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Offline ZawadxTopic starter

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War #11 - Round 9 https://elementscommunity.org/forum/index.php?topic=65503.msg1272449#msg1272449
« on: December 13, 2017, 01:42:56 pm »
WAR #11 Round 9
12 armies arrive at the glorious battlefield, each with their weapons drawn and their shields up ready for a battle. Each army is led by a daring General and a multitude of loyal troops, each ready to lay their life on the line for what they fight for. 12 armies will enter the battlefield, but only 1 will leave at the end.
Read the War Rules
Contact Warmasters

News
The best laid plans of mice and men often go awry.

Fire iz ded. Dawkness too.

Death falls below 50 cards by vault! But they have the SG relics to go on, so they must push forward!

Death and Aether fall to two matches per round.

Deckbuilding
Duel phase has started
Teams have to build decks for all players who are fighting during this round. All team members participate in the planning. Please do not post your decks in public or talk about them in chat.

All decks must be made ready before the timer goes to zero, after which, editing decks is strictly forbidden. Failure to have all of the decks ready will lead to a severe card penalty and/or automatic losses. It is highly recommended that all team members double-check their decks before the duels start.
Duels
Fighting ends!
Duel phase starts when deckbuilding ends.

PM your opponent and try to find a suitable time. Time Zone Converter might be useful here. If you cannot find a time when you both are online, please contact Warmasters--Zawadx and Jenkar--immediately. If the match does not happen, you both lose by default unless one of you is clearly more active and flexible.

Duels are "best-of-five", you must use the deck and mark built during the previous phase, and you cannot make any changes to your deck or mark during the round.

Please make sure to record your duels as shown in the Rules:
(Air Gen) KingKiller 3 - 1 (Water Lt) LordOwner
(Air Sld) KingKiller 3 - 1 (Water Gen) LordOwner
(Air Lt) KingKiller 3 - 1 (Water Sld) (Sub) LordOwner

(SUB indicates that someone else played instead of LordOwner)


Super Event Card




Each team is awarded an amount of 'Scaredgirl Relic's based on their round record so far.
Each team is awarded 1 SG Relic for rounds with 2 wins, 2 for rounds with 1 win and 3 for rounds with 0 wins.
From rounds 1 to 6, 4 win rounds subtract 1 relic from the total.
Teams receiving a bye are considered as having won all byed matches for EC count. So a team with 2-1 record with a bye will get 0 SG relics for that round.
1 SG Relic may be traded for the following perks:

  • Gain 2 Discard tokens
  • Add a soldier boost to any deck (can stack; Alchemist, Mercenary & Tinkerer can only be used once per deck)
  • Play 1 additional match, with salvage but no discard. (can be used multiple times a round)

When using perks, post it in a thread titled "R7-9 Super EC" in secret section. Relic perks must be declared during the deckbuilding phase.
If you wish to use the "Play 1 additional match, with salvage but no discard" perk, you must state the number of matches you will play 2 days before deadline. Deadline for this round: Time is up!
All additional match will be pooled together and matched up on the basis of vault size. If there are an odd number of teams wishing to participate, one of the matches will be randomly cut and the relic refunded. Priority for cutting goes to teams playing more additional matches, then higher vault size. If a team has more than half the matches, then their extra matches are refunded.
When building a deck for each such additional match, you may use the entire vault. The deck plays as a soldier with a boost. Relics and SG Relics may be used to enhance the deck.
The relics for R1-6 are awarded now. Relics will be awarded for R7, R8 and R9 the round after.
The relic award for R1 will be weighted as 2/5, and for R2 by 3/5. Final relic counts will be rounded. So the round 1 record will award 2/5 times the relics of the same record in round 3. These weights are based on the difference between a win and a loss in a given round.
SG Relics are useable for only Rounds 7 to 9. During R10 deckbuilding, teams will have to convert all remaining SG Relics into Discard tokens (2 tokens for 1 SG relic) or Relics (3 relics for 1 SG relics).
List of SG Relics.






Event Card



For each match, select Paper, Rock or Scissor. You may also select Dynamite.
Paper > Rock > Scissors > Paper.
Winning with Rock grants 6 extra upgrades this match.
Winning with Scissors grants 4.
Winning with Paper grants 2.
A player who selects "Dynamite" wins in the case of a draw.
If both players select dynamite, (inc. Rock/Dynamite vs Scissors/Dynamite etc.) neither player wins anything.
If neither player selects Dynamite and it's a draw, neither player wins anything.
You must send your choices by the deckbuilding deadline.
Upgrades are added to the deck before each game. So you may choose which upgrades to use, and change these extra upgrades as you wish.
The upgrades are added after removing cards for sideboard in case of the sideboard boost.



Stolen from War 9 Round 11. Credit to Helston.

Battles

Spoiler for Aether:
Spoiler for Death:
Spoiler for Water:


--------------------------=--------------------------


For this round:
Discards - 24 (15 from deck, 9 from vault)
Salvage - 6


When you play the game of thrones, you win or you die. There is no middle ground.

Offline hainkarga

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Re: War #11 - Round 9 https://elementscommunity.org/forum/index.php?topic=65503.msg1272458#msg1272458
« Reply #1 on: December 13, 2017, 03:37:13 pm »
Just to be clear; if just the loser selects dynamite, does it affect the outcome? ie. Rock vs Scissors/Dynamite
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Offline iancudorinmarian

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Re: War #11 - Round 9 https://elementscommunity.org/forum/index.php?topic=65503.msg1272459#msg1272459
« Reply #2 on: December 13, 2017, 03:39:20 pm »
Just to be clear; if just the loser selects dynamite, does it affect the outcome? ie. Rock vs Scissors/Dynamite
It does not.

Offline DoctorC

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Re: War #11 - Round 9 https://elementscommunity.org/forum/index.php?topic=65503.msg1272460#msg1272460
« Reply #3 on: December 13, 2017, 03:42:40 pm »
Rip Darkness. But hey, Life's still alive so that's a nice thing =D
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Offline hainkarga

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Re: War #11 - Round 9 https://elementscommunity.org/forum/index.php?topic=65503.msg1272461#msg1272461
« Reply #4 on: December 13, 2017, 04:02:13 pm »
Made a  quick value table.

« Last Edit: December 13, 2017, 05:49:40 pm by hainkarga »
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Offline CactusKing

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Re: War #11 - Round 9 https://elementscommunity.org/forum/index.php?topic=65503.msg1272476#msg1272476
« Reply #5 on: December 13, 2017, 08:37:08 pm »
I think Darkness can still live if we use SG relics for discard tokens
I spilt my blood against the :earth
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Offline Manuel

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Re: War #11 - Round 9 https://elementscommunity.org/forum/index.php?topic=65503.msg1272479#msg1272479
« Reply #6 on: December 13, 2017, 10:11:42 pm »
let darkness revive and do a new bracket it's totally legit i don't wanna face air another time they won the last war without shard they deserve it

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Re: War #11 - Round 9 https://elementscommunity.org/forum/index.php?topic=65503.msg1272480#msg1272480
« Reply #7 on: December 13, 2017, 10:19:13 pm »
let darkness revive and do a new bracket it's totally legit i don't wanna face air another time they won the last war without shard they deserve it

The war Darkness won was the 1st war WITH shards
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Offline Manuel

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Re: War #11 - Round 9 https://elementscommunity.org/forum/index.php?topic=65503.msg1272481#msg1272481
« Reply #8 on: December 13, 2017, 10:23:12 pm »
let darkness revive and do a new bracket it's totally legit i don't wanna face air another time they won the first war with shards they deserve it

fixed

Offline ZawadxTopic starter

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Re: War #11 - Round 9 https://elementscommunity.org/forum/index.php?topic=65503.msg1272491#msg1272491
« Reply #9 on: December 14, 2017, 07:54:17 am »
I think Darkness can still live if we use SG relics for discard tokens

So apparently my standings update didn't go live because gdocs is so precocious and needy. But Darkness is at 35 cards and 0 discard tokens after the transmutations and penalty. They have only 6 SG relics, right? So no, darkness cannot live. Sorry.
When you play the game of thrones, you win or you die. There is no middle ground.

Offline hainkarga

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Re: War #11 - Round 9 https://elementscommunity.org/forum/index.php?topic=65503.msg1272516#msg1272516
« Reply #10 on: December 14, 2017, 11:59:36 pm »
So I attempted to analyze this event card to find out the Nash equilibrium that would make everyone relatively content with their choice. I did this mostly for fun and I had time at hand. I went a bit methodic and noted even the most obvious. I did this with my entry-level, limited knowledge of game theory, there are approaches that require deeper skills. For anyone interested, I am going to write my notes below.

According to decision theory, the choice is obviously rock/dynamite with the expected value of 10 as max. But this is a multiplayer game, so it doesn't apply. This problem is under the domain of game theory. This is because if R/D was the absolute choice, then everyone would go for it only to be trashed by a troll team that goes for 4/4 paper. Left side is Player 1, top side is Player 2. Each colliding choices (cells) only apply to two players (elements teams), 6,-6 means Player 1 wins 6 upgrades, Player 2 loses 6 upgrades as a result of this choice.



Analysis of EC with game theory:
  • One player's win is other player's loss. Because if one side loses, they will have a disadvantage during the match. Players are not indifferent to other sides win. One side having 6 ups means other has 6 fewer ups
  • This is a two player, symmetrical, simultaneous, cycling, zero-sum, non-phased, non-cooperative game. Simultaneous because the choices are revealed at the same time (not by taking turns), cycling because if one side knew the other one's choice, he would change his decision, and this would go on infinitely. Zero-sum because there is no case where both parties win or lose and the sum of win+loss is zero. Non-phased because there is no second step of the game after both choices are revealed (which would require phased-game solutions or Markov chains). Non-cooperative because alliances are forbidden
  • Game is not in Nash equilibrium. Because there is no mutual best response strategy. To see that, you put an asterisk to every highest profit on each row and column. If there is a cell with two asterisks, then both players go for that option and you get a mutual best response
  • No strictly dominating strategy. Because any single option (pure strategy) for a player is not greater than his other options
  • No pure strategy Nash equilibrium. Because no single outcome (cell/intersection) satisfies both players. There is always a more profitable deviation in the same column of that cell for player 1 or row for player 2
  • No weakly dominating strategy. Same as above, but deviation doesn't have to be more profitable, equal profit is enough.
  • This game has finite number of players and has finite number of options. So there MUST be a Nash equilibrium in which both parties are indifferent.

The solution to Nash equilibrium is a probabilistic distribution over multiple strategies. An example would be; "Team Water selects two strategies, Paper/Dynamite & Scissors/Dynamite. we randomize our choice but with the weighted numbers of Nash equilibrium. Say P/D is 1/10 and S/D is 9/10. We will roll a d10 dice with 9/10 sides saying choose S/D".

At this point, I tried to solve probabilistic distribution between only two strategies to find the equilibrium but there is no 2 strategy combination that can possibly have zero-sum. Below is an example,



The red cells cannot possibly be zero for either player as P1 is always positive (2 & 4) or P2 is always negative (-2 & -4) and neither can be zero when subtracted from each other (after being multiplied with their distribution. also, other cells of the row could be). So you cannot mix those 2 strategies and reach an equilibrium. I tried the combinations but none of the two strategy combinations seem to solve it. If there were any, I could attempt calculating distribution. There is a solution for 3 or 4 or 5 or 6 mixed strategies but the formulas get complicated for me to do by hand. I tried to find some online GT calculator for it and I actually found for 5x5 matrix also an application on MIT website. But right now they are not capable of solving a matrix of this size. But to give you an idea, the equilibrium solution is a weighted dice rolling with some of the strategies are written on more sides. Aside from that, people are not fully rational. So some may act predictable, some can mindgate the others or just be very lucky about their choices. If I can manage find a calculator for 6x6 mixed strategy solution, I am going to post it with a suggestion for everyone. But in any case, modeling is half the solution.




« Last Edit: December 15, 2017, 01:14:24 am by hainkarga »
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Offline ZawadxTopic starter

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Re: War #11 - Round 9 https://elementscommunity.org/forum/index.php?topic=65503.msg1272517#msg1272517
« Reply #11 on: December 15, 2017, 01:29:32 am »
I already calculated the mixed strategy. #BetterThanMIT

It really shouldn't be too hard for a computer though. Maybe the app you found was just not made with these parameters in mind.
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