Weekly Featured Cards poll - Light

[Bloodshadow]

The featured card is chosen!

Ice Shield | Permafrost Shield

Sorry, guys. I forgot to lock the voting last night.

Now, if someone can find that Permafrost math thread for me. If I remember correctly, that thread says Permafrost Shield blocks approximately 53% of all attacks or something.

[smuglapse]

Now, if someone can find that Permafrost math thread for me. If I remember correctly, that thread says Permafrost Shield blocks approximately 53% of all attacks or something.

Except at turn 1, 100% goes through. Also, it's not 30% of the critters getting frozen, it's a 30% chance for each critter to get frozen.
[edit]
Turn 1: 100% of damage gets through.  (30% gets frozen, 3 turns wait on it).
Turn 2: 70% of damage gets through (30% has 2 turns of wait, another 21% gets 3 turns of wait).
Turn 3: 49% of damage gets through (30% - 1; 21% - 2; 14.7% - 3)
Turn 4: 34.3% of damage gets through (21% - 1; 14.7% - 2; 10.3% - 3; 30% unfreezes)
Turn 5: 54% of damage gets through (14.7% - 1; 10.3% - 2; 16.2% - 3; 21% unfreezes)
Turn 6: 58.8% of damage gets through (10.3% - 1; 16.2% - 2; 17.6% - 3; 14.7% unfreezes)
[/edit]

From a per creature perspective: on average, 3 of 10 attacks will leave the critter frozen for 3 turns. Hence, on average, for 10 successful attacks there's 9 turns of frost.
10 of 19 turns worth of attacks = 47% blocked.

One of us is obviously not quite right. If you can spot anything wrong with my arguing, please point it out. (Language is almost certainly wrong, but lets focus on the maths for now.)

[sSethia]

Never mind, smuglapse beat me to it.

[Bloodshadow]

I've got a math exam tomorrow for my summer school, so I spent the most of today studying. Anyone who's interested, write me an analysis on Ice Shield to make my life easier. "The community" is supposed to write the analysis anyways, instead of only myself

[Bloodshadow]

Guh... Nobody wanted to help me? Sigh...

Oh well. At least I aced that math test... I think. It was very easy, and I lol'd when other people were whining about how hard it was.

Ice Shield | Permafrost Shield



Ice Shield is one of the most powerful defensive cards in Elements. Like most shields, it reduces the damage from enemy creatures, and each time a creature attacks, it has a 30% chance of being frozen for 3 turns. Alone by itself, the defensive power of Ice Shield is unparalleled.

Like Fire Shield, Thorn Carapace, and Procrastination, Ice Shield is a form of creature control that activates automatically whenever a creature attacks. Each time a creature attacks, there is a 30% chance that it might get frozen for 3 turns. At a glance this percentage doesn't seem very high, and you might think that Ice Shield is not very useful compared to the other auto creature control shields with higher chances of activation. However, if triggered, Ice Shield prevents a creature from attacking at all for 3 turns, and stops it from using its ability at the same time; the frozen creature might as well not exist. Combined with its damage reduction, Ice Shield is arguably one of the best shields to have.

Now you know that Ice Shield is more powerful than it looks, but how much damage does it actually block? Here is a detailed mathematical analysis on Ice Shield, by Delreich from the official forum. This is explained in a turn-by-turn manner.
Turn 1: 100% of damage gets through.  (30% gets frozen, 3 turns wait on it).
Turn 2: 70% of damage gets through (30% has 2 turns of wait, another 21% gets 3 turns of wait).
Turn 3: 49% of damage gets through (30% - 1 turn; 21% - 2 turns; 14.7% - 3 turns)
Turn 4: 34.3% of damage gets through (30% unfreezes; 21% - 1 turn; 14.7% - 2 turns; 10.3% - 3 turns)
Turn 5: 54% of damage gets through (21% unfreezes ;14.7% - 1 turn; 10.3% - 2 turns; 16.2% - 3 turns)
Turn 6: 58.8% of damage gets through (14.7% unfreezes; 10.3% - 1 turn; 16.2% - 2turns; 17.6% - 3turns)
From a purely mathematical perspective, the percentage of damage getting through can be defined by a recursive sequence, where the nth term of the sequence is equal to 1 minus 30% of the three terms before it. As n approaches infinity, the nth term slowly converges to the value 10/19, or 53%. Therefore, the actual block chance of Ice Shield is 9/19, or 47%.
If you're not the math type, then in short Ice Shield blocks 9 out of 19 attacks; the block rate is roughly 47%. But that does not even count the damage reduction of 1 point, or 2 points when upgraded. In short, Ice Shield is an extremely powerful shield that blocks more than half of enemy attacks. Combine this with Flooding, or an Arctic Squid, and you can often stop your opponent cold; using Shockwave can even instantly destroy your opponent's frozen creatures.

Ice Shield is one of the cards that become significantly more powerful when upgraded. Permafrost Shield, the upgraded form of Ice Shield, blocks 2 damage from every attack, as well as blocking 47% of all attacks by freezing. Such a shield significantly cripples your opponent's attacking power, and combined with some healing it can often render you nigh invulnerable. Because of this, Permafrost Shield is often used in fully upgraded False God grinder decks.

Quick Facts:
Each time an enemy creature attacks, it has a 30% chance of being frozen for 3 turns.
In total, the freezing blocks 9/19, or 47% of all enemy attacks.
Combining that with damage reduction, Ice Shield can block more than half of your opponent's attacks.

Use This Card Together With:
Flooding | Inundation
Shockwave | Shockwave
Shard | Shard of Gratitude

Decks Using This Card:
PuppyChow's FG Rainbow
Essense's Iceberg AI5 deck

[Kuroaitou]

Guh... Nobody wanted to help me? Sigh...

Oh well. At least I aced that math test... I think. It was very easy, and I lol'd when other people were whining about how hard it was.

Ice Shield | Permafrost Shield

Don't be silly BS!

http://elementswiki.co.cc/cards-water/ice-shield-permafrost-shield/

Essence has already written an 'analysis' on Ice Shield on the New wiki - using that as a source, I thought that it be easy to give some credit and get some ideas off of Essence's part. (I would have written one for you, but when I realized that the Permafrost Shield already has some of it on its page, I thought you could have handled it). Sorry ^^;;

[Bloodshadow]

The mathematician inside me has awakened. To me, it seems like the block rate of Ice Shield oscillates from low to high to low, and approaches a certain value as the number of turns approaches infinity. I'll try to derive an equation of Ice Shield's block rate as a function of turns.

But right now, I'll accept Delreich's math...

Gah... It's almost midnight, and I don't feel like doing this anymore. I'll finish it tomorrow.

And at midnight, I've figured out a general formula that perfectly describes the block chance of Ice Shield as a function of turn number. It's some sort of recursive sequence...

t_n = 1 - 0.3t_n-1 - 0.3t_n-2 - 0.3t_n-3
t₁ = 1

This is the percentage of attacks that get through. Can any math nerd confirm whether the behavior of this sequence is periodic or convergent?

[Bloodshadow]

I made a little program in my graphing calculator, and I found that for the recursive sequence of Ice Shield, t_n converges to 10/19 as n approaches infinity. Seems like Delreich was right after all...

I finished the analysis on Ice Shield, but I'll wait for some feedback before I put it on the wiki.

Also, the new poll is up. I predict that Hope wins - it's the most powerful shield in the game! And I'll hate everyone who votes Holy Light, the one card I absolutely hate in this game.

[RedWarrior0]

Solar Buckler FTW.

[Kuroaitou]

I made a little program in my graphing calculator, and I found that for the recursive sequence of Ice Shield, t_n converges to 10/19 as n approaches infinity. Seems like Delreich was right after all...

I finished the analysis on Ice Shield, but I'll wait for some feedback before I put it on the wiki.

Also, the new poll is up. I predict that Hope wins - it's the most powerful shield in the game! And I'll hate everyone who votes Holy Light, the one card I absolutely hate in this game.

Because of the bold part, I shall now vote for Holy Light | Holy Flash.

Personally I would like to see strategies/details on Guardian Angel, considering its synergies with various cards due to its +5 reusable healing ability. Also, thanks so much for the Permafrost Shield article! (It looks great)

[Bloodshadow]

I'll be surprised if someone votes for Solar Shield. I agree with Jmizzle that it is the worst card in Elements. Its Death equivalent, Skull Shield, are at least somewhat useful in Aflatoxin decks to block enemy Malignant Cells from attacking.

I hope that Solar Shield is at least changed in some way before I have to write an analysis for it. *shudders*

[ddevans96]

Light has two really good shields as it is. I mean, this card was there first, but it just isn't very good at all.

I voted for Holy Flash. That 10 healing isn't much if you use it on you, but it can be really good against a death or darkness deck, and this can also heal creatures for more than any other card in the game.