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

[Cruxx]

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.

The math is sound, it depends how you look at it though. You will lose half as many games/draws statistically speaking, which is the same as doubling your efficiency compaired to the previous state.

Only questions remains: How much do you value winning 19 out of 20 times compared to 18 out of 20 times? That's up for everyone to decide for themselves.

As stated previously I personally don't like de-valuating every other goal I already put into my deck by adding more cards for one specific goal. I always try to find a trade-off within the optimal boundaries.

E.g. for my Wrath of the Wulven deck I decided to get ridd of 2 Bad Santa and add 1 NYM and 1 Captured Prey instead.
Reasons behind that were that I can't pull off a Santa Bomb due to no cost 1 cards and later in the game situations were really scarce to get an additional benefit from it: Since my deck isn't designed for heavy early game play, most of the times my opponent would have less cards than me, thus Bad Santa would benefit him more than me. Also the deck is min/maxed to no end, so most cards I draw are useful most of the time -> Sticking with 4 Bazaar and 2 Shadow Knights for card draw only.

Creature control is very important against most decks (but DC stall which is decided by item destruction timing), so I upped my card total from 6 to 8 for that goal.

If I would have added those two cards on top of everything else, I would have hurt my chances of stepping up to DC stalls (less likely to draw item destruction) or Burn decks (less likely to draw my damage immunity/healing cards).

[EPITAPHEVERMORE]

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.

+1.. also refer to 'who's the beat down' by he-man(I'm sure you have all read it anyway..)

a great example of this is armoured sandworm.
against a mage, this guy can be a game winner, because it will allow you to maintain board presence right through a supernova.
against a human warrior, sandworm (in most cases) should be an auto-sacrifice because you know that he will most likely be retreated or worse, crippling blowed.

As The Beatdown is most likely the person who gets 1st turn, the problem in deck building is finding the right balance between 'aggro' cards and 'control' cards.
Shadow Era is predominantly a race for advantage. (board presence mainly) this is because it is makes it alot easier to cause damage to the opposing hero with advantage than without.
If you choose all aggro cards, you will always have weaknesses.(Think of zaldar spewing out entire hand by T4 then top decking.)
By adding control cards, you can reduce those weaknesses signifigantly.
You should be searching for the correct 'aggro/control' balance for your specific strategy.

Here-in lies the problem. by having more than one 'goal', you need more cards.
The question is, is it better to reduce the amount of cards associated to a specific goal, or to simply increase your deck size, and slightly reduce the effectivness of all your goals?
This is a judgement call that I think only you can only make for yourself.

[crazygambit]

I would agree if we were still on 30 card limit decks. In some decks I had much more success for exactly the reason you put forth with decks of around 35 cards. 30 was extremely consistent, but didn't offer much adaptability. Also you had to factor in that some decks required about 8-10 cards sacked as resources to play optimally. So it was easy to run out of juice in those decks with only 30 cards.

40 cards always felt too inconsistent to me and performed worse. So I believe there's merit to what you're saying, but for most decks the sweet spot will be somewhere between 30-40 cards, not over IMO.

[kamman13]

The math is sound, it depends how you look at it though. You will lose half as many games/draws statistically speaking, which is the same as doubling your efficiency compaired to the previous state.

Only questions remains: How much do you value winning 19 out of 20 times compared to 18 out of 20 times? That's up for everyone to decide for themselves.

Your math is correct, I was only taking issue with the phrasing of your logically derived conclusion at the end of your previous post. What you said above if correct, depending on how you define efficiency, of course. I just wanted to point out that losing half as many games, in the way you are referring to it, is not the same as winning twice as many games, which is what you seemed to be saying in your original post. I think we're on the same page now, and I think the question you posed in the quote above summarizes everything quite nicely.

[kamman13]

@DND

I definitely hear you about the lack of control, and I think it is a bit of a shame in this game that more control doesn't exist. I don't think we're ever likely to see it though since the developers are intent on keeping this game simple, and fast. But it is what it is.

On a related note, I have a question for you. Let's assume SE and MTG had no card minimum. What would be the ideal deck size to you for both games, and would that deck size be the same for both games? I only ask because to me, at some point adaptability should triumph over consistency leading to the "ideal" deck size, and that size is probably certainly lower than 60 (which is my MTG decks should never go above 60), but definitely higher than something like 10.

Certainly for aggro decks consistency is more important than for control decks, but even then I've been finding it's not quite enough. Example- I want to run a weenie rush deck. At 40 cards, I can create an extremely consistent deck that ran the weenie rush better than everyone else. But then DC throws up a 3-4 invulnerability streak, and there's no way to hit him. Mages and priests have efficient multi-target spells, warriors have JD allow them to both kill weenies and have the extra resources to slap down retreats and crippling blows on my allies. Basically, as consistent as any aggro strategy may be, there will still be counters for it, and without adaptability, I cannot respond to those counters.

For me, DC is the real killer in 1.28, because he breaks out of the usual mold. I can build a deck that has consistency and responds to most decks just fine for under 40 cards actually, but then I autolose to DC. Adding in the counters to DC puts me over 40. If I remove cards and limit myself to 40, I lose the ability to respond to a different sort of deck, or have to reduce the numbers of cards in my general strategy, making it less consistent. Thus for me to counter DC, the slight loss of consistency of 42 cards is not as bad the consistency loss by cutting those two cards from my general strategy.

Basically, if DC and his stall strategy didn't exists, then the "ideal" deck size for me would be under 40, and there'd be no reason to go over it. But with DC, I find the ideal size is now 40-43, depending on the hero.

[Cruxx]

For me, DC is the real killer in 1.28, because he breaks out of the usual mold. I can build a deck that has consistency and responds to most decks just fine for under 40 cards actually, but then I autolose to DC.

Don't get me wrong, but you don't feature item destruction in your normal decks? Beating DC basically boils down to item destruction. I only have 4 Shriek in my deck and beat most DC's coming my way (though it is super boring and exhausting for both players, which is why I don't like playing stall myself.)

[MistahBoweh]

In Magic?

Channel
Channel
Banefire
Banefire
Black Lotus
Black Lotus
Black Lotus
Pact of Negation

That's your deck. 8 cards.

On a serious level, an aggro (not combo) deck in Standard Magic should be able to win over the course of five turns, so if you're second that means you'll go through 13 cards in your deck before losing. Doing this in the right numbers can literally make it so the exact same thing happens every game. The only problem is that mill is an actual thing in Magic and so can't be compared to SE. SE first of all has no Tome Scour, and second of all running out of cards is not an auto-loss in SE. Also, plans can be disrupted much easier in Magic than they are in SE.

If magic today changed the rules to add any card amount, mill would probably be the deck to beat. Sanity Grinding is one tough mofo. Eventually, aggro decks will probably end up around the 35 card mark, enough to be consistent and yet still deal lethal damage before getting milled out (hopefully).

In SE, the card's aren't as fast, your opponent can force your weenies into combat, and life totals are higher. Basically, I'd want to be playing mages, and with just enough cards to be able to deal 40 damage and still afford to sac 5 cards. Mages have the bonus of most of their dd affecting board presence, so not only are they the fastest racer but the strongest counter to any other rush strategy in the game, plus the burn pushes straight through DC fog loops and such. So basically, I'll be playing 30c Majiya style list. The exact card number would take a little math that I don't feel like doing, but you get the idea.

[Atomzed]

Phew, after a long day, i finally able to sit down and digest all the posts. Good discussion points from various ppl.

I like to re-emphasise that in my post, I did admit that consistency is better in a smaller card deck. That's no question about that. But I want to point out is that doing the maths, looking at cards drawing probability, the addition of 2 cards may reduce consistency a little but increases your adaptability so much more than its worth it.

Doing a thought experiment here. Let's say you have a wonder Elemental deck at 40 cards including hero. Your deck have a great mix of cards, and you tuned it extremely well such that all the cards were necessary. You play 100 games, and you roughly win abt 90 games (90% win rate). Then some genius/joker came up with a wonderful/boring milling deck that caught on within SE community. Suddenly, you see an increase in that particular hero in QM; in 100 games, you see an increase of that hero usage from 5% to 30%. Your deck has 30% of winning such a milling deck, which is terrible cos you are so used to winning 90% of the time. And you realise that Eternal Renewal is a great counter card to the milling deck and will increase your win% to 100% against that milling deck.

What i'm describing is simply the shifting meta. There can be a few responses (not all the possible responses are listed here) to such a scenario
1) You suck it up and just prayed hard that you dont meet the milling deck hero
2) you revise your deck and replaced some cards with ER. What it means in Cruxx "Rule of 6" lingo is that you have reduced the consistency of a particular goal in your deck, and added in another sub-par efficiency goal.
3) You add in ER cards, with out removing any cards from the original deck, increasing your deck size to 42. This is what I'm arguing for.

In both scenario 2 and 3, you reduce your consistency of your original deck.Bec of the shifting meta, you have to added in an additional goal of "milling" to win the game. What it means in probability term is that. In 30% of the game, your win rate increases from 30% to 100%. In 70% of the game, your win rate drops.

In a highly tuned deck, removing any cards will have a great impact on how the deck plays out. You might have to reduce the no of weenies, heavy arty, item destructions, etc to accomodate that additional goal of "milling". Depending on your deck composition, your win rate in 70% of the game may suffer alot bec of the reduction in card draw engines, or reduction of item destructions, etc.

And this is where my statistical analysis comes in. I'm saying that "hey, by adding an additional 2 cards to your deck, the probability of drawing the cards at T1 is reduced by abt 2%, at T2 is abt 2%..." And my conclusion from the analysis is that the additional 2% change at each turn may be worth it to add in CERTAIN cards. Cards like Eternal Renewal bec you prob only cast it once per game. Or resurrection.

This is not just applicable for milling. It can be applicable to other game strategies. Say you have a great Warrior deck that plays well with a good mix of allies and weapons, but no armour. You may just want to consider adding in 2 KP bec the chances of drawing certain card at various turns is abt 2% drop, and I argue that its worth the 2% drop to have the options of using a KP in certain game.

This approach CANNOT be used for all decks nor for all cards. Cruxx stated the example about removing 2 BS to accomodate 1x NYM and 1xCP. I'll say that this is a sound approach, because NYM and CP are cards you play at T2 onwards. You want to draw them as early as possible to give you the option of using it.

But for cards like resurrection and eternal renewal, you only need to play it late game. You might not need to play it at all actually, but it does gives you the added option of using it in those crucial 30% matches with the milling deck. To a lesser degree, this approach works for KP bec if your original deck already works well with the cards in your deck, i dont need to cast KP at T7 to win the game. But the KP may help me to swing certain games around, and could be worth the addition.

(however, if your strategy revolves around casting KP at exactly T7, then i suggest what DNDfreak has suggested, add in 4 KP. Off the top of my head, 4 cards gives you about 75% chance of getting KP at T7. having 3 KP gives you about 60+% chance of getting KP. so if your deck revolves around KP at T7, you need to have 4 cards to increase the chances)

TL;DR. My argument is that you can consider increasing the deck size over 40. The point is back up with the argument that a 2% reduction in drawing probability MAY be worth it to get the option of using SOME cards, specifiically cards like Eternal Renewal and Resurrection, which is cast once per game, but is game changer. Some of my A1 guild members agree with me that the added adaptability is worth the slight reduction in consistency.

I am aware that certain individuals look at the 2% reduction in drawing probability as crucial. I am also aware that certain individuals see the addition of only 2 cards makes for a sub-par goal achievement, and will add in 4 cards to ensure consistency. Some of my guild members belong to this 2nd group and prefer more consistency.

[Atomzed]

To reply to certain individuals,

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.

You are absolutely right. X refers to the EXACT no of cards you want to draw by that turn. So to calculate whether you get at least 1 card, the easiest way is to calculate probability of 1- P(X=0). In simple terms, if the opps of me drawing 0 cards at T3 is 20%, it means that i have 80% of drawing at least 1 card at T3.

@ Cruxx, the way you viewed miss chances is a refreshing perspective. I think both of us will agree that both view points are supported by statistics, and it only differs in how much emphasis we placed on card drawing/ preventing card miss.

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.

@ DNDfreak, you do realise that I had no T1 decks posted in SE forum, had never organised any tourney, had not put up any videos, had not submitted any card suggestions. And this is my first article And boy, i don't think the first article i wrote is very much appreciated :P

I just have to let you know that I did sought permission from A1 to re-post my article. There were no objections from my guild members, even though some of them disagree with my conclusions. I didn't see it as as a "controversy" as you put it, just differing opinions on the same set of data, which leads to different conclusions.

And as mentioned before, I did not ever stated that my posts have backing from ALL A1 members. Which is my point when i mentioned abt your article. I find it hard to believe that ALL TJ members agree with ALL the points in your posts, purely bec there are always differing opinions (like say whether Shrieks are better than Smashing blow, or whether Logan is better than Eladwen, etc). I just find your standard of judging my article as unfairly high, in the sense that you assume that any article put up MUST have the support of ALL members.

I assume you will be writing an article on this and i eagerly await to see your points.

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.

This is a very good topic for discussion. In my opinion (and i emphasise that its my opinion, and mine alone :P), control and aggro are not a unidimensional construct. A good deck will have both elements of control and elements of aggro.

A priests deck that plays weenie rush. Does it means that he should not have Tidal wave? Bec tidal wave is strictly a control card.
An elemental deck that is ally heavy (weenie plus heavy arty). Does it means that it should not have AoA. Bec ApA does not help in the ally aggro.

Maybe our difference in perspectives relate to how we define control and aggro. Maybe you see aggro/control as a "dominant form of strategy in the deck". But when i hear aggro and control, i look at how each card contributes to that goal. For example, in my v1.27 banebow decks, i play an ally heavy deck. But i still have 4x arrows which is strictly a control card bec i find that it helps me in board control and increases my chance of winning.

[kamman13]

In Magic?

Channel
Channel
Banefire
Banefire
Black Lotus
Black Lotus
Black Lotus
Pact of Negation

That's your deck. 8 cards.

On a serious level, an aggro (not combo) deck in Standard Magic should be able to win over the course of five turns, so if you're second that means you'll go through 13 cards in your deck before losing. Doing this in the right numbers can literally make it so the exact same thing happens every game. The only problem is that mill is an actual thing in Magic and so can't be compared to SE. SE first of all has no Tome Scour, and second of all running out of cards is not an auto-loss in SE. Also, plans can be disrupted much easier in Magic than they are in SE.

If magic today changed the rules to add any card amount, mill would probably be the deck to beat. Sanity Grinding is one tough mofo. Eventually, aggro decks will probably end up around the 35 card mark, enough to be consistent and yet still deal lethal damage before getting milled out (hopefully).

In SE, the card's aren't as fast, your opponent can force your weenies into combat, and life totals are higher. Basically, I'd want to be playing mages, and with just enough cards to be able to deal 40 damage and still afford to sac 5 cards. Mages have the bonus of most of their dd affecting board presence, so not only are they the fastest racer but the strongest counter to any other rush strategy in the game, plus the burn pushes straight through DC fog loops and such. So basically, I'll be playing 30c Majiya style list. The exact card number would take a little math that I don't feel like doing, but you get the idea.

Damn, 8 cards. Ok, I concede that point.

Without DC, I'd argue hands-down a mage 30-card burn is awesome, but with DC, the issue changes. If DC can get WBT and SS in play, he can do 6 damage per turn with his ability. 4 turns of this, and the mage is gone. Plus, the mage's DD spells can't eat through his ability or full moon, so can prevent damage from the mage for several turns, ensuring he wins the death race, I can work through the math if you don't buy it. Add lone wolf to heal while the mage can't attack, and it gets more difficult. Thus, to defeat DC, a mage needs some item destruction and allies- item destruction for full moon, and allies to cast during DC's ability to ensure they'll still have something to do damage the turn after DC's ability and stay damage competitive. I'd be surprised if a 30-card mage can get better than 25% win records against a 40-card DC, but a mage with a larger deck size can do better against DC. So even the class that would benefit most from small decks is messed up by DC.

Additionally it's a minor point, but mage DD is not the most effectively to any other rush strategy, as Birgitte messes with targeting of spells. I'd argue priests with ice storm and tidal wave, or warriors with their abilities, JD, and crippling blow provide better counters to ally rush strategies.