or 3rd.

The conversion to a score out of 15 is not difficult and many other games use scoring systems that must be converted to scores out of 15. I think the scores I posted are a reasonable measure of everyones relative success at this game.

Sorry for not (yet) including your suggestion. The reason why it is not my #1 preference have to do that your system is essentially like Hoshitori, i.e. uses weighted results. The top 1 method counts threefold, the top 2 method twofold, and the top 3 method once. If weighing (weighting?) the results becomes so central to the game, and if the score does not immediately reflect a 15 wins scenario, so the results have to be converted into a 15-win pattern, we could just go with number of wins per picked rikishi. This suggestion was made before, but I still would prefer something that can be calculated immediately by players themselves.

If the current suggestion also leads to results that are imbalanced, I am sure that both your suggestion and the one by Susanoo will be taken into account (that is, if someone still bothers to play after two "failed" bashos.

Oh, and it was a boy. Born yesterday. We just got home. The little fellow was good enough to wait until the tournament ended.

<{POST_SNAPBACK}>

Congratulations from me as well!!! I hope mother, child and father are fine!

About Makushita Game : another beta-test in september ?

<{POST_SNAPBACK}>

As can be seen from my comment to Itachi - yep, seems we'll have at least one more beta-test.

Anyway, I would suggest to take the sum of scores from the Nagoya Basho (Top 3 method) and from Aki Basho as the basis for a first Makushita Game Banzuke.

[Torideyama 32]

I don't remember seeing this suggestion in the thread, bu then again, maybe I missed it.

Why not keep the 15 blocks? Then, for each block, you get a win if your rikishiki gets a kachikoshi(4-3, 5-2, 6-1, 7-0). You get a loss if your rikishiki goes makekoshi (3-4, 2-5, 1-6, 0-7).

Alternate - you have to pick 3 rikishiki per block (45 total). Then you have to have 2 out of 3 go KK to get a win in that block. I know that this option triples the work for the gyoji.

I really like the game concept, and I realize that eventually my lack of knowledge will start to show in my scores, but it is a fun game to play.

Thanks for listening. (Laughing...)

Torideyama

[Randomitsuki 2,843]

Interviewer: Randomitsuki, do you have problems in making decisions?

Randomitsuki: Yes and no....

OK. First of all: Your input for devising a scoring method is appreciated (at least by me).

This game has many constraints in order to work:

Constraint #1: The Makushita Game should be different from other games. That's why I like the idea of 15 rikishi in 15 brackets giving you 15 chances for a win.

Constraint #2: The Makushita Game should be easy to play in terms of effort: This discards solutions like picking 45 rikishi.

Constraint #3: The Makushita Game should be easy to score - not for me, but for the players. I love games where you can in principle calculate the results for yourself. This discards solutions where your scores will be transformed.

Constraint #4: The Makushita Game should not be too easy in terms of random picking. The ideal would be if random picking gives you somewhere between 6 and 7 wins on average. This discards solutions like counting KK as a win.

Constraint #5: The Makushita Game should not be too difficult. We should have balanced standings. That is, our actual average number of wins should be at least 6.5.

I think that everybody likes the 15 rikishi in 15 brackets idea the most. The method of 15 discretionary rikishi from all over Makushita not only robs one nice game element, it also makes gameplay (choosing the rikishi) more difficult. Thanks, Itachi, for pointing that out.

In other words, if we can find a method where you pick 15 rikishi in 15 brackets, in which scores do not have to be converted, where random picking would give you about 6 wins, and where our own picks would at least be 6.5 wins - then we had a near-perfect solution. Agreed?

OK. Therefore I withdraw my "final" say on the rules for the Aki Basho, and suggest a new near-final solution. If you do not disagree with me too much, I would like to implement it as follows:

You pick 15 rikishi from 15 brackets.

A 4-3 gives you half a win.

A 5-2 gives you a full win.

A 6-1 gives you 1.5 wins

A 7-0 gives you 2 wins.

Yeah, I know that 2 wins for one rikishi is something to get used to, but I think it is the best suggestion so far. If you end up with half-wins (e.g. 6.5 or 7.5) your score will be rounded up!

A new advantage of this method is that picking 6-1 or 7-0 rikishi will be rewarded. Most methods suggested so far (except for sansho regulations) have not included this element.

Results of a test run:

Random picking (without rounding up) has an average of 5.99 wins.

Our Nagoya results (without rounding up) had an average of 6.27 wins.

Our Nagoya results (including rounding up) had an average of 6.5 wins.

I know that one has to get used to those half-wins. And I know that you might feel cheated seeing that your hard-earned 8.0 wins count just as much as somebody else's 7.5 wins. But remember that next time you could be the one with 7.5 wins.

I hope that you can live with this solution. Otherwise, we can discuss this game over and over again (which I do not hope).

Edited July 29, 2005 by Randomitsuki

[Doitsuyama 1,192]

I like your solution. You just should add that the maximum possible score will be 15-0. :-D How would the test run have been with that scoring?