Deck size & Probability - A case for (slightly) bigger deck

[Atomzed]

Look mate, I said I posted it in the A1 forum, and are re-posting my posts again. There are differing opinions on my interpretations of adaptability vs consistency in my guild, but those are not my posts so I'm not at a liberty to post them.

So for the articles that you posted, everyone in your guild absolutely agrees to them?

I'm glad I posted it here bec I got some better understanding of the maths.

[MistahBoweh]

I've posted one thing since joining TJ, and aside from the 4x KP throwaway that I expexted to get some hate, yes, actually. Keep in mind that all I've done here is write. I have no t1 decks, no history of organized play, no videos, no card submissions, just my articles. If they weren't appreciated then I'd be nowhere.

I don't see what this has to do with anything. All I'm doing is talking about the subject matter of the article and how it looks upon the reputation of your guild. Personally, were I in A1, I would be mad seeing something with internal controversy posted on the main forum with the A1 name slapped on the front of it. That's what I mean by it, if this is all I had to go by of A1 then I would want nothing to do with them. In the future, try asking around before pulling something like this, as I myself intend to do with TJ. If you want to just go ahead and post something, no one can stop you, but don't act like you have A1 backing if you actually don't.

My apologies, I realize I've come off quite harshly to the guilds, both of them in fact. And as for the article itself, I forget sometimes that while Magic doesn't have much left unturned for theory, games like SE still need places to discuss these matters. Some of the best in MTG have still tried debating the value of card #61 at one point or another.

[TripleHBK]

http://stattrek.com/Tables/Hypergeometric.aspx

Population size = Deck size
Number of successes in population = Amount of specific card in the deck
Sample size = How often was drawn? 6 for 1st player in T1, 7 for 2nd player in T1, 7 for 1st player in T2...
Number of successes in sample (x) = Set to 1 if you want to know the "normal" probability
Last line = That is the % we are looking for, don't excactly know why it isn't the first result line, but you can easily verify with some examples.

It should be because that P(X>=x) gives you the probability you get at least x wanted cards by that given turn. P(X=x) gives you the probability you get exactly x wanted cards by that given turn.

[Raphael Majere]

This article is a horrible, horrible idea. Don't do it. Adaptability is strictly worse than consistently. The only reason you should ever need to adapt to many different gamestates is if you're already losing, and that's because control really doesn't exist in SE. The MOST important thing in any tcg is consistency. Every deck has a plan to win and loses when that plan doesn't pan out, so why would you EVER make it any less likely to get what you need when you need it?

If this is the kind of bull being tossed around behind A1, no offense to you guys, but I'm glad I'm not a part of it.

Everything's great about the post except the last line. Has nothing to do with the OP.

I've posted one thing since joining TJ, and aside from the 4x KP throwaway that I expexted to get some hate, yes, actually. Keep in mind that all I've done here is write. I have no t1 decks, no history of organized play, no videos, no card submissions, just my articles. If they weren't appreciated then I'd be nowhere.

I don't see what this has to do with anything. All I'm doing is talking about the subject matter of the article and how it looks upon the reputation of your guild. Personally, were I in A1, I would be mad seeing something with internal controversy posted on the main forum with the A1 name slapped on the front of it. That's what I mean by it, if this is all I had to go by of A1 then I would want nothing to do with them. In the future, try asking around before pulling something like this, as I myself intend to do with TJ. If you want to just go ahead and post something, no one can stop you, but don't act like you have A1 backing if you actually don't.

My apologies, I realize I've come off quite harshly to the guilds, both of them in fact. And as for the article itself, I forget sometimes that while Magic doesn't have much left unturned for theory, games like SE still need places to discuss these matters. Some of the best in MTG have still tried debating the value of card #61 at one point or another.

If you read the OP, it's not stated that A1 is backing atomzed for this post. (I am sure some of us are.)

He merely stated that he posted it at a1.

There are members who agree and disagree with atomzed. We are not 'zombies' who follow a prescribed diet. As with any community, like this forum (or a1), it's made up of individuals each with their own freedom of thought and expression.

It's unrealistic to make everyone like everyone. But, there is always a nicer way to write or convey our thoughts.

Anyways, the OP is about consistency vs adaptability and probabilities. So I hope we go back on track. Nice stuff from ringel and cruxx.

[MistahBoweh]

I don't want any bad blood between us. You're right, it's a hasty assumption. I know our factions have been at each other's throats, but I came on after all that and have no motive to dig it all up.

The article itself has started some good discussion and better points, and for that I have to tip my hat.

[Raphael Majere]

Yeah, no one's at nobody's throat.

Atomzed's article is interesting. Esp, for people used to playing and winning 99% of the time with 30 card majiya in 1.27. this current version forces everyone to play at 40 or more.

Some expert 30 card players have trouble transiting from 30 to 40. Hence this article would be insightful to them. 42 or 43 makes less difference as compared to 33 vs 30.

[MistahBoweh]

Ugh, You're really making me itch to write something on this myself if I wasn't already doing another topic.

Also, it would undoubtedly be on the sarcastic and bitter side. So that may be a good thing. I'll put it on hold, though. Might do it in a week or two.

[kamman13]

5 point increase around the 90% mark:
90% -> 95%

We now want to look at the "miss" chance, that we do not draw our card.
100% - 90% = 10%
100% - 95% = 5%

This gives us a ratio of
10 / 5 = 2
-> It is 100% more likely to draw the card compaired to the previous value.

Sorry Cruxx, but your logic is off. You are looking at the miss chance, and finding that you are twice as likely to NOT draw your card compared to the previous value. This simply means instead of not drawing your card once every ten games, you don't draw that card once out of twenty games. It's the difference between getting a winning hit 19/20 games rather than 18/20 games In other words, not a big difference.

You're ending sentence should read:

It is 5% more likely to draw the card compared to the previous value. You will not miss drawing your card 100% more frequently compared to the previous value. Of course, that frequency is so small to begin with (not getting that draw twice every twenty games instead of once every twenty game), that doubling a really small value still leaves you with a really small value. Which is the whole point of Atomzed post.

Of course, in competitive games, every little bit matters. The true question here is, will the cards that you add to the deck help you win more than once in every twenty games, versus not having those cards? That is a tough question, but occasionally the answer is yes.

@DNDfreak

I want to echo what Raph said, Atomzed isn't speaking for all of A1 clearly, but I find his conclusions completely sound and wholeheartedly support them. I played some MTG, not competitively as you have, but SE has distinct differences from a game like MTG that make sticking to the minimum number not always the best strategy. The reason to me is because your resources come from the cards themselves, there are not separate "land" cards as in MTG. Thus, you will always lose some portion of your deck to create resources.

I'm not sure if you were playing in 1.27 where the limit was 30 cards, but it was my experience that 30 cards was not enough for a well rounded deck. 30+ decks would often beat 30 card decks, due to having the flexibility of more cards that made saccing choices easier. I had a really decent win record with my 40 card Nishaven deck on QM, especially against 30 card opponents. The extra cards gave me an advantage- I could always find cards to sac every game, and never had to choose to skip saccing due to have a limited set of crucial cards. This allowed me to gain more resources than my opponents, which allowed me to play more cards than my opponents, which ultimately lead to victory. In fact, because choosing how much and when to sac is such a key component of SE, so is card draw, as it allows you to best implement your saccing strategy.

In a game like SE, flexibility is key. Because you need to sac cards to do well in the game, every card does not need to be vital for every opponent. In fact, a good deck has one set of cards for one opponent, and a different set for another opponent. Against different opponents, it may even appear like a different deck entirely because you sacced the other part of your deck. I think Cruxx pointed this out well in his rule of six.

Easy example- let's say the minimum deck size was 10 cards. Would you run a 10 card deck? I'm guessing not, you'd never win (same would go for MTG, I suppose). For a game in which every card doubles as a potential resource, deck size needs to be sufficiently high to accomodate the resource load of saccing. In my opinion, the ideal size for a deck given no limits is somewhere between 35 and 45 cards, depending on the hero and deck type.

One last point- I find going over 40 cards especially relevant in this meta. The two dominant archetypes are quick burn/weenie rushing, and slow, drawn-out hiding/invulnerability spells with items. These strategy differ so much in speed and card type (allies vs DD spells vs. items) that the counters to combat the strategies involve totally disparate cards. I find it hard to include counters to all potential deck archetypes, along with a strategy of your own, and stay under 40 cards. To limit yourself to 40, you either need to a) make yourself weaker to one of the other deck archetypes out there, or b) make the cards involved in your own strategy less relevant. If you go above 40 (I find 43 works well in this meta), you can then include all cards you need to deal with all potential deck archetype, at the cost of slightly reduced percentages. Thus, here comes Atom's post showing that, yes, it's not a bad idea to do this because your percentages don't get thrown that far off.

Having said all this, I realize it is just my opinion, and I'm happy to hear your thoughts, especially considering your experience in TGC's. No hard feelings intended, just trying to provoke a useful discussion, particular on whether the nature of resources in SE makes adaptability and larger decks a more important consideration than consistency.

[Raphael Majere]

Yeah, let's try to have a cool discussion and debate.

[MistahBoweh]

Okay, the problem is that you're talking all about defensive strategies, trying to counter specific opponents.

SE does not have control decks.

Period.

Any strategy you have for winning is strictly better than a strategy for stopping a given opponent from winning.

And yes, I first played SE in 1.23. And I've played 30 for as long as I could, and won because of it.

Basically, the difference between aggro and control is that aggro has a plan. It knows how to win and that's what it will do as quickly as possible. Control is reactionary. It tries to stop the opponent from winning as quickly as possible, and then just happens to kill the opponent however it feels like. Control needs options, but all aggro needs is consistency. Aggro needs to follow the plan.

In Magic, options are gained through deck manipulation. Drawing extra cards, search effects, looking at the top few cards and moving them around.

SE has more than enough card draw, but lacks the other options, this is true. So how to recover?

SE has you use your normal cards as lands. Where in Magic, you don't get to choose. Think of it like On turn five, you've gone through five extra cards in your deck and removed the ones you don't need as much. So you have just as many options in SE as you do in Magic, in fact you have more. Magic decks typically have 36 nonland cards at most, and since the deck is 50% larger you're also drawing less relevant cards each turn.

So if you really need those cards and you can't find ones you want to replace them with in your deck, then you don't need those cards after all.