Entropy

• Brampton Booster
• Apr 25, 2014
• Comment

Ever had a non-trigger card in your hand and wished “Man. I hoped I could have gotten this card one turn earlier” or its converse “Why couldn’t I get this card a little bit later, I need to guard right now”? What you have experienced is usually known as ‘dead’ cards. With all the moving pieces in any sort of deck events like these are bound to happen. I’d like to present analysis on this property [Which has been coined ‘card entropy‘] ¹ and provide a quantitative way to measure how much ‘card entropy’. As an overview, I will be:

• Defining ‘regular’ entropy and ‘card’ entropy (which I would later just refer as entropy)
• Explaining unavoidable and negligible entropy
• Listing steps to measure card entropy
• Dividing entropy into sub-games
• Testing card entropy
• Using a few decklists as examples

Defining Entropy

Thermodynamic entropy is a measure of the disorder in mass and energy. Thermodynamic entropy increases over time because the universe spontaneously disorders itself. Spontaneous means that there is a natural tendency for something to become disordered (contrary to the believe that it happens “instantaneously”, which is why spontaneous combustion is redundant and stupid). When you shuffle a deck it becomes more random, and hence more disordered. We perform tests to determine entropy to be able to make it more efficient (aka, reducing entropy). It is helpful to note that there is no solid way to calculate entropy alone ² , but entropy changes are possible to measure. Lastly, I might use (del)S as notation for the change in entropy if I feel lazy.

In general card entropy is loss of value in a card. This loss can be reflected in its inability to generate a plus, having a lower plus then normal, or just being unable to use the effect. With the concept of sub-stages, we can reasonably assume that the contributions of a card is split into these stages. Three possible situations exist:

1. Activating a card effect in any sub-game returns the same value compared to the other two.
2. Activating a card effect in one sub-game returns a lower value compared to the other two.
3. Activating a card effect in one sub-game returns a higher value compared to the other two.

For (1), the entropy changes for these cards is zero. Perfect Guards are decent examples for this phenomena, since it is equally useful in all stages of the game. Number (2) is rare but is found mainly for units that superior call like High Dog Breeder Akane. By far the largest section is (3) which is just about every single clumped limit breaker / break ride card in existence.

To continue this train of thought we’ll let every three-four copies of a card be represent just one piece. For example, if we had 4 Akane (a type-2 card) Then in the specific sub-game she does not excel at (the endgame) the (del)S will increase.

The hardest for me is trying to pinpoint how entropic would a card be ³. I went about it like this: Given a set of 3 or 4, if the card would not be used in that sub-game I’ll give it a solid 1. If it did have a use, but the condition to use it may be decently improbable, I’ll give it a 0.5. Point fives have also been given to on-hit rg skills whose effect diminishes and having a hard time to land. If you have a set of 1 or 2, you halve the entropies. Due to the nature of entropy, it is best to have a separate value of entropy score for each sub-game.

After we calculate (del)S for each sub-game, we can organize the information in a chart, and then provide terms to describe the build. Some terms here are provided:

Early entropic	Options unavailable in the early game
Mid entropic	Options unavailable in the mid-game
Late entropic	Options unavailable in the endgame
High entropy	Inconsistent, sub-game specific plays
Low entropy	Consistent, sub-game non-specific plays

Anomalies

Now before we get to deeply into this I’ll mention the very common entropies that is expected in all decks. Since I only want to get numeric values of units that separates it from another deck, we need to exclude some forms of entropy. Firstly it is reasonable ⁴ to expect that once your back row is filled in there is no need to replace the cards with others. This means that by the endgame all grade 1’s should have +1 (deL)S each. Obviously we can’t have this erroneous data floating about so we’ll cut that out. Same case applies to grade 3’s in the early game (Don’t you just want to draw a grade 3 whenever you need it and never extra?). So when you apply entropy evaluations you only take the set of cards which exists in that area.

Another form of entropy arises from triggers. In the endgame criticals don’t perform as well as they would during the rest of the game. Stands then take precedence in this area and actually outperform criticals. Since most decks should have the same line-up to avoid gracious flip-flops we can ignore them too. In general we just disregard the entire trigger setup.

The Test Run

These are close to the optimal builds for both decks, in case you didn’t know:

BED	EDD
4 Dudley Emperor	4 Eradicator, Dragonic Descendent
4 Bad End Dragger	4 Eradicator, Vowing Sword Dragon
2 Juggernaut Maximum
4 High Speed Brakki	4 Supreme Army Eradicator, Zuitan
4 Dudley Mason	3 Fiendish Sword Eradicator, Cho-ou
2 Charging Bill Collector	4 Eradicator, Spark Rain Dragon
4 Cheer Girl Marilyn	4 Eradicator Wyvern Guard, Guld
4 Reckless Express	4 Sword Dance Eradicator, Hisen
4 Wonder Boy	4 Eradicator, Demolition Dragon
1 Medical Manager	2 Ceremonial Bonfire Eradicator, Castor
1 Mecha Trainer	1 Eradicator, Strike Dagger Dragon
8C/4S/4H	12C/4H

Early Game

So at this point, we do not consider Grade 3’s.

1 Mecha Trainer	1 Eradicator, Strike Dagger Dragon
Skill can be used early to quickly fetch any grade 1 to facilitate the field {+0}	Used for superior riding Descendant,If you don’t have him in hand {+0}
1 Medical Manager	2 Ceremonial Bonfire Eradicator, Castor
As a 1 copy, it doesn’t really matter what is here, it is almost always +0. {+0}	When you have two copies, you halve the entropies. Here Castor’s wash is sightly 0.5, but halving it makes it negligible +0. {+0}
4 Wonder Boy	4 Eradicator, Demolition Dragon
Great for rushing and general support {+0}	Great for rushing and general support {+0}
4 Reckless Express	4 Sword Dance Eradicator, Hisen
As this deck is inclined to the BR, Reckless’ effect wouldn’t be used at this point. It technically can work, but in general it is sitting there. {+1}	In the early game this facilitates the superior ride,So this is useful. We aren’t going to get it every game,but certainly when we don’t have EDD in hand. {+0.5}
4 Cheer Girl Marilyn	4 Eradicator Wyvern Guard, Guld
Never a dull moment {+0}	Never a dull moment {+0}
2 Charging Bill Collector	4 Eradicator, Spark Rain Dragon
Bill Collector is a solid beat-stick {+0}	Another solid beat-stick to throw early {+0}
4 Dudley Mason	3 Fiendish Sword Eradicator, Cho-ou
Puts on the pressure since turn two {+0}	I’m kinda mixed on this since you won’t always use it but this is an option you would sometimes activate {+0}
4 High Speed Brakki	4 Supreme Army Eradicator, Zuitan
Like Reckless, I’ll increase entropy here {+1}	This can serve two uses, one for the ride chain, and another for its pointless on-hit {+0}

Middle Game

Now we add in Grade 3’s. (I’m omitting the cards that are {+0} to save space)

1 Mecha Trainer	1 Eradicator, Strike Dagger Dragon
Skill is still viable {+0}	At this point he does nothing but as one copy, he isn’t hurting anything either {+0}
4 Reckless Express	4 Sword Dance Eradicator, Hisen
Not yet. Just wait {+1}	Nice descendent booster for any kind of push, but this requests you have 2 of them. {+0.5}
4 Dudley Mason	3 Fiendish Sword Eradicator, Cho-ou
The opponent has enough to stop this threat and likely you’ve already built a field too {+0.5}	Fair game here {+0}
4 High Speed Brakki	4 Supreme Army Eradicator, Zuitan
Like Reckless, I’ll increase entropy here {+1}	What are you counterblasting at this point? {+1}
2 Juggernaut Maximum
You would usually tag these so you can recall them later {+0}
4 Bad End Dragger	4 Eradicator, Vowing Sword Dragon
All the Limit Break cards are locked out {+1}	{+1}
4 Dudley Emperor	4 Eradicator, Dragonic Descendent
{+1}	{+1}

End Game

By now, the row is filled and our grade 1’s will leave the set.

4 Dudley Mason	3 Fiendish Sword Eradicator, Cho-ou
Still okay if you miss Brakki/Juggernaut {+}	Still okay here {+0}
4 High Speed Brakki	4 Supreme Army Eradicator, Zuitan
It’s time to show your stuff {+0}	Will it even hit? {+0.5}
2 Juggernaut Maximum
{+0}
4 Bad End Dragger	4 Eradicator, Vowing Sword Dragon
All the Limit Break cards are locked out {+0}	{+0}
4 Dudley Emperor	4 Eradicator, Dragonic Descendent
{+0}	{+0}

Results

To put the numbers together in a nice chart:

(del)S in its respective sub-games

Subgame	BED	EDD
Early	+2	+0.5
Mid	+4.5	+3.5
End	+0	+0.5
All	+6	+4

We can kinda guess BED has a higher entropy then EDD, and it should be obvious. After all, they are less consistent and suffer from a more clumped prototype. Everything is used to set up the one-turn explosive crush rush and that leaves no room for any other gambits. But let’s go into each sub-game:

• Early :: BED does have Brakki and Reckless, but unfortunately it is unwise to use their effects at this point. (For BED-specific decks at least) Hence the large entropic gap as your options are limited. EDD however has a chance to perform a superior ride, cutting back the inability to do things. In fact, any deck with ride assistance reduces the entropy of the early game.
• Mid :: The main problem with Limit Breaks is that they don’t do anything mid-game. Break rides further facilitate this fact and makes the mid game very very boring. All Set 5 and lower have low entropies for mid-game since their skills aren’t restricted. [Legion] is attempting to bring back the mid game, and I just we’ll have to see if it does.
  BED is atrocious at this stage as Juggernaut is the only thing they can do, and to add insult you don’t want it to eat too much soul! EDD however has a personal booster, a retirement option and an option to swap. Unfortunately, it is nothing like mid-game centred decks.
• End :: The great thing about BED is that once you BR, everything works. Even triggers become deadly and you have tons of targets and options here. This is partly why BED can haul itself back form a poor mid-game with this extensive toolbox. EDD doesn’t fair any worse since the entire gambit relies on just one card (which again, makes EDD so consistent).
• All :: As I’ve said, combining the scores doesn’t give much information. The only thing you can really tell is that BED is less consistent on average. Think about this; 0[0[3 and 1[1[1 both give a final score of 3, but are completely different in execution.

Okay, so hopefully after going through my example you kinda get how entropy works. Here I’ll provide a couple more decklists and cover some extremities:

SDR Daikaiser	AquaForce Rush
4 SDR Daikaiser	4 Tear Knight, Cyprus
4 SDR Goeagle	4 Tear Knight Theo
4 SDR Daiyusha	4 Storm Rider, Eugen
1 Enigman Storm	1 Random 8k
4 Dimensional Robo Kaizard	4 Splash Assault
4 Enigman Wave	4 Random 8k
4 Diamond Ace	4 Emerald Shield, Paschall
4 Enigman Ripple	4 Random 8k
4 Dimesional Robo	4 Shortstop Brave Shooter
1 Enigman Flow	1 Advance Party Brave Shooter
12C/4H	16C

(del)S in its respective sub-games

Subgame	SDR	AqF
Early	+0	+0
Mid	+7	+1
End	+2	N/A
All	+9	+1

Most of the entropy stems from the fact that ride chain pieces and grade 3’s are useless after turn 3.

So from here it looks like this tier 1 deck has some serious entropy issues, while the tier 2 deck list looks spot on perfect. This just goes to show you that entropy does not effect the tiering system. What’s more important then entropy is consistency, and the SDR deck is sufficiently consistent. There is a strong secure ride and options to force the vanguard as Daikaiser. (In fact, future sets make this even more consistent). I’d like to relate to you that if the ride chain was removed, the resulting entropy in the early game would increase drastically. And this is true in general:

decrease in consistency \Rightarrow Increase in entropy

However, its converse is not true. In other words:

Increase in entropy \not \Rightarrow decrease in consistency

Surrounded

And this point needs to be stressed. Entropy is not the same as consistency, but it is a measurement of what kinds of plays you can make at any given sub-game. Entropy is not advantage, but does tell you when you are going to gain it. Entropy is not something that is easily calculated nor has a set amount, but outlines the areas where options are limited. Entropy is not something that entails a decks success, but entropy should be minimized once all other qualities are set.

I wonder if you asked yourself why you should care about entropy. Well, an important part of card games is the ability to make choices, and decks are more interesting to play with the more options you have. But even if you try to fill your deck with lots of options, entropy can still increase and limit your available scope. But as I’ve tried to show, entropy doesn’t have a significant impact. And this is one of the reasons I find vanguard well built: every card is flexible you can’t truly* be screwed over by a ‘bad hand’. Hence why we don’t need multiple mulligans, mandatory searching cards nor a side deck

Well grade locking is a thing and it sucks, but the chance of getting grade locked is far less then getting a bad ygo/mtg hand. And that is really the only fault of vanguards brilliant strategy of mitigating entropy.

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