Sunday, June 19, 2016

Caylus (凱呂斯) 量化分析

Caylus 是個經典的工人放置遊戲 
http://boardgamegeek.com/boardgame/18602/caylus
目前在 BSW 和 BGA 上都可以免費玩
我想要提供的不是一個固定的策略,因為多人 Caylus 中很可
能不存在一個死板的最佳策略。我要介紹一個 "量化" 的方法
,讓每個人都可以憑自己的風格和經驗,找到最有勝算也最適
合自己的策略。

目錄:
第一章:初步估計
第二章:增值動作分析
第三章:房子的價值
第四章:效率和限量
第五章:賞賜
第六章:風險和戰爭

感謝 ptt 版友 noyarc, meir 對本文初版的批評指教。





第一章:初步估計

遊戲最後比的是分數,但是遊戲當中你最常直接得到的東西是
資源和錢。所以建立任何戰術最重要的第一步,是瞭解資源和
錢的價值。我推薦的計算方式是:

     一個資源 = 一塊錢 = 一分

金塊一個三分的廢話就先不提。請先注意,這個算式是為了將
來的計算做基礎,而不是直接拿來估計你下一個動作的價值。
幾乎在任何時候,手上比別人多一顆資源,是比多一元來的好
,也比多一分來得好。然而這裡說的“好”,是根據遊戲的進行
隨時在變化,而無法死板的量化的。我的目的就是要透過簡單
的計算,讓你靈活的在更種狀況下,能自己去分析到底“好”在
哪裡。


所以我定的基礎價值是被市場決定的。所謂 "市場",泛指所
有不同東西互相轉換的機制。前期的中立建築確保一塊錢常常
被轉換成一分;第三階段的城堡確保大量的資源可以被轉換成
平均一個一分;拉監工,使用銀行和教堂也確保錢可以直接變
成一個一分。在一般的遊戲狀況下這些管道的暢通使得以上的
估計方式算是可靠。

當然,有一些細節必須注意。一塊錢算一分是建立在大家的錢
在一個合理的範圍,後期大概是十塊左右,前期則略低。在第
二階段,當你有十塊而兩個對手都只有五塊,那你確實有五分
的領先。當你有二十塊而對手有十五塊時,顯然並沒有領先很
多。特別是遊戲快要結束而多的錢花不完的時候,剩下來的錢
是幾乎沒有價值的。

因此,在你金錢領先的時候,請千方百計的發動 "拉監工 (小
圓盤) 的戰爭" 。先不管最後結果的細節,大家一起花錢就是
對你有利。要怎樣發動一場 "拉監工的戰爭" ,是 Caylus 
中最經典的部分,我會之後再詳細說明。多餘的錢常常會讓你
在這個可能性中取得優勢地位,而一塊錢價值一分這件事已經
把這個隱性的優勢計算在內了。

在確立的初步的價值估計之後,我們會發現遊戲中的動作大致
上分為兩類:
(1) 轉換:
花一塊錢派人去拿一個資源,買分或買金塊,或是蓋城堡沒得
賞賜。這些行動並沒有(或是很少)直接讓你的總資產增值。
(2) 增值:
蓋房子,蓋城堡得賞賜,比武場得賞賜,得到金錢,用木造或
石造資源房。

轉換的動作通常即使你兩手空空依然可以去做。增值的動作常
常需要你手上有資源,有時還需要大量且特定種類的資源,才
能夠執行。一場遊戲下來,執行最多次 (總效果最大) 增值動
作的玩家就是贏家。這不表示你隨時都直接搶增值動作。當你
可以執行轉換動作確保接下來某些增值動作只有你能做,你也
是搶到了那些增值動作。舉例:拿石頭確保敵人沒有,那造石
場就是你的;拿布而敵人沒有,那比武場就是你的;確保資源
多樣化可以蓋出較多城堡,那城堡就是你的。


等你瞭解哪些動作增值多少,再想想你要做多少準備才能去執
行,你就會開始瞭解各種動作的“好”在哪裡了。


A Quantified Guide to Caylus

Prologue:

Caylus is an epic “worker placement” game, http://boardgamegeek.com/boardgame/18602/caylus. It is currently available on both BSW and BGA for free online play. Thanks to that, a large number of games have been played and recorded. Inevitably, most of the online games are between 2 players, which gamers call “2er”s. Due to the lack of intrinsic luck factors, 2er Caylus can be rigorously calculated, and there exists a framework of dominant strategy focused on using the 4th track (building) favors.

This post will not be about such dominant strategy, since you can find a good description elsewhere. Actually, I will barely talk about 2er. I will instead focus on multiplayer games, 3er, 4er or 5er, where there is no dominant strategy. Don't get me wrong. The building favor is still useful, and a related strategy can still be efficient. However, that should not be the only strategy you know. If that is the case, such lack of flexibility not only decreases your own chance to win but also makes the game boring.

Disclaimer: This is NOT a strategy guide. I will not tell you exactly what to do. Instead, the main point is to demonstrate a framework of calculation and quantification. This is because multiplayer Caylus is too deep for any linearized strategy. I am simply providing the tools that everyone can use to find his/her own favorite strategy.


Chapter One:  Basic evaluation
Chapter Two:  Productive actions
Chapter three: The value of buildings
Chapter four:  Efficiency and quota
Chapter five:  Favours
Chapter six:   Risks and wars



Chapter One:  Basic evaluation

Victory is determined by victory points (VP), but during the game you will often directly acquire money (coins) and resources (cubes). We need to establish a baseline conversion rate in order to perform any calculation. Here is what I will use:

1 coin = 1 cube = 1VP

In addition, 1 gold = 3VP.

Please note that this equation is not for you to directly evaluate your immediate next move. They form the baseline of our calculation because they come from the most frequent, and usually guaranteed actions (that if one player choose to do so, others cannot or will not stop him)  throughout the game: (1) neutral buildings turn one coin into one cube and are continuously used through out the game, (2) multiple castles in the last stage turns 1 cube to 1 VP and it is common to have a lot of castle building, (3) Bank and Church turn coins into VP or equivalent golds in exactly this rate. Even you are not a very good player, you can expect this basic conversion from coins to cubes to VP to happen naturally for you, in at least this rate.

As you get better, you will manage to get yourself better conversion rates. The purpose of this guide is to provide a framework to quantify how much "better" you can get, which is convenient determined by comparing to this baseline rate.

The true value of coins and cubes are of course highly situation-dependent. By the very end of the game, you certainly prefer 1 more VP than anything else. Earlier in the game, 1 more cube can usually give you an advantage much larger than 1VP. The value of having more coins depends sensitively on how much your opponents have. Early in the game, when you have 7 coins while your opponents have 2, that is a solid 5VP lead (or maybe much more). However later in the game, when you have 20 coins while your opponents have 15, it is obviously not as good.  A smart arrangement to induce a ``bribing war’’ on Provost can efficiently reduce everyone’s money, therefore maintaining the value of your extra coins.

In addition to the actions that established this baseline value, which by definition only ``transforms’’ one form or resources into another form without increasing value, there are other actions which are “productive”: they allow higher conversion rates than the baseline. Being able to perform more and better productive actions wins the game. 

However, this does not mean transforming actions are weaker than productive actions. That is because productive actions often require you to have certain set of resources, which you can only get from doing a few transforming actions as preparation. If you are the only one who is ``prepared’’ for these productive actions, you almost guarantee that they are yours to take. For example, the Jousting Field (1 Favour) requires a cloth (purple cube), and there is absolutely no way to get a cloth before the Jousting Field activates in the same round. Therefore, if you are the only player who has a cloth left from the previous round, you pretty much guarantee the usage of Jousting Field. Likewise, being the only player to have stone somewhat guarantees your usage to the Mason. 

So getting the right transforming action is a integrated part to help you get more productive actions. Exactly how to do that, is tactic/strategy, which is not my focus. Since you eventually have to do some productive actions to win the game, my goal is to help you understand their values. Otherwise, you might have beautiful planning, getting all the productive actions you want, and still lose the game, simply because you ``wanted’’ the weaker productive actions. That would be a shame, right?