Classic Tetris World Championship and the evolution of competitive gaming

CTWC 2020 Group C final, Dog vs. Koryan G3.

Classic Tetris World Championship (CTWC) refers to the tournament on NES Tetris that has been flourishing in the past 10 years. Unlike modern games like Tetris Battle and Puyopuyo Tetris, the rules for NES Tetris is quite different. That's because new Tetris games must follow a given set of guidelines in order to get the trademark. 

But before that we had the Grandmaster series that used the Akira rotation system (ARS) or Sega rotation system (SRS). Even more primitively there was the Nintendo rotation system (NRS) for NES Tetris, where most modern mechanics like lock delay and wall kick did not exist. 

*For more about NES Tetris and CTWC this is a very nice introduction video.

So what's fun about this ancient system of tetris that is hard to deal with, and even theoretically not sustainable forever?

It turned the game into a really good candidate of extreme solo e-sport via score attack.

The brutalness of the classic rules ensures players to adopt already special techniques to start with, either the delayed auto shift(DAS) or hypertapping. The absence of lock delay means that the reaction time will be extremely limited. Together with the lack of hold pieces and "7 bag" pseudo randomness that requires a balance between aggressiveness and sustainability, which further boosts the difficulty of making the right decisions. The lack of wall kick and modern spins makes planning harder, but the game is a lot more accessible to general public -- you can place the pieces in a certain position if and only if you can do that with reality physics. NES Tetris, the one with the most simple rules, is simply the easiest to understand.

Extreme input requirements, balance between strategies and high accessibility combines into a potent game for extreme e-sports: unlike FPS or other multiplayer games, these are stages for soloist to show what happens when you push the game to its extreme, to the boundary between software restriction and hardware restriction. 

CTWC has been held since 2010, but it had very little attraction until recent years when memes were grown out of nowhere [boom tetris for Jeff] and a great community is eventually built. 

Throughout the years, we have observed a steady growth of the average skill level among the players.

In early years, players may start from as low as level 9, and level 19 gameplay was treated as a premium. Maxing out a game was extremely rare (in 2010 Harry was given the automatic spot just because he had a max out -- not even in a given set of time but in his gameplay history). Then in the years after the choices were usually between level 15 and 18.

[Note: simply speaking level 15, 18 and 19 are the three fastest feasibly playable speed in NES tetris. One may choose to start from higher level to gain higher score. Starting from level 18, a change to level 19 occurs at line 130, which is known as *the* transition. There is another transition to "kill screen speed" at level 29 or 230 lines from level 18. Level 29 speed were thought impossible to play for no more than a few pieces, but this has changed in recent years.]

Starting from the reign of Jonas however, flexing in level 19 had became the standard among the upper seeds. Players are expected to reach the kill screen and score above 800k regularly. 

More recently with the bloom of hypertappers, reaching the kill screen is nothing special anymore. We are not just observing players at "maxout pace" before transition, but they hold on and actually maxout occasionally. 

Among the hypertappers Joseph (@JdMfX_) is definitely one of the best. His hypertapping skills allowed him to play extremely consistently at level 19 and actually made level 29 gameplay possible. He can casually reach level 30 (10 lines into kill screen) and all the way up to level 35[https://www.youtube.com/watch?v=1k7bk3ynKjA]. 

He outflexed Jonas in 2018 and had a great match against Greentea in 2019.

Then in 2020...he was knocked down in the quarterfinal.

So what happened? Well, the top 8 this year is completely composed of players that are almost as good as him. His match with Huff isn't exactly the best from him, and together with same bad luck he was out. 

CTWC 2020 is entirely different from CTWC 2019. Not only that Joseph was knocked down, but all the veterans and even players ranked up high in the 2019 tourneys were taken down in early stages like Jeff (he still got a lot of booms and neck and neck commentaries though), Jonas, Svavar and Koryan. They were just taken down by players out of nowhere (that is, unless you are a close follower of the monthly tournament too).

Among these the battle between Koryan and champion Dog is the absolute must-watch. It ended up as a 3-0 sweep but the stats are just crazy. 5.9 maxouts (one 989k) and 4 1.1mils; 5.9 kill screens (one 229 lines) and 4 234+ lines (and one level 30). 1.1 mils and playing into level 29 is simply unimaginable in the past, yet it happened in real matches this year. Even more thrilling is that the last two games ended up with a score difference of about 1500 and 400 respectively. Had Koryan optimize even the slightest he could have won one or two games -- this is how close the match was. 

There are a few reasons behind this great shift in competitiveness, but they boil down to the fact that the community grew big enough to produce enough hypertappers that flooded the tournament.

CTWC gained more attraction since 2016-18 and that had paid off in recent years. A big portion of new players said that they started playing NES tetris because they watched 2016-19 CTWC. It is difficult getting people to play NES, so this is a big step forward.

They are also successful in running the online community. There are now classic tetris monthly (CTM) and other streamed tournaments. They collaborated with tetris effect which ended up with a classic tetris mode. They are getting more sponsors every year and this year they were even sponsored by Xbox. These are all signs of a flourishing community.

The final kick is of course the pandemic, which forces everybody to watch streams at home. It also forced the tournament to be held online. Being online means more were allowed into the tourneys, and more actually joined because they do not need to reach the venue physically. 

It is very important to have new players, because they promote more advanced idea. Instead of introducing new ideas, they adopt the frontline techniques and put that into mainstream among the community. Old players tend to stick with the way they played (for example Harry tend to have right well instead of left well even in competitive scenes in the past), but this isn't a problem for new players. Between DAS and hypertapping the latter is clearly more potent, so they simply start with hypertapping. 

The wave of new players comes with a side effect: the new players are significantly younger. The original player base is for sure, those who lived the NES era who are rather aged (in the perspective of gamers) in 2020. New comers are in general younger, but for competitive games this is even more extreme because reaction speed, concentration and bursting power all peaked when one is of the age of adolescents. Among CTWC top 8 the ages are 13, 14, 15, 16, 18, 18, 19 and 23 respectively, and it's quite unimaginable that players of such age are so much into a NES game.

Average age of top players decreases as the game become more competitive is nothing new after all. Just think about the top players in Osu, from 2008 where Cyclone was #1 and Alace was easily #30, to Cookiezi and Whitewolf in 2014, then to Whitecat plus many more in 2020. It becomes clear that they can really play the best when they are high school students. Similar scenarios are also observed in mainstream e-sports, although the peak varies with game genres. 

From the perspective of a long term follower (kind of), I have a mixed feeling when the community is heavily flooded with new players. On one hand they come with fleshing techniques and marvelous gameplays, but on the other hand we lose our connection with all the old players that we used to watch. 

But one thing is here for sure, CTWC 2021 next year is again what I will be looking forward to.

Thoughts on Simon Marais 2020

Simon Marais 2020 was held on October 10, which is long ago. Due to many coincidences I and my affiliated school missed the chance to take part in the competition. At the same time I didn't have the chance to review the questions until now, so this is a very brief and irresponsible review on the exam this year.

A1: closed curve and stupid pigeonhole. 

A2: clear once you figure out how the piling interacts each other, especially when $k \mid n$ or not.

A3: nicely formulated question, although the solution reduces drastically to a bound instead of some fancy sets. The beauty of the solution lies on fact that this sum can be optimized greedily. Locally this is simply year 1 differentiation, and you will reckon that a specific geometric series will do the job.

A4: yeah it sounds fancy and intimidating, but someone may as well brute force all the way with coordinate geometry techniques. I do not see that to be more difficult than IMO-level questions that can also be defeated using co-geom brute force techniques.

B1: this is more like assignment question...not even interested to do that. Question of such depth should not even appear in these contests.

B2: oh unit fractions. This is also a nicely written question. The solution lies on the fact that you can order arrangements in $S_k$ such that raising the sum means a descent in order, which means that it does not go forever.

B3: this is the kind of question that I do not like, where you either know one trick that you easily solves the question, or you have no chance at all. We have had enough cat and mouse questions.

B4: Again, possible (a) and impossible (b).

We see that the difficulty has been pretty consistent in the past years, but we have yet to observe more abstractly formulated questions as in the Putnam exam. Questions that can be formulated rather easily, but the solution requires further thoughts. Again I strongly recommend the removal of Q1, and extend the exam into 6 questions with a more approachable difficulty ladder.

Oh well, I have had a nice afternoon solving these problems.

18/11/20

 總覺得那個舊網頁標題banner有點礙眼所以拿掉了。其實那個是當年剛買到繪版時的試筆，蠻有記念價值的……只是跟現在的我有點脫節了。

其實這個網誌也是啦：2007年我寫的東西、2011的東西、2015年的東西跟2020年的東西也是天差地別，要我翻回看的話還有點臉紅。不過我肯定不會下架以前寫的東西，畢竟這是我存在的證明。

所以，也許，該找一個合適的新banner了嗎……？

On the day of the 2020 US Election

 Result as of 6:07 ET.

It is now 11PM ET. Trump is looking good towards his second term, and regardless of that, the turnouts are clearly in favor of him relative to the mainstream media polls.

The question is, where is the error coming from?

I write lots of things on my blog, including politics. However in this article I really wanted to look into the statistical aspect of the problem, instead of who is more correct politically or is more capable of making America great again. This article is not meant to be extensive -- I am sure there are more statisticians or data scientists who are more capable of giving precise figures than I do. This is a record of my own observation. 

The traditional polls

In traditional statistics there are two stages in the process -- you first collect the data, then you do the inference.

When collecting the data there are two roles of course, the data collector and the samples.

On the data collector side things could be biased based on how the poll is done. These includes designing leading questions, or hinting the presupposition during the poll. While I do not have clear evidence for these -- well I did not look into the polls -- we have another potential sampling error here. That is, to sample from an unrepresentative pool.

There are a few categories where polls may look into. They either take samples from adults, registered voters or likely voters. Likely voters of course have a (much) higher chance of voting hence are more influential. A number of mainstream media polls focused on adults of registered voters only, and that seemed to be dems biased -- or maybe because they know that collecting data in this way could be biased in the favorable way so that they decided to take such method?

Responses from the crowd certainly heavily affect the outcome. First the weighing might shift from what happened in 2016 or even 2018, especially given the volatile political environment right now. Even assuming that to be constant, the big problem comes from the 2020 version of the Bradley effect -- how many voters are the so-called shy-Trump-voters who are not willing to express their opinion in the polls? People are skeptical about that, while big data and early results say otherwise. Bradley effect is clearly taking in place.

Now we look into the inference part. If we believe that the poll makers will follow the moral of statistical inference (which is a bold statement to make from what's been observed), then what could go wrong?

It's mainly about the margin of error [https://www.pewresearch.org/fact-tank/2016/09/08/understanding-the-margin-of-error-in-election-polls/] -- when you give a confidence interval on the lead instead of of the poll percentage, the margin of error is doubled. That's because whatever that does not go to one party -- let's assume that the liberal party...or Kayne West are negligible -- goes to the other, creating a doubled difference. 

Alternative methods

There are a few polls who tried new methods of investigating shy voters. Trafalgar group adopted a mixed method [https://www.thetrafalgargroup.org/polling-methodology/] in order to prevent the "social desirability gap". Democracy Institute tries to figure out the true preferences of the voters by asking extra questions like whether or not they think Trump will win, or who they think their neighbors would vote for. Although Project538 apparently does not like the method, but traditional methods are off as far as we observed. That may as well open a whole new area on studying how to obtain the true data when interviewees intentionally hides their true preferences. 

Of course there are models too. These models in nature aimed to figure out the willingness of people voting for particular candidates without really making a poll. These include the famous Primary model [http://primarymodel.com/]. Others include a delayed correlation on media noise and so on. Some of these are also digitalized and measured on online platforms. 

Interestingly these are in general more favorable towards Trump -- some even gave predictions that are too good to be true. For example the Primary model predicted 362 -- while 300-plus isn't impossible, anything above 320 seems very unlikely. The thing is that the electoral college is not a smooth scale. Not only that the electoral votes jump according to the votes assigned to the states, it's also because states beyond 320 are all deep blue. The chance to flip any of them would be exponentially harder than the swing states. While the models are designed to reflect who will win, they may not extrapolate to landslide victories.

Models that are not done state-wise is certainly having similar problems. They failed to distinguish what happened in different states, and that could produce a huge difference when it comes to votes predictions.

One final thought

The unusually high voting rate is special for this election. Given the same poll result, the outcome with a lower voting rate will certainly be different with the outcome with a high voting rate. That is because the group of people on the edge of going or not going to vote, is also not scaled smoothly. 

This is hugely different from elections in Hong Kong, where we may comfortably assume that pro-government voters are fully utilized regardless of the overall willingness to vote. Thus any extra votes will be heavily biased to the pro-democracy side. 

Such assumption is false for the US election, because the voter composition of both parties are highly sophisticated and dynamic. We can easily give numerous reason on why the extra votes would be biased on one party or the other. 

For example, Biden supporters may say that extra votes are more likely for the dems. That's because we are observing a historical high on absentee ballots, which contains surely a lot more dem votes. 

On the other hand Trump supporters are justified to believe that the extra votes are in favour of the reps: the rally showed that Trump supporters are more active and more motivated to vote. One also raised interesting observations that covid which triggered distant learning, which reduced peer pressure from college friends who are in general leaning to the dems.

If we keep going deeper, how does the the variation depends on the default stance of the counties (or, as shown on the polls)? Or variation against county population, income, age distribution and so on? 

No matter what the answer is, we will learn much from exit polls of the current election. Together with all the new polling methods and models, there are too much for us to investigate, scientifically.

6:00 AM ET 4/11/2020 (yes, 7 hours after I started writing this, because the live feeds are overwhelmingly interesting to watch)

*At the moment WI, NV and AZ are in extremely close match. Oh this election is so interesting...

01/11/2020: 秋番簡評

當我拔出第二把刀時，女主角就會從天而降－－

來源：這是妳與我的最後戰場，或是開創世界的聖戰第1集

很好看不過不在本次介紹之列。

已經過去的夏番季度持續受到冬季和春番延期的影響，成為近年最貧脊的動畫季度之一。不少作品比如地下城都挑了秋季這個最快的季度將動畫推出市場，使得今年秋番名單異常擁擠，這季我預定要追的番一開始居然有二十部之多。

雖然本季作品數異常地高，但卻沒有發生紫羅蘭VS國家隊VS PPTP這種神仙打架的局面。本季的巨無霸當屬地城和魔劣兩部都是成名已久兼為續作，粉絲自然不會吵起來。在地城和魔劣以下的實力派亦有一大堆，每部都有自己獨特的賣點，大家專心看番也不用吵誰才是本季霸權。以下就由我來推介幾部本季有趣的番，順便說一下看了兩三集後的感想。

<以下可能含有劇透，小心服用>

催眠麥克風 3/12集 7.5/10分

人權證明。

男性向賣歌的虛擬偶像企劃。我從企劃伊始就有在看，從CD到live跟手遊都有課過……應該算是原作粉絲吧？

動畫化目前看起來套路甚至內容本身都非常貼近現有的drama跟漫畫，所以看點就是動畫能否將聲畫的效果合一形成更佳的感受。在這點來看動畫的效果基本上就是drama與漫畫的放大版：動畫的藝術設計非常足本，rap段動畫可以看成手遊rap動畫的進化版，從動圖變成了3D特效，但角色風格還是一致地表達了出來。

當然，整個企劃的「尷尬」感覺也隨之而放大了：兩隊大男人拿著麥克風對戰的場面，一言不合就rap起來，而且還在街上一邊跳一邊rap……本來聽drama或者看漫畫都沒這麼尷尬，但看動畫這感覺則變得很明顯。不過這也不算壞事吧？另外提一點，主角們的眼睛眉毛十分妖艷，看漫畫和玩手遊時還不算顯眼，但動畫用全屏看的話很難注意不到。嘛，畢竟是主角呢。

整體上符合預期，效果比以往的形式都好，就看編劇有沒有打算補完一些細節了。

全員惡玉 4/12集 7/10分

以數碼龍克(cyberpunk)風格大阪(關西)為主體的惡人組合番劇。

數碼龐克的風格與浮誇的大阪可謂天作之合。動畫花了大量分鏡描繪出用霓紅燈堆砌而成的虛構城市「關西」，加上通天閣等幾棟名物，不需太多旁白描述而觀眾自然會有「啊，果然是大阪」的感覺。制作組沒有滿足於開場對關西的影頭，每一集都為這個城市添加了新的元素；另外第三集在酒店房間的打戲從角色走位到燈光(顏色)與佈景運用都十分流暢，絕對是電影級別的藝術。

數碼龐克的另一個特色是反烏托邦設定，而這個「關西」也不例外。大阪有臭名昭著的西成區，這裡整個關西都是相對於關東下的貧民區。以核幅射與高壓統治將人民鎖在「關西」裡，正正就是數碼龐克的反烏托邦社會。在這種壓抑的社會下變革的火花自然不是甚麼好人，一群「十惡不赦」的惡人加上陰差陽錯(？)地加入的女主，一躺豪邁的旅程自此開始。

這部的角色設計真的沒話說，而且打戲也畫得很精緻。雖然這種一人一種超能力(搭一個平凡人)的故事倒是挺套路的，但看過第四集後關西與關東的對比似乎有更深的意味。目前女主與其他角色的互動略嫌不足，不過這也可能是因為三集實際對應的時間只有短短幾天吧。這方面可以往後再評論，但不論如何這部番幾可肯定是觀賞性十足的一部。

總之就是很可愛 4/12集 8.5/10分

把頭髮染淺色一點，你就可以去當管家了。反正老婆都是大小姐嘛。

來源：總之就是很可愛第3集

火田老賊(畑健二郎)與聲優老婆的狗糧番，與你與我最後的戰場並列本季閃光之最。女主角聲優不選用淺野真澄反倒是一種另類的曬老婆吧…？

不論是男主的內心小劇場與實際上的精明能幹，跟女主整家的互動，再到路人和細節的各種neta處處散發著旋風管家的味道。這就是火田老賊的風格，用簡單的線條編織出的故事一點都不粗疏，每集23分鐘體感時間可能只有三分鐘，但這三分鐘足以讓你已經吸收了整杯台南甜度珍珠奶茶的糖份。

這種番真的不用太多言語描述，隨便上youtube看一下剪緝就知道了。看完這番順便回去再看旋風管家吧，要TVB(聰聰21)配音的。

憂國的莫里亞蒂 4/12集 7.8/10分

福爾摩斯式推理之所以迷人，是因為它沒有借助現代鑑證的力量，是一般人所能推理的極限。比起所有提示都明確寫出來的本格推理這種敘事方式更適合在動畫中展現。

比照套路，主角當然要是高富帥，身邊再帶一兩個助手(華生)，男女不拘。女的話必然是女主然後走戀愛路線，比如京都寺町三條商店街的福爾摩斯。(題外話，這部作品的手遊根本就是Candy crush，而且吃電吃的不行……)

然後要選一個時代的話果然還是1900年代作為世界中心的倫敦最好。處於歐洲文明黃金時代的世界中心可以滿足任何價值衝突的背景，比如封建與資本、法治和人治……像大逆轉裁判甚至是Princess Principal那樣半架空兼蒸汽龐克的動畫都以那個時代的倫敦為參照背景。

憂國的莫里亞蒂就是集齊以上三個王道設定的作品：在19世紀末倫敦的帥哥的推理作品，更貼切來說是犯罪作品，男主透過對推理的理解操控身邊的棋子以進行自己理想中對社會的變革。

動畫本身到目前為止真正有案件的只有第一集。比起相對平淡的劇情本身，我更感興趣的是動畫用了非常多的蒙太奇技巧將犯罪本身用更藝術性的方式表達出來。比起直接拍出犯罪本身，染血的聖母像和地上的血汗不但能避開18禁的內容，亦能假借剪影的內容向觀眾暗示出罪行本身之齷齪。片頭兇手動手與片尾男主行刑用上的手法，兇手的飢不擇食與男主的穩操全局對比，更能表現出男主的神祕感與手段之高明。

動畫中的推理比起其他同類作品只能算是合格。有些透露出來的資訊是多餘的，但不屬於誤導觀眾的資訊，單純放在那邊讓觀眾胡思亂想而已。部分應該是從漫畫版刪減時沒處理好的部分。比如第二三集中老莫里亞蒂說過自己知道為何被要求領養孩子，但動畫中對他著墨太少，觀眾根本猜不出甚麼來。漫畫版中莫里亞蒂父母與哥哥的戲份明顯多很多，莫爸與其他貴族的互動引證了他虛榮勢利的性格，答應收留養子只是為了搭上公爵千金而已。類似因刪減造成的BUG不少，希望編劇能注意一下。不過聽說原創的部分相當多？

要在前幾集就斷定動畫劇情好壞很難，不過這部番的分鏡與特效處理跟全員惡玉一樣有特別下功夫，OP畠中祐的Dying Wish也是我喜歡的半古典歌劇風，而且主角還是有點病態的帥哥。光是這樣就值得追下去了吧？

成神之日 4/12集 8/10分

麻枝准終於把注意力從護士小姐姐那邊拉回來了。這次是他收下大家對他Charlotte的指教後第一部大作，是反省還是報復，尚未可知。說起來Charlotte也是Angel Beats後的報復……

不過可以肯定的是，麻枝的招牌元素肯定都在。當初大家開賭盤猜棒球會第幾集出來，沒想到第一集就殺大家一個猝不及防，此外麻雀也會在第四集出現。另一個沿用下來的元素就是請佐倉綾音為女主配音了。佐藤雛跟友利奈緒在性格上當然有很大的分別，但她們傲嬌起來倒是十分相似，精神分裂式用各種語氣進行吐糟正是佐倉的強項。Charlotte首播的2015是佐倉的巔峰時期，但在2020年還記得她的配音功力真是太好了。

有些人會說前面陽太的互動對應都是麻枝本人的反省，我是沒有在這方面想太多。我看到的是前面是稍帶一點科幻但整體是是青春滿溢的男子高中生暑假日常。不過隨著平行故事線逐漸浮現，加上第一集就開始倒數的時間，我只能做好下一集就開始胃痛的心理準備……

不得不說，麻枝准在輕鬆搞笑方面真的沒讓人失望過。棒球那不存在的第四好球、拉麵的味精層次都讓人笑個不停，只是麻雀新役種的話我笑完頭還會開始痛起來。這種一集一個主題的日常效果真的很好，但別忘記Angel Beats與Charlotte分出高下正正在於進入胃痛部分時劇情會不會暴走。大河內一樓的Princess Principal之所以完滿結束是因為最後兩集編劇換成別人了，但是是Key社和麻枝的話當然沒法換人。所以甚麼時候胃痛，是好看的胃痛還是難看的胃痛，全在他的一念之間。

我們在這段時間就先好好欣賞佐倉的演技吧。

*

最後補充一句，今季的番實在太多，我也不打算逐一細評和介紹。熱門番如地錯與魔劣都不需要我再推廣甚麼，因此我選的都不是最熱門但我認為有趣的番。

不知道我有沒有空在季末再寫一個總結，不過有空的話我應該會繼續寫小說呢。

01.11.2020 滋賀

01/10/2020: 我的桐人與網頁遊戲

攻略到97層的各位相信按挑戰的表情跟上面略有不同

好久沒寫點甚麼東西了，這次還是網絡懷舊系列。

最近玩我的桐人有點瘋。這個遊戲將SAO跟其他動漫梗成功合在一起，加上毛場自成一格的品味，成為了這個暑假殺時間的最佳網頁遊戲。

不過比起我的桐人，我更懷念兩款舊時代的RPG頁遊。

早期RPG頁遊可以數到十五到二十年前風靡中港台的江湖遊戲。玩家可以扮演武俠練功，可以打怪推王也可以惡意挑戰玩家。不想走PVP路線的話也可以收集資源成立門派，帶領你和你的朋友們一統江湖。

我還記得小學時十幾個同學圍著一位同學，看他用聲稱是從自己哥哥的朋友aka這個江湖的創辦人借來的GM帳遊玩著。他還聲稱自己每個月能從哥哥那邊領到二百塊工資，作為當GM的酬勞－－其實這些江湖遊戲都是非營利的，網絡也還在那個沒有動態廣告的清淨年代，只因為當江湖GM就發工資其實就……嗯。當然他同學面前拿著GM帳修改自己本帳的數值然後惡意殺掉路人引起其他玩家集體不滿，那又是另一個故事了。

說是「這個江湖」，是因為那個年代的江湖類頁遊實太多了。雖然江湖本身不是開源(何況那年代根本沒有開源這概念)，但大家建出來的江湖看上去都差不多。與其說是面向公眾的多人線上遊戲，更不如說是創辦人和身邊圈子的自建社交平台，能不能吸引新玩家都是隨緣。

說句題外話，江湖遊戲其實也有輪迴系統的。不過轉生代價太高而惡意PK成本太低，使得玩家難以長期投入在遊戲裡。如果當年的江湖引入了SAO的紅名系統的話，吸引力應該能提高一截吧。

如果說江湖是帶社交功能的RPG頁遊的話，帶RPG頁遊的社交平台的最佳例子則非Discuz論壇莫屬。Discus用的語言是語言相對容易理解的PHP，與PHPwind、phpBB等其他論壇架構比起來最大特色是空前絕後的插件系統。無視安全隱患的話其靈活度之高造就了當時人手一論壇的榮景：有能力的自己買網域和儲存空間架論壇，沒能力的也可以找一些網站申請，通過後不用自己動手也能拿到一個簡化版論壇。雖然是論壇但比起其討論功能，大家更在意的是安裝自己最愛的插件，把論壇裝飾成自己喜愛的樣子。

各種插件就在這個時代背景下應運而生。從普通的銀行、每日任務到紙娃娃系統到魔改論壇的管理優化系統、置頂助手等，只要想得出來的幾乎都有人寫過。對於那些小圈子論壇來說遊戲類插件比其他都來得重要：有將flash小遊戲整合到論壇積分的插件、也有即時PVP的大逃殺插件，但我自己印象最深刻的還是那套RPG遊戲的插件。

RPG插件具體作者是誰已不可考，可能是AL8論壇裡的高人，也可能來自大陸或台灣。從RO裡抄出來的小人隨你的指示砍下一隻又一隻波利，但不論你砍再多隻，提升的等級仍不足讓你打通每一層的boss。後來我才知道，打boss對裝備與點數配搭都有著嚴苛的要求，亂砍是不能過關的。但那個年代的資訊有限，縱然不少人玩卻沒有專門討論這遊戲的地方。當時的我又沒想到可以把PHP拆開解析計算，更不說沒有腳本要進行大量操作是一件多麼痛苦的事情。

如果同樣的網頁RPG出現在2020，那又會發生甚麼事情呢？

首先會有人成立這個遊戲的Discord伺服器，然後來自不同論壇但在玩同一款RPG插件的玩家都會進到這個伺服器裡面。很快玩家之間就會出現一批能高效通關的攻略組。有人會向公眾提供玩法，但大部分的攻略只會在小圈子中流傳。

外面的人會為了得到攻略而用盡方法混進攻略組裡面，有些人會混進去後將這些攻略公開。漸漸地攻略組的圍牆被打破，攻略組之間逐漸分裂成向外公開訊息與轉化成更嚴密的小圈子兩種流派。

但對遊戲的理解演化是不等人的。後進的玩家接收了攻略組的資訊逐漸將本為祕密的理論完善起來，更實用的攻略落入大眾玩家手中，他們快速攻略同時也為攻略本身帶來反饋。更好用的攻略又會令更多玩家受惠，攻略在大眾玩家之間形成正循環。

跟以前的PHP架構不同，HTML5寫出來的頁遊腳本掛機起來更方便。各種自動化系統被研發出來。從簡單的javascript指令到tampermonkey插件，從discord bot遙距控制到驗證分工，到最後新進玩家不用費多少功夫就能打出職業玩家的水準。(每次提到驗證分工我又想起clickclickclick，這種分工程度在2008也是傳奇了……)

以上並非純屬虛構，其實就是我的桐人的前線發展史。不過仔細想一下的話就能理解，知識的傳播過程不都是這樣的嗎？當然啦，如果大家研究的是RPG插件的話把PHP代碼拆開來算一算就知道了，只有我桐這種戰鬥過程是黑箱而且高度隨機的遊戲才會被一直研究著而沒有最優解。

至於那些更高強度更混沌的PVP頁遊，比如某隻被戲稱珍惜生命的，嗯……

01.10.2020 滋賀

夢．十夜 (5) The Guild Battle

鬼魅般出現在我旁邊的卡羅，身穿紅色皮外套與黑色恤衫；本來cos成雷伊的黑色頭髮也變回銀色，耀眼的項鍊和指環讓他看起來更像樂團主唱。也許是服裝變化太大，身邊其他熟客似乎都沒有認出他的帥氣樣子－－咦，從甚麼時候我認定他長得帥的？

他把食指放到唇上阻止了驚訝的我，然後把旁邊的桌椅拉過來坐下。他的位置剛好背著其他顧客，這樣就不會被認出來了。對面的熊熊倒是十分淡定，顯然不是第一次與卡羅見面。

「呦～」他一臉輕鬆地向我打招呼。

「哈囉……我該吐糟你為甚麼出現在這裡嗎？」

「你要不要吐糟是你的自由對吧？如果你在意我的話我會很開心的。」他輕輕在餐單上戳了兩下，示意讓熊熊幫忙點餐。他點的是厚熱香餅和香橙熱巧古力：用75%可可製成的巧克力一點都不甜，但柑橘香氣讓人產生一種似甜非甜的感覺，不用加糖也能讓人禁不住一口接一口喝下去。「我只是剛好在附近，熊熊又問我要不要來而已。順便我也想找你聊一下攻城戰的事情呢。」

「該不會跟熊熊的提議有關吧？還是……嗯……被盯上這件事？」

熊熊：「小紅被盯上這件事說起來我也感覺到，你的遊戲留言版熱度異常的高呢。」

遊戲裡每個玩家的頁面都有一塊討論板，但嚴格來說玩家並沒有管理該板的權限，他們只是比較容易看到自己的討論板而已。正常來說玩家會待在自己或自己朋友的討論板上聊天；又或者向交易對象留言、提價或者競標等等。雖然沒有明文規范，大家也不會到處霸佔別人的留言版。

不過我的討論版最近也太多人了。很多都是來問戴娜戴娜(六星排名獎勵)賣不賣的，也有問我五星獎勵的，也有想問聯絡方式的。留言都洗得很快，我從一開始逐個回覆到用罐頭回覆，到最後大部分詢問也懶得回應了。

卡羅：「你也注意到了嗎？新入榜的玩家得到大量查詢並不罕見，因為前排很多人都不怎樣賣卡，而新入榜的玩家比較好說話。不過這張是限量100張的獎勵，按道理說來問的人不會這麼多。而且一上來問聯絡方式的，嗯……該不會是有人用你ID搜出你的社交帳號了吧？」

－－才不會。我用的帳號名字都是當時即興用身邊的字串組出來，基本上跟社交帳號毫無關係。

「如果不是被肉搜的話，只能用有人對你感興趣來解釋了吧？」熊熊還是那個愛交易的熊熊：「我也希望來找我交易的人跟你板上一樣多呢。」

我苦笑回應道：「嘛……你想的話也可以天天在我的板上找交易對象啊。」

「很遺憾這樣是行不通的，在你板上出現的玩家大部分我都見過。找新入榜玩家宰的人，多半是不會跟我交易的啦。不過找你的玩家實在是太多了，所以卡羅才會說你被盯上了吧？」

卡羅在手機上展示了幾張截圖。那是在競技場活動結束幾天後熊熊對著我的留言板截的圖。在遊戲所能展示的最近十五條留言裡，第一條與最後一條留言僅相差四小時，幾乎每一條都來自不同玩家。也就是說，大概每二十分鐘就有一位玩家來找你呢。而且廿四小時都有玩家來轟炸你，這也是挺奇怪的。」

一陣香味打斷了我的思緒。店長親自端著食物過來，卡羅也低調地打了個招呼。大概店長早就留意到他了吧？

「嗯……所以我被盯上會有後果嗎？這種排名活動裡很難狙擊一個特定玩家吧？我也跟其他勢力無仇無怨啊。」

「在排名活動裡的確沒差，不過接下來就是攻城戰了。我猜熊熊把你找出來也是跟攻城戰有關吧。在競技場上打出好成績的玩家，往往也是攻城戰的可靠戰力，如果可以拉攏你的話對隊伍成績可是有很大幫助呢。」

「沒錯，我跟小紅達成了協議：她來當我的看板娘，我就借卡讓她打攻城戰。這樣她就能用超強力的隊伍了呢。」

「咦？要我當看板娘嗎？不對……你又不是經營實體店是要怎樣當看板娘啦！」

卡羅輕啜了一口熱巧克力繼續道：「這就是問題了，攻城戰要觀察玩家的活躍程度更為容易，天知道他們之後會不會一直騷擾你。所以我在想有沒有方法讓你先躲一下－－如果你有興趣來攻城戰的話，要不要改用小號參戰？」

公會戰的組成是九個玩家組成一隊，但其中兩個名額有規定等級上限。原意是讓新手加入強隊享受攻城戰，不過結果當然是由強隊自組小號進去。

「如果用小號的話直接用卡羅你上次的主力隊伍就好了？我記得你已經組出新一隊了吧，這樣看上去也比較好偽裝。」熊熊在手機上滑出上次攻城戰的截圖。

卡羅上次的隊伍以比較親民的防守型角色為主，看來這段時間他已累積了不少強力角色。用這種隊伍是很方便，但被說得好像已經確定要打攻城戰一樣我就不樂意了：「我還沒決定要不要肝下去，讓我再考慮一下好嗎！」

熊熊一臉抱歉地道：「也好……你慢慢考慮一下吧。用卡羅的舊隊或者從我這邊要一隊新的都可以，或者要其他補償也可以哦。」

卡羅倒是一臉輕鬆地切下一塊剛端上來的厚熱香餅放入口中，吞下之後對我說道：「用新人名額的話你喜歡上來打，沒空不來打也可以哦？這樣就更像新人了不是嗎？」

聽上去很誘人，但我很清楚自己一旦投入進去就不可能『沒空就跳過』：「這樣會成為你們隊的負累吧……」

「攻城戰沒拿到第一檔的獎勵的話算上人力物力注定要虧的，所以要打進第二檔或是在第五檔放羊都沒所謂。但是對你來說，沒有甚麼比第一次參戰就能坐在後座觀戰更刺激了不是嗎？」他再切下一塊熱香餅，叉住沾上果醬伸了過來：「今天的水準也一如以往地好呢。來，啊－－」

「唔」我沒有回答他，但是一口把熱香餅吃掉了。微熱的熱香餅裡面的水氣與果醬的甜味在口裡迴旋，形成絕佳的口感……

*

還是那漆黑的房間，肥宅繼續向銀髮少女報告。

「……我們發現與上次Rainmi0031(小雨)和aoisora2(Sora)一起刷進前百的還有Lampbear(熊熊)和RedMeipuru(小紅)兩人。Lampbear是有名的商人，跟aoisora2也走得很近。」

「那另一個號呢？」

「……似乎是新的帳號，等級還在新手範圍。看起來不太像小號而是主力帳號才對。我們一直在她的留言版上留言觀察她的作息時間，再加上與她比較接近的Rainmi0031和aoisora2，基本能確定他們是同一夥的。」

「嗯～真有趣。你覺得這戰法誰想出來的？」

「那三個玩家開服不久就在玩了，沒聽過他們有特別的打法。不過是不是RedMeipuru想出來的就不知道了。」

「真有趣，不知道她會不會在攻城戰出現呢？」

「他們三個這次也有參加攻城戰，隊裡除了兩個小號所有人都是老面孔。據說其中一個小號的隊伍是Karlow(卡羅)上次用的隊伍。我感覺這兩個小號其中一個應該是那個RedMeipuru，但是攻城活動期間沒法確定。」

少女抬起大腿搭到另一條腿上的情景被鏡頭完整捕捉到。肥宅呆了一秒後繼續問到：「所以……請下達這次攻城戰的指示。」

「今次就隨便打，以攻城戰的PVP數據為主吧。我感覺下一波戰力通漲快要來了。把把勝場調節到他們隊伍的附近，我希望跟他們打一場。我最近有點忙，剩下的你來負責吧。等你對上他們再叫我上線吧。」

「是……」

少女湊近鏡頭，愉悅地看著不知道看哪的他說道：「這次也做得不錯嘛。那麼……這次活動之後，說好的獎勵就先支付一半給你吧♡」

「真、真的嗎？就是那個……約、約會……」

「我可沒有說約會呢。」少女的俏臉瞬間冷了下來：「不過陪你走走還是可以的－－我很期待你這次表現哦。」

*

我就知道我當時就該拒絕他的。

現在是七天連戰裡的第二天第十場前夕。此前每打一場我就後悔一次：在街上我在打攻城戰、上廁所時我也在打攻城戰、甚至半夜那場我也迷迷糊糊地按了幾遍。

我現在的身份是happysky1(distortion)，看起來就像卡羅的小號，用的也是卡羅上次攻城戰的卡片。順帶一提，這次的參戰成員還有卡羅、熊熊、小雨、阿飛(和他的小號)、亞歷克斯加上還沒見過的Sora跟阿秋。

攻城戰的卡片組合與競技場的稍有不同。瞬息萬變的實時戰鬥中不可能針對對方的隊型而特化，所以大家組隊的目標都以輸出和挑對技能為主。同樣星級的卡片間數值並沒有差太遠，因此使用帶有特定技能的卡片就更重要了。當然，最強力的技能都留給了新卡包和活動最高檔次獎勵的卡片，一般玩家只能用帶有常見技能的卡片。所謂平民卡，就是帶有這些技能且相對便宜的卡片。

兩張「赤銀騎士」雷音(Rain)。強大的防禦加上四連擊的技能使她成為扛前鋒的不二之選。
兩張「無畏劍士」西薇爾(Silvia)。兼有麻痹和擊退能力的她可以在中堅位置阻截對方的攻勢。
一張「靜默無聲」德蕾婭娜(Deanna)，這張卡一點都不平民：她帶有新推出的狙擊技能，擁有極高遠程攻擊的她自然適合放在後排攻擊對面後方。這張卡本來是卡羅的王牌，但是他以「暫時用不到」和「這張看起來更卡羅」的原因塞到我(的小號)手上。

攻城戰可分為戰鬥與戰鬥外兩部分。在戰鬥以外的時間隊伍可以打主線任務去收集物品以提升戰鬥力，這方面有人肝下去就行了。

在每場一小時的戰鬥裡隊伍會站在3x3的方格裡保護後方的城堡。玩家可以不斷攻擊對方的陣列得分，當玩家手上所有角色HP歸零時則進入破防狀態。在前排全體破防後對方才可以攻擊下一排的玩家，如果所有玩家被破防的話對方則可以直接攻擊城堡得到大量的分數。破防的玩家可以使用AP(Action Point)回復，而攻擊本身也會消耗AP。AP會隨時間回復，但在高強度戰鬥裡大家都會一直喝藥水把AP補回去。

除了白刃戰得分以外，玩家可以進入探險模式在戰場上搜集火藥以發射砲彈。砲彈可能直接命中城堡化為大量分數，也可能命中對方一整排玩家、甚至落空。如何運用砲彈是破局的關鍵，但玩家進入探險模式時沒法參與主戰鬥，這時如何分配人力就變得重要。

戰鬥的勝負會以雙方得分決定，隊伍按勝場會有排名獎勵，玩家個人得分也會有分數和排名獎勵。

我一直站在隊伍的後排上。前幾場我們匹配到的都是雜魚隊，前四場我甚至沒有留下任何戰鬥紀錄。

第五場我主動要求換到前排。不過對面大概在睡覺，整隊只有四個人在線，對面打了兩下就放棄了。

第六場我在睡覺。不過人在歐洲的Alex帶上阿飛的小號，輕鬆把對面滅掉。我半夢半醒之間成功上線，但站在後排似乎根本沒被碰過。

第七場終於有比較強的對手，所謂比雜魚強就是會一直打過來而已。沒滿員甚至沒有湊齊六星卡片的對手根本沒法構成威脅。

第八場的對手實力更貼近我們了。我們有七個帳號在線在線而對面也八個，但卡羅的新王牌「天選之人」比布里亞(Biblia)所率領的隊伍每回復一次可以扛三次對方的攻擊，大幅削減對方的得分效率之餘也讓我們可以放開攻擊。因為有餘力防守我跑去發砲了。一次命中城門拿到角色攻城兩倍的分數，一次命中對方陣地讓對面全員HP減半，剩下三次都落空了。到現在我還是沒法確定發砲的價值，特別是戰況膠著的時候。

第九場我們匹配到排名第二的隊伍，輸得十分乾脆。對面每個玩家都帶有卡羅等級以上的強力隊伍，而且帶上活動加成卡片每一擊都能額外獲得五成分數。打了五分鐘卡羅便示意我們停手，但對面為了衝分數並沒有停下來，把我們揍了整整一小時。

第十場，也就是現在，我們的對手是目標進入前十(第二檔)的強敵「奧林匹克神眾」(Gods of Olympia)。裡面全是個人活動的前排常客，但聽說隊伍比較鬆散所以沒有上一場對手那麼強。他們沒有指揮，打法以強攻為主，是一個測試戰術的好對手。

現在是晚上十點四十五分，我躺在床上滾來滾去，公會戰使我精神異常興奮。距離開戰還有十五分鐘，大家已在聊天室紛紛報到。

卡羅：「小紅也上線惹！」
天天下小雨：「哇小紅！」
亞歷克斯：「剛見完客，回酒店途中，20分鐘後見！」
飛：「我也準備好了！」說罷貼了一張用電腦模擬器與手機雙開的照片。
Lampbear：「( º﹃º )好像是這次活動首次滿員？」
Sora：「因為是強敵當然要全員應戰啦。這次的獎勵也很好看喔－－」然後他貼了兩張卡片：

粉髮少女「魔戰使」伊卡麗絲(Eclipse)
她的手下對她的命令從不懷疑，
只要她們彼此合作，奇跡就會發生
「我們個體可能不強，但我們從不孤單！－－」

金髮軍裝麗人「大佐」克里斯汀娜(Christina)
一陣大砲聲響起，
城牆與這個國家的未來同時崩塌
她愉快地笑著：「也太快了吧♪－－」

飛：「好看是好看，不過我們拿不到一檔的獎勵啊……」
Sora：「這是二檔獎勵啊，雖然不知道有沒有機會拿到( > <)」
Lampbear：「_(┐「﹃ﾟ｡)_這就要靠小紅了」
我：「我連真正的激戰都沒體驗過呢……」
卡羅：「檔次的問題以後再想吧。難得滿員就是要漂亮地打一場！」
「「哦哦！！」」
卡羅：「我、Alex和飛大號站前排，後面就隨意吧。中排的注意一下回復，大家一起用力打就好。」

他下達了指示後又私訊我道：「以對手的隊伍強度來說你可能沒法扛住太多攻擊，不過你按自己的感覺行動吧。下去攻防或者發砲也可以～」

我盯著手機上的倒計時。在歸零那一剎那我迅速按下「進入戰場！」的按鈕。隨著聊天室裡一連串「開始啦」的留言，這場攻城戰正式開始。

「開火！－－」

(待續)

**

◯戰幻想的攻城戰是我記憶中最投入最剌激的公會戰之一，遠超武俠MMORPG的公會戰，現在的碧藍幻想古戰場與公主連結的公會更是沒法與之相比。

一個「有趣」的非動作類即時公會，卡片入手門檻不可能太低。公主連結打的旗號就是組隊低成本(相對其他遊戲)，幾乎大部分隊伍都有辦法用同一隊「meta(主流)」、同一種戰法去推王－－這樣土豪的投入感便差上了許多。公連的成功是抓對最大的中低消費客群，然後設計出來的角色也很能迎合他們的胃口。但論到頂端的消費公連是遠遠不及其他大手遊的。而◯戰幻想的消費門檻應該穩站西方市場的頂端，成功聚集高消費客群的他們才有辦法以偏小的遊戲規模打進app store課金榜前三。

比起碧藍式的單純拼輸出，公會戰更應該強調兩隊之間的互動。使用者生產(User-generated)的內容永遠比千遍一律打王的變化來得多。這也是為甚麼攻城戰辦了七年一共幾十屆大家還是樂此不疲地投入－－以遊戲的卡片代謝速度來看(奇妙的是卡片本身的戰力通漲並不高，但組合一直變)每兩個月一次的攻城戰裡對手的隊伍可以變得完全不一樣，理解對方的卡片並制定戰略才是遊戲的樂趣。

順便一說，七天35場的肝度真的很可怕。後來遊戲也改成七天28場再到五天24場，畢竟廿幾場足以穩定分出前三檔隊伍了。不過對於一天五場需要全取的頂級隊伍來說還是很辛苦。這就是國際服的壞處：碧藍一天打十八小時還有六小時休息，這邊一天五場你頂多能睡三小時。

這就是所謂的燃燒青春，對吧？

對了，所有卡都可以在這裡找到。一切資料名字以英文國際服為主。另外我很討厭他們的中譯名字(況且我沒玩中文服)，所以我會自己譯成中文。

我很希望能再一次看到類似的手遊再次出現。不過其大前提－－可交易卡片這個模式在現今很難存活下去。甚至◯戰幻想本身後期也不得不引入綁定制度。另外可以量產高質量卡片兼能撐起世界觀(並沒有)的遊戲，古今中外就真的只有它了。

咦？你說封面圖片劇透了嗎？

咳咳。如有雷同，實屬巧合。

8/7/2020: TWEWY animation and Mr. Driller

First of all, the animization of The World Ends With You is something I have never dreamed of. The switch game certainly failed to reach the same height as the DS version did, both operation-wise and story-wise (on top of the original 3 weeks), but the main story, character/art design and the music design is absolutely top notch. They are basically all you need for a great animation.

Their decision to modernize Shibuya as well as the phones is a bit sad to me, because these characters really live in Shibuya in the late 2000s. The only uncertainly is how much should be shown in 12 episodes -- given that Neku grew in the span of three weeks, it would be weird if they only do the first week or two. Some extra daily interactions will be welcomed, but only if they have enough time to display the whole main story. It would be nice if the animation gives extra answer to what was not fully explained both in the DS and the switch sequel.

Here is the trailer, in case you haven't watched:



*

I have been playing ring fit during the lockdown everyday, but I do not plan to give a review on the game. I also bought touhou mahjong but there is not much to say either.

Instead I want to talk about Mr. Driller Drillland. Unlike the DS version this is a complete remake of the 2002 version. I haven't played the 2002 version but I definitely enjoyed the DS version so I bought the switch one once I saw that on the store.

I cleared all Lv2 and finished the Lv3 Drindy adventure. I realized the technique to clear other Lv3's but lacked the time and temper for it, so I will stop here for now.

Before commenting on the game, I have a concern when others comment on games -- why are remakes valued less?

One shall not value remakes lower just because it is a "low effort" production. The pricing of a game depends on the development cost (of course), but the rest depending on marketing consideration on how the team think the game is worth.

You can say that a remake "probably" worth less because the game cannot keep up with the recent standard, or that the change in console alters the feeling of gameplay. The World Ends with You is a good example: the heavily stylus based control of the DS game feels off when it comes to switch. The extra content is nice but also left a gap between the main story and the extra story. This is why fans are not feeling as happy as in 2008.

> My review on The World Ends With You Final Remix < 

Nintendo and Sega made their old games ported onto switch at a really low price. This is not necessarily solely about effort (actually, getting the game mechanics right for these really old games are not super easy, although Nintendo already did it once for Wii). This is also a way for them to promote their IPs, which is worth more than selling the games itself. That never justify why remakes should be sold cheap.

After some research on the original one, I would say this switch version is basically the 2002 one moved to another console, just like how it did for the PC version. It completely copied the merits and weaknesses of the original game. The weaknesses meanwhile is relatively easy to fix and these are less tolerable in 2020, so the game got a mixed review (still beating TLOU2 by a huge margin, OF COURSE!)

On the good side they preserved all the game modes in the original version, which is well rounded comparing with the DS version which is pretty much just an extension of the world drill tour. The gameplay is pretty much the same because all you need is really a D-pad and the AB buttons. I always prefer D-pad over stick when you only need four directions -- the same happens for Tetris99.

On the bad side...the game lacks any tutorial or instructions. Lv 1 is quite hard for beginners to start with even with the beginner friendly mode. It would be nice if there is a really short and easy stage like 200m or 300m (which the DS version has).

Having 3 levels are the classic setup, but the gap is pretty huge between the three. There is no in-game instruction on how you can unlock the next one either.

I also wish to see more interaction among the characters, instead of just one or two vocal lines when the level is unlocked for the first time. I also wish to use Ataru on every single level on every mode. I know they assign characters to their suitable mode...but I just like Ataru more.

So...it is really a classic 2002 game, which some parts of it can be improved to fit the 2020 taste. I still like it, but how much should it be priced? I don't know because I don't buy games every day. At least for me I would happily take the $29.99 offer.

Outbreak stages classification when it is out of control: July updates

This is an update on my model based on test count vs positive rate. For the introduction please refer to these articles:

1) Classification of outbreak stages by variation of test count and positive rate
2) Typical stage shifts: May updates

*

We have seen the potential of this model predicting the case trend in the next few days, but it does not give strong indication on whether we are shifting to the next stage. Even if we are to make predictions based on the model, there is one important assumption that we made.

We assume that the government would thoroughly eliminate the local infection chain to the point that only isolated cases would occur after a certain time.

This is certainly false when from what we have seen in the last two months. These countries are divided into two categories: either they lack the ability to eliminate the virus (passive herd immunity), or they try to strike a balance between public health and economy, which miserably failed. This will be the main theme of my July update.

Just like the May update, we present the trend since late March or whenever data is available, but data after May 10 will be shown in bold.

*

Countries that cannot control the virus at all

When the virus was spreading in South-East Asia and Africa, we feared that the pandemic could be out of control because of a less hygienic environment and less efficient/reliable government etc. This turned out not the case -- Africa is too hot for the virus, and SE Asia actually did a good job controlling the damage. Thailand and Vietnam did particularly good, for example.

But when it arrived South America such worry finally came true, as the virus easily spreads among the passionate (in other words, unhygienic) Latinos. The whole South America is quickly approaching towards herd immunity, not because they wanted to, but they have no other choices at all. The hospital was of course overloaded, and the government lacked the ability to response. The living habit of South Americans would only accelerate the infection. Rumors were in Brazil where gangs asked residents to stay at home and isolate themselves -- although unlawful this could really the be the right thing to do against the virus.

Confirmed cases for Columbia and Costa Rica exploded around late May when the shock wave finally arrived South America. Despite the slow increase in testing scale, we see no signs of things under control, at all. Columbia has been testing left and right, but they still need more -- at least 5 times of the current scale -- if you compare with other big European countries like France.

South Africa is the singularity in Africa because its climate is quite different from the rest of Africa, which is bad because they are in winter now. But the bigger problem was that the government wanted to restart the economy so they lifted lockdown too soon. Daily confirmed cases doubles every 1 or 2 days since then, and the tragedy follows from slow reaction of the government. That is a pity -- we thought they did enough to shoo off the virus, but one mistake and it was all over.

*

Countries that cannot eliminate the virus

When everything is under control, the next step is to eliminate the virus locally so that the economy can reboot without creating more infection. However part of the population is always kind of disobedient. They get themselves infected and eventually get others infected as well. It has been a dilemma in western countries: rebooting the economy earlier implies that you will never get the virus eliminated, and it builds a constant pressure on the health care system as well as everything else. Most countries chose economy anyway, and we are observing more of these "long tail" infections.

The fact that Japan successfully suppressed the virus on the edge of a widespread infection shows their high standard of public health maintained. This is however, not necessarily true in every single corner of the country. Most recently reported cases in Japan are actually happening in the food and service sectors -- in particular pubs, (erotic) salons, maid cafe and so on.

It would really be a hard decision to shut these shops again. The industry is extremely fragile and already took a heavy blow in the past 3 months. On the other hand, infections are likely to happen in these places again as long as the virus is not exterminated completely, that they could be forced to shut indefinitely.

Russia as well as Singapore and some other middle-east countries are of another story. The infection is confined to the circle of foreign labours, whose are socially isolated from the general public and have a below-average living standard. Given their status in the host countries, it was deemed not worthy to eliminate the virus within those communities, so an alternative is to isolate all these workers as a whole, and hope that herd immunity would develop eventually there.

The United States case is so complicated... each states has its own problems. First of all the protests. Regardless of their motives, this is bad for disease control. Secondly lockdown was lifted a bit too early in some states like Florida and Arizona. The southern states also received an influx of patients from Central and South America, where things are apparently uncontrollable. Imposing the lockdown again is the right choice, but protests and the effects from neighboring countries would drag back the effectiveness of the lockdown.

*

For the rest of the world, UK is apparently reopening its border for most travelers knowing that their own immunity is good the point where taking ill travelers is of no big deal anymore. We are also observing relaxation of border control among countries that eliminated the virus like Taiwan and New Zealand. It would be fun to observe half of the world recovering, and the other half still fighting hard against the virus.

Ref.

[1] Total confirmed cases vs total tests conducted, retrieved 5 July 2020.

24/05/2020：逆戰、桐人、哈利同人

來分享幾件事好了，反正現在封城解禁我也不想外出。

跟Fanta難民聊了一下，公會戰果然是大家永世難忘的活動，尤其是前兩三次的地獄35連戰。我開始整理出了點頭緒，卻找不到可以當背景的餐廳－－我被封城令困住了啊啊啊啊！

最近我在沉迷MyKirito－－大部分都來自現有遊戲的機制：回合制養成、轉生系放置、後台台詞插入、爬塔制度等等，不過加上SAO一整合起來就爆發了。努力值和修行的平衡很好，但遊戲的潛力似乎也見到盡頭了：將EV[努力值]配好打某王就有某機率過關，剩下只有execution和肝力問題而已。所以說，ACGN好遊戲不玩嗎？

玩放置系遊戲自然會有CD要等，我把這些等候的時間都花在看哈利波特同人上去了。除了Z大的MWPP以外，起點某本金(銀)毛傲天將英國史揉進世界觀的故事也不錯，尤其是那個對整個大格局的解讀－－仔細想想，搭配書中魔法的潛力，正傳裡與那個不能說名字的人的對抗其實也就小打小鬧而已。這也是為甚麼一些人更嚮往夢幻飄逸的祖世代(四位始創人)和山雨欲來的魔世代(對葛林戴華德feat.二戰)而不是小打小鬧的現代(父/親/子世代)。既然魔法世界被設定/塑造成一直停留在近現代的話，現在與過去又有何區別呢？

*

香港的情況差得使人逃避、使人絕望。但我們不可以害怕，也沒條件可以害怕。議員權力一再被限縮，香港的公民力量卻從未停止過。只要大家緊守崗位，我們所盼望的必將到來。

Model on outbreak stages classification: May updates

It has been 20 days since I last posted my analysis on the pandemic using a test count vs positive rate model. Here are some quick updates, particularly from those countries that I posted last time.

For graphs below, the "new parts" are indicated by a thicker line, starting from Apr 15 up to 5/6 May.

For further reference this is my first analysis

Classification of outbreak stages by variation of test count and positive rate

*

Stage 2->3

Pretty scary, right?

Strictly speaking, the positive rate that we are using is not the positive rate respective to the group we tested. Instead it is the ratio between confirmed case and testes case on that day.

In wealthy countries, tests are supposed to be done now within hours since we do not rely on DNA tests anymore, so such statistics would somehow reflect the positive rate of the day. In less developed countries however, this is less reliable.

Theoretically, a "positive rate" of above 1, even after smoothing, is possible though not sustainable. It means some delayed tests returned positive. Apparently this is not the case for Ecuador here. In the raw stats, both the test count and the confirmed count spikes quite often -- a big spike that cannot be wiped out by taking week average.

But such fault does not change the trend after all. We can see that Panama enters stage 3 with their extended tests. Meanwhile Ecuador could be still in stage 2 considering that the last spike only occurred 1 week ago (11183 -> 22719 on 27/4), we are still experiencing the drop as the spike moves out of affection. The daily confirmed case shows no signs of improvements, so I doubt things are under control for now.

Mexico is actually another country with spikes in their raw data so that the positive rate rockets above 1. The more worrying news is, they failed to expand the testing scale to cope with the emerging cases!

Stage 3->4

Once countries enter stage 3 it is almost sure that the countries did take proper measures, so as long as they do not lift the lockdown too early things will go improve.

Italy's 50000 daily test count is enormous given its size, but also understandable given how bad the outbreak was. It is certainly working and the positive rate drops vertically. She's in the end of stage 3 and will enter stage 4 once the testing capacity is in excess.

Indonesia is seeing similar improvement. Early spikes are due to religious events, but there was never an uncontrolled outbreak. With their testing capacity gradually improving they will enter stage 4 soon, too.

Stage 4

These are models for reference -- what happens after gaining full control over the virus?

Estonia is a rare example in Europe that avoided a full-scale outbreak. She's able to slowly put out the virus with constant testing.

New Zealand, who announced an early lockdown, is close to a full elimination. She's now ready to re-open again, but the test is not going to stop anytime soon to prevent any accident.

Updates on large countries

Canada was under the risk of favoring weather for the virus, but she proved that proper antivirus measures definitely helps regardless of the environment. I would say it is stage 2 to 3.

US is definitely improving. Not necessarily nationwide but at least for most states, including New York. We expect similar development for the rest of the states, but things may change if the governor decides to lift the ban early. US is surely in stage 3.

Russia: I mentioned last time that it is weird to see the outbreak with extensive tests -- the test count is even comparable with US! But now we know why is that the case. It is the poorly treated foreign labours, similar to what happened to Singapore (but well, Singapore provided no data). Russia is in stage 1 to 2.

Japan and UK

Two countries that are not tackling the virus like the rest of the world, so I was really curious what would happen next after I wrote my last analysis. Here are the result.

UK: well, apparently their limited hospital capacity did not limit their will to test more. They drop along the "isotherm" (green line) meaning that they have a constant rate of daily confirmed case, but the outbreak potential is slowly declining because there are less hidden patients now. Unfortunately the damage has been done, and UK is one of the most severely infected country in Europe. UK is in stage 3 and it takes some time before they reach stage 4.

Japan: probably the only well-developed country that does not really like testing. Although the emergency state order is not as restrictive as in other countries, the society slowly adopted the right measure and the outbreak somehow dies down. Everything seems to work in wonder, but I would not say Japan is out of danger really...

*

So that's all for me today. I don't think another update is necessary, but we will see. With outbreaks currently occurring in South America, the globe's economic nightmare is far from over.

Ref.

[1] Total confirmed cases vs total tests conducted, retrieved 6 May 2020.

夢．十夜 (X4.5) Hot Spring Trip

打音遊最爽的是甚麼？

將一直卡死自己的譜面打通？自己的本命曲完美通關？還是將機台裡面的排名通通刷下來換成自己的名字？

通通都不是。

打音遊最爽的是進入一種無我的「空靈狀態」。全身完全放鬆卻能保持極高的集中力，眼前除了那些音符以外一切變得模糊；手腳變得輕盈，不經思考就能準確打中所有音符；自己知道自己進入了這種狀態，胡思亂想卻依然跟得上節奏。直到歌曲完結為止才如夢初醒，不捨地嘗試找剛才的感覺卻又發現它比夢更為虛無飄渺。回到一般狀態的你只好繼續打下去，希望再次找到這種感覺。

類似的狀態在其他運動員身上也會出現：棒球員某天大開殺戒並聲稱自己那天看飛過來的球特別慢特別清楚，第二天身手卻又變得平庸；平時從不進攻的足球員突然自己帶球連過數人然後勁射破網等等都可以歸類為這種狀態的表現。

另一方面，打音遊所發生的通靈狀態則往往持續兩三分鐘，直到歌曲完結為止。期間玩家舉手投足都可以看出與平時的不同；對外界反應的減少、多餘動作的修正、更準確的發力和應對等等。聽上去很模糊但只要看到真人的話立刻就能明白所謂的通靈狀態是怎麼一回事。

我眼前就有這麼一個活生生的例子。

眼前的少女正在仿鋼琴機台Nostalgia(ノスタルジア)上挑戰蕭邦的練習曲Op.25-11(冬風練習曲)。

雖則遊戲譜面比實際的鋼琴譜簡單太多，但畢竟不是真的鋼琴，就算會彈原曲下來也不保證會打得好。遊戲讀譜與實際鋼琴譜完全不同，彈下去的時候也必須緊隨遊戲裡設定的速度與節奏，稍為用自己的步調演譯便很可能打錯，這點在古典樂曲尤其明顯。想拿到高分的人只能拋棄情感與理解，像打地鼠般將所有音符打下來。這個方法十分有效，卻也少了一重享受。

要將一首音域極廣的曲子改編到只有三個八度的「鍵盤」上其實是一件極難的事情。在冬風練習曲的遊戲譜面中，右手部雖然簡化成了八度的來回，但是音符從最高音幾乎延伸到最低音的部分，對於站著打的人來說要彈好這串實在非常辛苦。

眼前少女卻似乎有辦法按自己的節奏彈出這首困難的練習曲，除了速度不變以外，輕重與手勢都與鋼琴演奏無異。與亮眼的成績相對的是放鬆的手指與平穩的呼吸，看來就是進入「狀態」了。黑色長髮隨她擺動而飄舞著，她的身姿讓我想到四月是你的謊言(四月は君の嘘)裡井川繪見演奏的一幕。我一邊感嘆著太可愛了啊，一邊將專心打音遊－－不、演奏的她拍下來。

隨著最後一個音符結束，她重重地呼出一口氣並回過神來。屏幕上顯示的分數是982750，比自己的P B(Personal Best) 高了四萬多分。對於這首遊戲最難曲目之一來說這應該是無比漂亮的成績了。

「你剛才在偷拍我吧？」少女一副氣鼓鼓的樣子，似乎剛打出來的成績並沒有為她帶來太多愉悅。

「難得你進入狀態這麼可愛就忍不住拍了啊～哎呀別打－－」

「彈完新出來的練習曲10-4和E小調華爾滋以後就會忍不住彈其他蕭邦曲子呢。我本來想去打中二(CHUNITHM)解鎖『長野勢』稱號的，現在剩半小時時間不夠了啦。」

「嘛～每首三首加起來七分鐘，要打三道還是可以的。」

「才不要。打完nos(ノス)去打中二的話指法會變得奇怪，我肯定打不好的。」

「……卡拿來，我幫你打好了。」「……嗯，不過掉rating你就死定了。」

長野站徒步十分鐘的小型機廳，平日下午二樓的音遊區只有他們兩個在大放閃光。

距離溫泉旅館接送車起行，還有四十五分鐘。

*

大概過了二十分鐘，接送車離開須坂市進入山區。旁邊的農地不少都積了一層不厚不薄的雪。縱使外面仍然在下毛毛細雨，我心中對雪景的期待還是越發濃厚。

GPS的高度計停了在九百米左右，外面也從暗角有積雪變成路邊厚厚的一層。接送車停了在上信越高原國立公園的門口，司機確認大家的目的地都一樣後便向溫泉村深處出發。

藤井莊，傳說中森鷗外數次拜訪的旅館。

儘管溫泉村裡還有數家溫泉旅館，藤井莊的氣派與排場顯得鶴立雞群：前門從日式庭園連接着大堂。古典優雅的大堂裡面瀰漫着香薰，安靜寧神而又不嗆鼻。脫下靴子後我們便被帶到一邊並奉上點心抹茶，其間登記手續早已辦好。抹茶的細滑在預想之中，漿果米餅的香氣則比較是驚喜。米餅微甜入口即化，漿果的酸味則化為香氣隨化開的米餅灌進鼻腔和喉嚨裡。少女輕咬一口口已忍不住整塊吞下。

旅館的工作人員早就準備好帶我們進房間。映入眼簾的是一間超過六百呎的和風房間：踏進玄關後就能看到會談室(不過工作人員把行李放了在會談室的榻榻米上，大概覺得住客不怎會用那邊吧？)﹐沿走廊走兩邊依次是廁所浴室、廚櫃、之後是20張榻榻米拼成的超大主房間。

房間外面還有觀景用的陽台，地上鋪上了木條，顯然為了不讓旅客凍傷和排水排雪而設計。陽台的彼方是草津群山，比較可惜的是樹上積雪還是不多，陰冷的小雨加上日落後的寒風實在使人提不起興致出去，還是躲進被爐裡最實際。

當然，明天下雪的話……

晚飯時間可以選六點或七點，選了七點的我們當然不會放過先去泡個溫泉的機會。倒不如說，我是為了先去泡溫泉才選了七點吃的晚飯。

溫泉不是很大，只有一個主池和室外池。旅館本來人就不多，溫泉在這個晚飯時間就更顯冷清－－其實就只有我一個而已。15米乘8米的主池已經非常寬敞，從滾燙的出水位挪到稍熱的另一端再淋上一盆冷水實在是人生一大享受。

溫泉旅館另一種必備神器當然就是露天溫泉了。這邊的露天溫泉就在主池的落地玻璃外，以兩層拉門隔開，確保在泡溫泉的人不會因為有人出入而受到影響。因為天色全黑的關係外面看不到太多東西，但有一點可以確認：外面確實是貨真價實的山景。

我回到房間已是六點半的事了。房間的暖氣十分充足，但少女仍興奮地抱着暖桌不放：「啊～要被暖桌妖怪吸進去了～～」

我嘗試把她拉出來，少女絲紋不動：「別玩了啦，差不多到晚餐時間了。要不要先去試下當地清酒？先試一下晚飯比較好下決定嘛。」

……等下選錯酒可別怪我喔。少年心中如此默念。

*

在獨立的和室我們嘗到的是以睦(一)月為主題的信州懷石料理。

首先上來的是七福為題的茶碗蒸。藕片、小蕃茄等七種食材融入到蛋香裡。每一種食材柔和又不至於失去特色，湯匙每挖下去一點就能發現新一層食材，好吃之餘又不失趣味。

與茶碗蒸一同上桌的是用茶壼盛著的清湯。茶壼被放在桌上的小火爐上加熱，保証客人能嘗到滾燙的鮮湯。湯裡面海帶與鮑魚菇的鮮味自不用多說，當中的豆皮與蘿蔔泥更是吸收湯中精華，讓人禁不住一口氣將壼中食物清空。

提鮮的前菜之後是刺身，不過不是沾芥末醬油而是沾蛋黃。順滑的蛋黃強化了三文魚入口即化的口感，之後改為拌碎蔥與薑末則可以將口腔中蛋黃的滑膩感清除掉。另一碟刺身則是當令的鮭魚，同樣不用醬油而是輕輕地鹽漬過，紫蘇和柚子皮與微鹹的剌身形成絕妙的平衡。

剌身過後便是藤井莊的招牌菜ぽんぽん鍋，其實是一個串炸鍋，ぽんぽん的聲音代表的是油炸時發出的聲音。職員一邊為我們解釋，一邊將炸好的炸串放到油鍋邊上的鐵環上。這樣一來可以讓多餘的油回流到鍋中，二來也可以保溫－－當然我們炸好就拿去吃就是了。

六條炸串、彷如一個迷你的完整菜單一般：
第一串、芝士與信州豬肉。液體狀的芝士讓豬肉不會過熟，咬下去是完美的鬆軟狀態。
第二串、單純鮑魚菇(アワビ茸)。不加任何調味料的炸法，讓客人感受到最原始的菇香；沾上竹鹽則令鮮味更上一層樓。
第三串、小芋頭與白果(銀杏)。這串白果與一般熬過湯的口感完全不同，咬下去更像是烤過一般，濃縮起來的味道一次過爆發出來，其咬勁也跟烤芋頭形成有趣的對比。
第四串、年糕蝦丸。炸出來看似普通的龍蝦丸，實則是年糕在外而蝦肉在內。
第五串、蕃薯片。既可以說是定番，也可以說他們對在地農產品有信心的表現。香軟蓬鬆的蕃薯只會讓人想再來一片。
第六串、作為甜品收尾的蘋果與杏桃。這串類似烤焗的效果更為明顯，杏桃雖然收乾了但與一般買到的杏桃乾不同，吃下去酸甜多於泡糖水的甜。

在濃味的串炸後是清新的冷蕎麥，之後便是晚餐的另一個高潮、信州牛肉鍋。店員適時關掉火並再次端上蛋黃，牛肉毫無懸念地入口即化，她甚至將混有牛肉汁和醬油的蛋黃整碗吞了下肚。

主菜過後晚餐也進入收尾的環節，首先出場的是山葵葉拌飯與味噌湯。爽脆的山葵葉本身也帶有輕微的辛辣感，配上白飯甚至不需要任何其他的調味，我們輕鬆就把一整鍋飯清空。

甜品是無花果與梅子果凍，配上其他鮮果。不像西式甜品的金雕玉砌，卻能讓客人感受到每種生果的真實味道。

這種等級的料理當然少不了對應的清酒，我們點的是夜明け前的大吟醸。酒度與酸度幾乎都在正中間，蜜瓜般的果香在入口的瞬間擴散，及後那一點點辛辣感提醒我們這可以是一支餐酒，而且是一支可以貫穿整頓晚飯的餐酒。

至於我後來一直試夜明け前系列中不同的產品，那又是另一回事了……

*

本來是接待入住旅客的大堂，搖身一變成為客人飯後小敘之處「山之茶屋」。白天的山景為黑夜所遮蓋，漆黑中只有刻意照著的樹枝加上降雨與室外溫泉對碰產生的霧氣，可謂別有一番意境。

房間裡提供的是煎茶和蕎麥茶、「山之茶屋」提供的則是咖啡與紅荼。比較意外的是這裡也有提供德國老牌Ronnefelft的茶。這家德國老字號給我的印象是經典的味道，沒想到他們的香氣配搭上也有自己的一套。Feel Relaxed裡面有經典安寧配搭矢車菊與黑莓葉，南非茶則比紅茶更切合放鬆這個主題。最有趣的是茶裡亦有橙的香氣，橙色的茶色幾乎使人以為自己在喝橙汁。要我說的話，大概就是Mariege Freres的Midnight in Paris的變種吧？

我呆呆地看著窗外的霧氣，一邊回味剛才的晚餐。

兩個小時的晚餐一點都不短。但是兩小時內要仔細品味每道菜、聽服務員介紹和聊天再加上品酒的話就不太夠用了，要回味的話只能靠飯後茶這段時間。我瞄了她一眼，她果然也陷入恍惚狀態了呢。

「剛才的晚餐如何？」我望向旁邊還在發呆的少女問道。

「……好想再吃一次啊。」面對高級料理頗為挑剔的她給出簡潔有力的評價：「大量採用時令在地食材就是自信的證明，簡單的調味但不尋常的配搭將食材本身的味道完全展現了出來。吃下去就會覺得『只有這裡才有的味道』，就算想抄回去自己做也做不來，果然抓住客人的胃就是抓住客人的心呢－－」

放在桌子上的手機發出顫動的聲音。她以比平時更快的手速伸向手機並飛快地點開，然後尷尬說道：「嗯……今晚剛好約了朋友做個小實驗呢。能不能先讓我回房間呢？」

本來想說去旅行的話她會放下電腦專心享受，看來還是放不下呢……

少年嘆了一口氣，轉身去泡了壺新的Feel Relaxed。

*

外面的雨越下越大了。雖說雨點沒有吹到露台上，但從燈光往外照只有密麻麻的雨點。腳下的木條還是乾的，那陰冷的感覺還是讓人不太好受，我趕緊縮回房間裡去。

房間裡完全沒受到外面的天候所影響。暖氣平均地散佈到大房間每一個角落裡，甚至讓剛進來的我感到氣悶，但她若無其事地把身體埋進暖桌裡面……這樣不會熱死嗎？

桌面上放著剛泡好的蕎麥茶。現泡的蕎麥茶即使在日本也不太常見，這裡的蕎麥茶充滿了烘培的香味，跟自販機買到的完全是兩種等級。隨手抓起她的杯子把裡面的茶喝光，我把茶添回去後從後抱著正專心打字的她：「這是在做甚麼呢？」

她沒有轉頭看我，聲音裡卻有一種興奮的感覺：「我在做有關大壓制戰的實驗喔。」

大壓制戰(Grand Conquest)是火紋英雄的活動之一。玩家被隨機分配到一個池裡面再分成三隊，以回合制進攻別隊領地的活動。玩家可以按自己實力選擇挑戰的難度，難度越高分數越高，打出來的分數會加到自己選擇的領地上，也會加到該領地週遭(neighbour)的領地上。玩家在整局的戰鬥總次數是有限的，但每回合的戰鬥次數則沒有限制。每回合結束時領地上分數較高的隊伍就能在該回合佔領該領地並得到土地分數，某隊在一個領地領先太多的話也會立刻宣告佔領，且該回合剩下的時間沒法在該領地戰鬥。最後勝利的隊伍會依照各隊土地佔領變化決定。

簡單來說就是典型的戰爭型戰棋。

本來這樣的活動有很大的PVP潛力，可惜官方並無往這方向發展的想法。敵人的隊型幾乎都是在玩家隊型中抽樣出來的隨機隊伍，活動獎品也是休閑PVE活動的等級。所以除了佔比最重的最後一回合外平時大家都只是抱著清體力清任務的心態去打，所以並沒有太多隊伍對抗的狀況。

「我看到一篇Reddit上說希望大壓制戰裡增加溝通和求援功能的帖子，被罵得很慘呢。」一如遊戲殘缺的交友系統，這種高度策略性的活動居然沒法跟任何其他隊員交流。這樣玩家認真打的動力就更少了：「所以我朋友就弄了一個大壓制戰的戰棋版，我們正在調較參數呢。」

「如果改成戰棋的話，戰鬥變成某幾塊領地的集中對抗吧。這樣的戰棋不太好玩吧。」每次大壓制戰的地圖都略有不同，那都是按本傳裡的地圖改編的。這就決定了部分領地在成了min-cut(最小割)理論中的橋頭堡，大部分回合的戰鬥都會圍繞這些領地而展開。

「不過這遊戲也不完全是線性呢。同隊不同玩家都在同一領地上戰鬥的話會有倍數加成，我們把它簡化成每個行動都屬於不同玩家就好了。另外我們把地圖設計成有多個min-cut(最小割)解的話玩家就沒法大量投入兵力在某幾個領地了呢。」

她一邊向我介紹一邊展示著屏幕上的棋盤。上一回合她巧妙地偷襲了一塊領地，使得這個回合這領地成為三隊都可以爭奪的地方。另外兩隊為此大打出手，她則可以把兵力省下來鞏固自己其他領地。

「可是大壓制戰裡面每隊玩家可以投入的資源跟領地多寡無關吧。這樣會不會到最後形成消極平衡？」多人零和遊戲本來就自帶恐怖平衡。問題是如果這種打法偏偏是最優解的話這遊戲就失去博奕的意義了。

她試圖把兵力省到最後一回合，但不知怎的對面兩隊竟然一起攻了過來。她只好固守其中一邊，而對另外一隊的大肆侵掠視而不見－－這是分化對方，將對方一隊的戰線拉長吸引攻擊的打法。把這些都設置好後她想一下道：「嗯～如果我在正中央多加幾塊領地呢？如果玩家想達到平衡必須拿到這些中間的領地的話，他們就只能大打出手了吧？」

「這樣平衡會以另一種形式出現吧？誰佔領了中間都好，玩家也可以自行調節外圍的領土分佈達成平衡啊。」

她發出幾下得意的笑聲道：「哼哼，這就輪到我出場的時候了。中間新增領地的數量必須除三餘一，11個回合裡第一回合中立領地不屬於任何玩家，剩下10回合都會由玩家佔領。這樣三個玩家的佔地-回合數加起來也是除三餘一，這樣我們就有辦法決定贏家了呢！」遊戲踏入最後一回合，她在前面省下的兵力比另外兩隊加起來都多。她一口氣把所有兵力投下去，消耗掉對面僅除的兵力後用少數兵力就把對面領地逐個擊破。結算下來，一路小幅落後的她在最後一回合成功逆轉勝。

將伸懶腰的她順勢抱進懷裡，她繼續發表她的想法：「不過感覺還是差了一點……那就是用分數換取效率的問題。」

在真正的活動裡，玩家攻擊領地時可以選擇挑戰不同的難度。越高的難度打出來的分數就越高。最高難度的話就連重課玩家也要用腦慢慢打才有辦法完成。這樣的話打稍低難度每分鐘能拿到的分數會比較多，但總分反而會略降。

「你還真是喜歡這招呢。」

「是啊，畢竟這是網遊的精髓所在呢。能用錢買到的東西大家用錢就能拿到，要動腦的的東西卻不是大家動腦就能得到的呢。」

在2020年的今天，手遊已經成為龐大的產業鏈。龐大的競爭使得優化的需求水漲船高：用甚麼隊、怎樣打都有明確的「作業」可以抄，甚至到了「A和B的劍呈30度時發動技能」這種精細的程度。在這種大環境下她還能找到可以改進的地方實在是難能可貴。

更重要的是，她研究遊戲全神貫注的樣子十分可愛。每次坐在她旁邊給出不太有用的意見後她總能從中提出有用的資訊，然後改進自己的計劃。從古龍同萌傳到終戰幻想都是這樣，將她的構想實行出來漸漸成為了自己最大的樂趣。

「嗯，怎麼你發呆了啦？」她抬頭向上仰，清澈的雙眼直視我稍稍發燙的臉龐。

「……沒甚麼，看到你這麼開心就好。」

「先旨聲明一下哦，這家旅館真的很棒。食物和服務無可挑剔，建築的話我搜了一下才知道是那個設計加賀屋的山本勝昭的出道作。如果C97那個時候可以給六十分的話現在可以給個八十五分啦。所以……」她有點欲言又止：「謝謝啦。」

「呵呵，大小姐居然也會道謝呢。比起那個，明天想去繼續找美食、還是去看雪景呢？」畢竟是長野那個嶺上怪物的老窩，多走走的話麻雀功力可能會進步。

「你喜歡就好了啦，但不要跟我說去新潟去喝酒……」

「放心，長野也是產酒大縣，要找好酒才不用跑那麼遠呢。不過既然都說我喜歡就好～那你覺得我現在想要的是甚麼呢？」我抱著她的雙手更用力了，隱約間感受到她嬌羞的顫動。

「……」

「我想要……」我在她耳邊低喃：「妳……」

「討、討厭……」

…………
……

夜幕低垂，但這晚對本是夜貓子的二人來說還很漫長。

老天彷彿回應著他們的期許一樣。滴滴答答的大雨滴在山谷上漸漸變得不再清脆，雨滴變成軟綿綿的雪雨、再變成潔白的雪花……

**

我是不是看惡役千金太多了？是說本季的惡役千金番挺好看的，也是少數在疫情期間沒有萬策盡矣也能維持品質的新番，聽說在開播前就已經拍好了。

不知為何，這一篇從十二月拖到一月再拖到五月。終於在封城的助力下我把它寫完了，但許多細節已經從我腦海中消失。

本來想以正常的遊記形式下筆，但我覺得自己對旅館構造的理解還是差了那麼一點。自己也一直拉不下臉一直用手機狂拍，拍最多的只有獨立和室裡面的料理而已。

FEH大壓制戰有變種成桌遊的潛力嗎？其實要解決的技術問題很多。首先當然是資源固定會鼓勵消極戰術這一點，然後是每回合可用的棋子數可能要到一百以上才會比較多戰術變化，最後當然是將時間效率抹消這一點－－在實際活動裡不時發生兩隊實時在同一塊領地上死拼，但其中一隊刷分比較快硬生生將領地打爆的事情，顯然這在桌遊版上很難發生。

不過這本來就是她一拍腦袋想出來的產物，也虧她可以想象到這個程度。話說回來FEH我已經快存到1000石了。新出的炎帝池本來我都忍不住抽下去了結果第一抽就出等了很久的織部翼。難道我真的要等到新風花雪月角、或者八月的Choose Your Legend活動才一口氣拼+10嗎？

這篇跟本傳沒多大關係的遊記完成以後終於可以回歸本傳。別看Fantasica活動十幾種，早期其實只有五六種而已。所以說，下次不寫攻城戰的話到底是哪一個活動，其實很好猜……

2020年5月1日
被封鎖在家中

Classification of outbreak stages by variation of test count and positive rate

Introduction

2 facts about the pandemic: the first is that masks do help. The second is that testing efficiency is crucial in controlling the disease due to the distinct feature of the virus that most infected are asymptomatic. The first fact is easily measurable by measuring its effect on $R_0$. The second fact however is not.

The constant $R_0$ is largely autonomous which is independent of nation parameters and current status but hygienic condition. Testing efficiency depends on amount of (reliable) testing kits you can get, which varies a lot among countries and in different time.

In order to investigate this we would like to plot testing efficiency against positive rate because we can divide the pandemic within a country into stages.

(I was inspired by the typhoon kinetic energy vs max wind plot. That was studied in a completely different way though...)

The parameters

Horizontal axis: log(daily test count)
Vertical axis: Daily confirmed cases/daily test count

We collect data from [1] and show some plots for countries with 50+ confirmed cases for more than 15 days (with the exception for some countries whose started announcing their test count very early on).

The daily count is smoothed by taking a 7-day average instead, to average out the weekly fluctuation.

The stages

If we plot log(testing capability) against positive rate we can observe the following stages:

Stage 0 - the isolation period. No signs of uncontrolled outbreak. Testing efficiency varies due to global trends in different time.

Costa Rica: isolated case from time to time and the virus never really rooted in the nation.

Taiwan: the country that did the best really. Fully masked citizens (with sufficient and affordable masks) and proper quarantine policies. Most cases are imported and identified immediately.

Character on the plot: wandering around and affected by random events rather than the exponential trend.

Stage 1 - the outbreak period. Testing capability expands but can't keep up with the growth in suspected cases so positive rate grows as well.

Typical examples as of now: part of South America (Brazil, Mexico), Russia

The most recent outbreak occurs in Brazil but they provide no testing data so I picked Hungary and Mexico here.

Character on the plot: as the positive count grows exponentially the testing capability simply cannot keep up with the growth. That results in a raise (kind of log-linear) in both testing scale and positive rate.

Stage 2 - the peak period. The testing capability is now able to keep up with the urgent needs. It stays steadily on the graph.

Typical examples as of now: part of South America, US

Character on the plot: the testing capability expands to the point the infection rate is primarily control and peaks for a while. On the plot it wanders around for a moment.

Stage 3 - the expand detection period. The reduction in new patients allow countries to put their effort on testing less suspected cases. The amount of confirmed cases may peak as much as the previous stage but the positive rate will drop while testing count increases. The curve on the graph drops along an "isotherm" that represents a given number of daily confirmed cases.

Typical examples as of now: Europe and Southeast Asia

Character on the plot: the testing capability expands further that more asymptomatic patients are identified. The curve first slides along an "isotherm" that represents a constant number of daily positive case then drop further. (From here we can see that the positive rate is in some sense a leading indicator than the positive rate!)

Stage 4 - the elimination period. By picking out most asymptomatic patients the spreading speed of the virus is greatly reduced. Countries may reduce their testing speed slightly with positive rate also dropping to a very low rate.

New Zealand: she did a marvelous job by announcing a decisive lockdown very early with citizens closely following the rules.

South Korea: after the initial outbreak, South Korea is one of the countries that applied large scaled quick testing. Together with high-tech tracing they successfully (almost) eradicated the virus. KBO is opening soon, too!

Character on the plot: when the daily new case drops drastically the testing pressure is reduced greatly. The testing target turns to the general public, but it will not be as frequent as before.

The large countries

First let us look at the plot for large countries. As you can see from the stage 2 graph the testing scale is affected by the population but there is not a simple way to scale it down -- it depends on the wealth, technological level and governance controlibility of the nation. So for now a better way to look at that is to compare just the large countries.

Canada: Stage 1-2? Not heavily infected yet, but worries are there an outbreak may occur anytime as the right climate is arriving.

Turkey: Stage 2-3. The outbreak almost peaked and should go down soon.

US: Stage 2. Due to population distribution we can hardly say the whole country is in a similar state. New York is definitely improving but some other states are still in bad form. The overall count seemed to be stabilized anyhow.

Russia: Stage 1. That is the most interesting case. They started large scale detection early on...yet they failed to prevent an outbreak. To this there are several explanations. First the testing accuracy may not be as good as the wealthy western European nations (although the kits are mostly from China anyway...). Secondly they may not be testing the right people -- most tests are conducted in the densely populated cities, but the patients simply spread the virus from its western border which is too hard to "defend". It is rather easy to close the Russia-China border, but closing border on the west is extremely hard.

The outliers 

Most countries followed this pattern, except for a few. The two main outliers are UK and Japan:

UK(aka the herd immunity): Stage 1. Yeah we now know that herd immunity is a joke and the government never really tried to implement that. However they are being dragged down by their inefficient NHS system -- they are not able to transform into a state-of-war medical system. They are also not expanding their testing capability enough. Sick people are simply asked to stay home unless their feel like they are going to suffocate. Hidden patients simple floating around the whole city and spreading virus swiftly. Although with lockdown already announced, the case count may not grow like Italy [see the stage 3 graph] -- but it is just the official number. The horribly high positive rate is sampled from seriously sick patients, hinting that the actual infected count is a lot higher. God knows when will it ends?

Japan(aka the Olympic host): Stage 1-2. They are finally willing to act a bit more after announcing the delay of the Tokyo Olympics. It is however too little too late, as the virus is already spreading independently in most large cities. Japan is also one of the few countries who is not willing to test widely, due to social pressure rather than government policy. They seemed to have controlled the spreading partially, after finally being able to shoo officers away from commuting alongside with partial lockdown and emergency state declaration. They also have better hygiene in general comparing with Europeans so the situation is apparently better -- until the uncontrollable outbreak begins.

Conclusion

So, are there anything we can tell from this plot?

- Testing more is an effective way controlling the outbreak. First on the suspects or people that had direct contact with confirmed patients, then on the sick during outbreak, and lastly on general population to eliminate.

- There aren't many countries that did not expand the testing scheme for those providing data. UK and Japan are in fact the only two -- UK is in a very bad state; Japan is worsening but they seemed to gained a little control with multiple alternate measures.

- This plot is a leading indicator comparing with the confirmed count and even more with the death count. However it gives less of a clue on when the peak period is over.

- The plot will be a stronger indicator if one manages to normalize the confirmed count by countries' capability, condition and population. In such way we can standardize and define clearly the classification of stages. The stages are still clear by identifying their shape though.

At least we feel happy that most countries are willing to test more, and adopting correct measures like lockdown, applying social distance and wearing masks, unlike what WHO claimed.

Well, that's all for me today. I hope everyone is safe during the lockdown again.

Reference:

[1] Total confirmed cases vs total tests conducted, retrieved 17 Apr 2020.

Calculating area enclosed by intersections

A small math question today.

Given a unit sphere and an arbitrary ellipsoid, calculate the surface area of sphere inside the ellipsoid.

Without loss of generality, we may assume the unit sphere to be centered at origin, then the question depends solely on the 6 parameters defining the ellipsoid, $c_i, \alpha_i$ for $i=1,2,3$ in $\sum (x_i-c_i)^2/\alpha _i ^2 = 1$. Without thinking too much about existence of analytic solution in terms of the parameters, we want to look for ways to calculate or at least approximate the problem.

My own solution is based on the famous Gauss-Bonnet theorem:
$\int _M KdA + \int _{\partial M} \kappa _g ds = 2\pi \chi (M)$

The curvature of a unit sphere is constantly 1, and the Euler characteristic of a disc is 1. As long as you can calculate the geodesic curvature you get
$|M| = 2\pi - \int _{\partial M} \kappa _g ds$.
The intersection is a union of finitely many closed curves we can just calculate one by one.

A simple example would be as follows:

Consider the intersection between $x^2+y^2+z^2=1$ and $(x-1)^2+y^2+z^2=1$. The intersection $\Gamma$ is given by $x = \frac{1}{2}$ and $y^2+z^2 = \frac{3}{4}$. This is a circle of radius $\frac{\sqrt{3}}{2}$ with geodesic curvature $\frac{1}{\sqrt{3}}$. Therefore we have $\int _{\Gamma} \kappa _g ds = \pi$, so $|A| = 2\pi \pm \pi$ depending on the orientation. The surface area can be verified using the formula from Archimedes $|A| = \pi (h^2+a^2)$.

*

Of course, obtaining the parametrization is sometimes too difficult. Are there any easier ways to approximate the answer? Here are two suggestions from my friends.

- Monte Carlo based: sample points on the surface of the sphere and check whether it is in the ellipsoid.

- Integral approximation: similar to Monte Carlo but instead we split the sphere into pieces using spherical coordinates, then the required area is the integral over the indicator function of the ellipsoid.

And of course we can get an estimation using the Gauss-Bonnet approach. Let us call the sphere $S$ and the ellipsoid $E$. We start from a point of intersection, say $x$. The curve goes in the direction $v\in T_xS \cap T_xE$, the intersection of the tangent spaces of the two objects at $x$. We know the intersection must be of dimension 1 because if the two objects are cotangent at the point then the intersection is a point which generates no area after all.

Obtaining this direction is simply algebra, where we find the intersection between two subspace. With this direction we can numerically obtain a closed curve. There is a gap here because we may not go back to the starting point using numerical approximation. We just assume by smoothness (well sphere and ellipsoid are very nice objects) by doing fine enough approximation things would work (actually I believe we can prove this but I am not an expert in numerical methods) -- then we have an approximated curve of intersection.

From here we can calculate its length as well as its geodesic curvature, and the estimated area follows.

Gauss-Bonnet seems quite universal even if we generalize sphere and ellipsoid to other bounded closed $C^{\infty}$ objects because they are manifolds anyway. The only worry being whether we can get a closed curve without any global features that promises convergence.

*

Well this is just a funny little problem that I enjoyed during the lockdown. I feel like I should write some maths before I go back to my creation whether it is literature, music or research.

Meanwhile I hope everyone is alright during the pandemic -- whether you call it COVID-19, or Wuhan virus. Stay indoor, and stay healthy.