|The Angle on Curves, Part Two
A Call of Cthulhu: The Card Game strategy article by guest writer Marius Hartland
|Call of Cthulhu LCG | Published 25 July 2011|
"You have always scoffed at modern science," I said, a little impatiently.
"Only at scientific dogmatism," he replied. "I have always been a rebel, a champion of originality and lost causes; that is why I have chosen to repudiate the conclusions of contemporary biologists."
"And Einstein?" I asked.
"A priest of transcendental mathematics!" he murmured reverently. "A profound mystic and explorer of the great suspected."
–Frank Belknap Long, The Hounds of Tindalos
There is an old saying that there are three kinds of lies: Lies, Damned Lies and Statistics. While the human psyche has evolved to predict the outcome of events before they happen – You probably can predict that say, setting fire you yourself will not end well, and that clicking certain buttons on your computer will magically summon a web page such as this one – there are certain things we're bad at predicting. Some of those things involve statistics. Lotteries make money off people being so bad at evaluating chance. The nature of statistics, however, is that some people playing a lottery are right, some of the time.
Probabilities are based on luck. There aren't really good ways to always win at lotteries, except for not playing them. On the other hand, there are ways to maximize luck in some cases. One of these cases is in building your Call of Cthulhu deck, so it is optimized to your needs. It doesn't guarantee anything, but at least you'll be right most often. Last week we sorted our decks on cost, to get an idea on how cost is distributed in a deck. So, what do we learn from this?
To make predictions, we will make a couple of assumptions, which will make calculations a bit easier. First of all, our deck is going to be exactly fifty cards. The minimum deck size ensures that there is the greatest chance a particular card is drawn. Also, fifty is the half of one hundred, which is convenient when citing percentages. The second assumption is that you are the player that goes second. This allows you to draw two cards, which, together with your setup hand of eight comes to a total of ten cards 'seen' in the first turn. Ten is also easy to use when percentages are involved, being a fifth of your total deck.
Strategy games that have a component of resource management often make use of the concept of a “build order” which is the optimal development to achieve a certain goal. The exact order depends of the goal of the player and also depends on how aggressive or defensive the strategy is. The domain system in Call of Cthulhu: The Card Game has a few strategic variations:
“Horizontal,” which is the most aggressive of orders. This allows you to play the most cards early on, but once your hand is depleted there are fewer cards to take advantage of it. On your turns, the number of resources on your domains will look like this:
Turn 1: 2-1-1, Turn 2: 2-2-1, Turn 3: 2-2-2.
Horizontal resource development sometimes even makes use of domain creation, like Eldritch Nexus (Core Set, F154) which works best if you have Character or Support cards with 1-cost abilities to make use of when your hand is depleted.
“Vertical” is the most defensive one. It looks starts slowly, but hopes to overtake the game with more expensive (and thus better quality) cards. Across turns it looks like this:
Turn 1: 2-1-1, Turn 2: 3-1-1, Turn 3: 4-1-1... etc.
Most strategies won't go all out horizontal or vertical though, choosing one of the more moderate versions, or even switching between these build orders depending on the situation and which cards are drawn:
Turn 1: 2-1-1, Turn 2: 2-2-1, Turn 3: 3-2-1 for a 'speedy' start or:
Turn 1: 2-1-1, Turn 2: 3-1-1, Turn 3: 3-2-1 for a 'steady' start.
Pulling It Together
So, what does it all mean? Well, your deck and your intended build order need to be in harmony for the best results. So, you want to go for speed? This means that in your first ten cards, you'd want to have two one-cost cards and one two-cost card. To achieve this in your average game, you'll need to put in five times as much: ten one-cost cards and five two-cost cards. Note that this is average. Depending on how important this start is to your overall strategy, you'll need to put in more, to make it more likely to happen. Putting in twenty one-cost and ten two-cost makes it far more likely, bringing around three out of four games in which you have the ideal start.
Sorting your cards on cost and seeing your 'resource curve' shows you which cards do not fit your intended build order. This hinders your chances in getting that perfect built order out, and playing the cards when you want to play them.
Generally, you'll want fewer of the more expensive cards, depending on how you plan to build your resources. Going more horizontal means you'll have four more turns before you can play, say, five-cost cards. If your deck isn't flowing, you can find what the problem is in making the most of your resources.
Fortunately there is some room for 'fudging' your numbers. First of all are the resources themselves. If you have cards you can't play right now, they make good candidates for resourcing. The more expensive cards have another bonus: They generally can be played when you've resourced more. This means more turns went by, and more cards were drawn.
Unlike a dice game, where it's possible to roll a dice fifty times and still not roll a 6, the randomization of your deck still carries inevitability. Each card drawn (in a fifty card deck) adds a 2% chance a particular card is drawn. This means the standard draw of two cards already adds 4%. If you want to have that Shub-Niggurath, The All Mother (Core Set, F121) at turn six, when you can play it, you'll have drawn twenty cards already. This means there is a 40% chance during a game you will have drawn it even if you only have one. Adding a second copy adds another 40% chance, that with overlapping scenario's gives you a 64% chance on at drawing at least one Shub-Niggurath in twenty cards.
So, lets take a look at a formula:
H (n) = C (X, n) * C (Y - X, Z - n) / C (Y, Z)
To make use of this, fill in the following:
- N is the odds of you not drawing a card.
- Z the number of cards drawn..
- X is the number of cards you are looking for.
- Y the size of your deck.
This is quite a bit of work, so why not making things a little easier? If you have some spreadsheet software on your computer (Most will have Excel, but you can also use Open Office or some other software, to taste...), it has some handy functions. Whatever you use, the function you're looking for is called a Hypergeometric Distribution. It will look something like: HYPGEOMDIST (N, Z, X, Y)
When you fill in the numbers (N, twenty cards, two Shub-Nigguraths, fifty cards) the result will be 0.36 as the odds. (1-N)*100 gives you a percentage, so 1-0.36 = 0.64. Multiplying by 100% gives you the 64% chance. 1-N itself gives you the average number of cards in hand, if you're even more lazy. So, after six turns, you're likely to have drawn 0.64 Shub-Nigguraths. Easy, huh?
Mind The Gap
When you look at your resource-curve, along the number of turns you plan to play before playing a card of a certain cost, you can calculate the ideal resource-distribution in your deck even without considering card effects themselves. You can always favor the cards that favor your strategy the most. Other things to consider, especially if you plan a more vertical build orde,r is looking at gaps. If your deck is mostly two-cost cards (indicating you plan to build more horizontally) but Shub-Niggurath is in there, you'll have a definite conflict in resourcing. It might be better to include some cards that 'curve out' towards a cost of seven. Include some three, four, five and six cost cards to make the best use of your big domain as you move towards calling the Ancient Ones.
When you go multi-faction there are even more things to consider. If you want to use cheap cards in both factions, you're best of going 50/50 to ensure the best possible resources. You will need at least two cards of your secondary faction: One to resource, one to play off that resource. If you really want Cthulhu, Lord of R'lyeh (The Wailer Below, 64) in your Agency deck, you might be able to get away with far less Cthulhu-faction cards, as you'll have ample of turns before needing a Cthulhu-faction resource.
Finally, the optimal deck might run suboptimal cards. When your metagame is overrun with Lunatics, either Sirens of Hell (Whispers in the Dark, F7) or Shotgun Blast (Core Set, F16) could be good solutions. Shotgun Blast is generally superior, even in mono-Hastur decks, as it's free to play on insane characters. The timing also offers more freedom and in a pinch you can resource one to use a second copy to wound a character with one skill. Lunatics can be fast and numerous, so why not play both? That offers the greatest chance to find a solution early and often.
So, that's the secret of building the best decks: Find a balance between individual cards and overall strategy. Plan your moves before even shuffling up and playing the game. Know the rules of your deck and be prepared to break these rules, when you need to, willfully and purposely.
Based on the fiction of H.P. Lovecraft and his literary circle, Call of Cthulhu: The Card Game takes two players deep into the Cthulhu Mythos where investigators clash with the Ancient Ones and Elder Gods for the fate of the world. The Living Card Game format allows players to customize their gaming experience with monthly Asylum Pack expansions to the core game.
"There aren't really good ways to always win at lotteries, except for not playing them." Hah, that's exactly what I keep telling people! :-D
Excellent article - thanks Marius!
Some good advices!!!!
Thank you very much