The Mathematics of Eternal Card Game - Deckbuilding and YOU

[aardvarkpepper]

INTRODUCTION:

To begin a serious study of a subject, you have to 1) have a general understanding of the system, and 2) realize you're wrong about some things you believe. Of course you will think you're right, but actually no, some of those things you think are wrong (and that's ok for now).

Almost everything you believe is in some part incorrect. But that's not surprising. Whether it's about human behavior or quantum mechanics, people think they know how things work, then further studies are done, and people realize they really don't know everything there is to know after all, and sometimes what they thought was right was wrong.

The more intelligent someone is, the more they're used to being right, the easier it is to fall into that trap.

Stephen Hawking bet Gordon Kane $100 that physicists would not discover the Higgs boson. But it was found in 2012. (Or at least some people think it was found.) Alan Greenspan addressed the House Committee on Oversight and Government Reform in the United States of America and had to admit “Those of us who have looked to the self-interest of lending institutions to protect shareholders’ equity, myself included, are in a state of shocked disbelief". The list goes on and on. Smart people make mistakes. Dumb people make mistakes. Everyone makes mistakes, and they don't know they're mistakes . . . until they find out!

That said, let's look at some incorrect assertions people have made about Eternal Card Game and similar games.

1) RNG (random number generator) is not a factor in determining game outcome. Everything can be controlled by a player that's skilled enough.

False. It doesn't matter how good you are, if you literally draw nothing but sigils, you are going to lose. Don't be proud and think you can control everything, because you can't.

2) RNG is the prime factor in determining game outcome. The meta (i.e. the decklists most commonly used by most players) stabilizes around a few effective decks and the counter to those decks, by the mechanic of players looking them up online or playing against those decks and attempting to copy or counter those decks. After a meta stabilizes (which happens fairly quickly), the game comes down to luck, whether you luckily played an opponent whose deck you countered, or your opponent played a deck that countered yours, or what cards and/or your opponent drew &c. Since the game is not particuarly difficult to understand, the process largely comes down to luck and grinding.

False. Much of that is absolutely correct, except the conclusion that RNG is the prime determinant. The reason is psychological. When you catch a ball, you are not consciously computing speeds, air resistance, prevailing winds, trajectories, gravitational constants, and so forth. You simply catch the ball. Likewise, you do not necessarily think consciously about what or why you play a card in a given situation. You simply play it.

Yet, there is actually a lot going on in even the simplest situation in Eternal Card Game. Your ability to understand and assess game states is key to your winning or losing.

Suppose you are playing a green/red Warcry deck against an opponent. On your first turn, you play a Seat of Glory (a Power card that provides red and green influence and is depleted unless you have a Sigil in your hand) and play an Oni Ronin (a 1-cost, 1 red influence requirement, 2/1 minion with Warcry 1). Your opponent plays Diplomatic Seal (a Power card that gives you an influence of your choice if you have two or fewer influence), chooses red, and plays Ticking Grenadin (a 1/1 minion that deals 3 damage to an opponent when it dies).

If on your next turn you play a Fire Sigil then have Seek Power, Torch, Champion of Glory, Crownwatch Paladin, and Sword of Icaria in hand, what should you do?

You could use Torch to clear the board, attack with Oni Ronin, and use Seek Power to get another sigil from your deck so you could have a guaranteed third power on the third turn to have a Sword of Icaria out to kill any minion the oppoent might put out. You'll potentially Warcry twice that turn, and the longer Oni Ronin stays alive, the more Warcry you'll get out of it. If your opponent doesn't have a ready answer, you will pile up more and more of an advantage.

Or you could decide your opponent is trying to bait out your removal, attack with Oni Ronin and let it die to the enemy minion block, then put out Crownwatch Paladin. On your third turn, you could Seek Power and cast Torch to clear anything else your opponent put out, and there likely won't be enemy minions around to block and kill Crownwatch Paladin. If you drew power on your third turn you could even put out Sword of Icaria and get even more Warcry. This is maybe the play you would do especially if you're guessing your opponent might play Argenport Instigator (a 3/3 minion that requires 2 power to play); using the Torch on the Ticking Grenadin would mean you wouldn't have any ready removal for turn 2 (unless you lucked into drawing another Torch, which you might not want to count on) - and the Argenport Instigator can kill the Oni Ronin in combat without dying itself so that would slow or even shut down your Warcry for a while (which would be bad).

Or you could decide to do a mix of offense and defense, and either attack or not, but play Champion of Glory, intending to use Seek Power on your next turn to get a Justice Sigil so your Champion of Glory would be a 3/3 Quickdraw Endurance, capable of both attacking and defending. After all, you know your opponent is trying to do something that involves direct damage to your life points since that's what Ticking Grenadin does. It's a good bet that your opponent is going to try to push for early damage, then do some sort of nasty combo later on in the game that will finish you off, so you need a lot of board control quickly. Even if your opponent kills your Champion of Glory, at least your opponent has to spend power and cards to do it, instead of putting more minions on the field, and if your opponent puts more minions on the field, you have Torch and Sword of Icaria after all.

So where exactly is RNG in all that decision making?

Then consider one of the hot meta cards right now for red and purple is Statuary Maiden, a 4-drop 2/4 with a nasty special ability. At 4 toughness, it's too large for a "traditional Warcry" deck's removal of Torch and Sword of Icaria unless you luck into a Warcry on a drawn Sword of Icaria (but you really can't count on that). Often you're looking at 2 for 1 removal against that card, and if you lose a minion in the process, your opponent will get a 2/2 equipment. At 2 power, Statuary Maiden it's strong enough to kill most of your early minion drops, plus it's Deadly anyways so can kill just about anything it can block, and since Warcry decks don't have all flying creatures, it's something you have to deal with.

So if you're building a proper deck, you're going to need Valkyrie Enforcer for its Silence (even though Valkyrie Enforcer doesn't have Warcry), or Charchain Flail to deal with larger enemy minions. (Magma Javelin works great against Statuary Maiden, but it doesn't scale up at all; if your opponent has a minion with 5 toughness, Magma Javelin has to trade in at 2 for 1 at best.) Or you could do Auric Runehammer or Flame Blast . . .but I digress.

If you don't have answers to your opponent's cards in your deck, you can't draw them, then your opponent can bait or you can be forced into 2 for 1 trades, then your deck runs out of steam, then you lose. Sure, you might have answers but you don't draw them thanks to bad RNG, but if you don't *have* them in the first place you will lose a lot more.

So although RNG has a lot to do with game outcome, it certainly isn't the only factor.

2) Proper deckbuilding is merely an application of mathematics to a game system.

False. A great understanding of mathematics helps build efficient decks, but even the best understanding of theory and mathematics is insufficient to building a good deck; knowledge of the meta is also essential. Assuming "good" is a function of win percentage (and that *is* an assumption; different players have difference preferences for what is "good") - a "good deck" can only be "good" if it has a good win/loss ratio against other decks. But any deck has different win/loss ratios against different decks. So if a deck performs well against *most* decks it plays against, it is a "good" deck on that day, but if other players decide to play different decks, then the "good" deck may end up being a "not so good" deck.

3) Someone that designs a game will necessarily be good at playing the game.

False. Most game design these days require proficiency in many fields, including mathematics, art, marketing, projected monetization, &c. Typically games are also multi-person projects, with different people working on different parts of the game, or sometimes multiple people contributing to a single part. Any one person may only play a very small part in the whole, and even though a person may make a number of key contributions, it should not be expected that a specialist in game design should have a broader theoretical knowledge that allows efficient game play.

Playing games well requires an entirely different skills ranging from risk assessment to anticipating an opponent's potential counters to guessing correctly when or when not to commit. A good game designer will be aware of these factors on some level, but will not necessarily be able to apply them all successfully in real life.

4) Someone that is good at playing a game will be able to effectively teach others how to be good at playing that game.

Teaching and playing games are different skills.

5) It is possible to get good at a game just by playing it.

False - to some degree. Players do improve with experience, and as already mentioned actual play experience and understanding the meta is key to doing optimally. But some players will be able to apply their experiences and be world-class without thinking consciously about it, and some will not be so able. Just because some people are able to do well without study does not mean YOU will do well. (And if someone's world-class anyways, they would probably not want to give away too much about how they prepare, as that would just give competitors more information to work with.)

6) It is not possible to get good at a game just by playing it.

False - to some degree. Some players DO get really good at a game just by playing it. They don't need to apply knowledge of statistical mathematics, or whatever such complicated procedure. The most "advanced" computer 'intelligence" game playing programs use vast databases of played games between high-level players, and apply "most-played in similar situations" algorithms to arrive at moves. (Or so I understand it.) Those computers don't necessarily understand why exactly they do what they do, yet they manage to beat world champions in chess and go. But again, just because some people and some computers get results using a method doesn't mean you'll be able to do the same.

[Celtic7Guardian]

Shadowcran lähetti viestin:

It's his thread. If he wants to retype, word for word, War and Peace or the entire Encyclopedia Brittanica, it's his prerogative.

Nobody is holding your eyes open, with a gun to your head, forcing you to read it.

No, but we are allowed to give our opinions on their thread, and I gave mine. I would find it far more interesting to read and debate if the posts were shorter. Posts that are overly long take away from the point they are trying to make. I can understand a long post when appropriate, but when every single one is that long, it just sounds like gibberish after a while.

So yeah, there's my opinion. It's been made, the TC saw it, I will leave it at that unless the TC wants to know why I feel that way in more detail.

[76561198363071207]

About flipping the coin....

I think I was missunderstood. I wanted to say that particular series are having a low probability, of course different by zero. So there is a chance that this particular set will be seen.

6 heads in a row is a particular set of events. Like 6 tails in a row. The probability to get 6 out 6 of the same type is 1.25%. Tossing the coin in series of 6 it will result in a number of times of getting 6 tails out of 6. Say out of 100 series of 6 flips, there will be "n1" times of 6 heads out of 6 . For the next 100 of 6 flips you will get "n2". After running enough numbers of 100x6 flips series, it will be obvious that "n1", "n2"...."nm" are nicely sitting on the most known curve describing normal distributions, Gauss Bell. Which will be obviously centered on the value of ...1.25%.

However, if lady luck is your personal friend you can get like for a number of 100x6 flips "n1"..."nm" around 50%...so any of your 100x6 series is containg some half sets of 6 heads. If lady luck is your mistress...than, what to say, you need heads, flipping the coin will give only heads.

Now take a set with a higher probability like 3:3 heads:tails. Chance to get this set is 25%. Meaning that the same measurement of 100x6 series will show that the values "n1".."nm" are sitting on a Gauss bell centered on 25%.

Coming back to our card games what I wanted to say is that particular sets of events should occur less more times than it actually happens. This does not mean that a particular lucky player will not see these sets much more often than others. Yes he will. Another player will. But not so many.

Practical example for Eternal : say you have a set comprising 4 copies each of 2 cards. Say for a certain game would be nice to have 5 cards in the first 15 out of the group of 4x2 = 8 cards. The probability would be only 0.609%. My practical experience is that I was seeing it to my opponents even 2 every 10 ranked games. 20% is far away from 0.609%% while considering different opponents.Most of the days was happening the same.

I know I was from the beginning off your topic, which was about deck building. However, I think that before touching deck building first one should address the RNG problems.