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  1. #1
    DP Visionary Atomzed's Avatar
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    Deck size & Probability - A case for (slightly) bigger deck

    This is an article which I originally posted in the A1 forum. Seeing that there was some discussion on deck size, i decided to re-post the article.

    --------------------

    The happy problem with Elementals and priests is that all of their cards are equally good, and it's tough to figure out what cards to retain/remove in a deck.

    As part of my obsession with tweaking an Elementalis deck, I have been fiddling with the hypergeometric calculator to figure out the best deck composition.

    And to my surprise, the minimum deck size does not really affect the probability of crucial card draw.

    In fact, it is better to increase your deck size to accommodate a crucial card, rather than swapping out with another card.

    Example,

    At turn 5 with a 39 card deck, with 3 PB and 3 SK, I have a 85.44% of drawing at least 1 5cc ally.

    Let's say I want to increase my chances of drawing SK/ PB by turn 5. I can increase 1 card each, and say swapping out 2 eternal renewal.

    At turn 5 with a 39 card deck, with 4 PB and 4 SK, I have a 93% of drawing at least 1 5cc ally. Good, an increase of 8%.

    But with this card exchange, I will lose 2 crucial ER.

    However, If I just add 2 5cc allies to my deck, I will increase the draw % to 91%. A drop of 2% compared to a 39-card deck, but I think its a good trade off for the additional adaptability with ER.

    Putting it in % terms, replacing the ER gives me a net gain of 2% (for 5cc allies), but a loss of 100% for ER ( Not having the ER removes my option of using it, so it's as good as a 100% loss in the game).

    How about the impact on other cc cards? Still very negligible. Holding all values constant except for deck size, the changes are as follow:-

    Turn 1, draw at least 1x1cc allies,
    77.4% (39) to 75.3% (41)
    Turn 2, draw at least 1x 1&2cc allies, 94.2% (39) to 93% (41)
    Turn 3, draw at least 1x 3cc allies,
    82.9% (39) to 80.9% (41)

    You see that the drop in % is no more than 2%.

    Of course, having said all the above, a lower card deck is still more consistent than a higher card deck.

    But there *may* be a sweet spot for slightly bigger decks, where you lose negligible consistency for the added adaptability. This is especially true for cards that are used typically only 1 time, late in the game, but can change the flow of the game. Cards like resurrection, eternal renewal and soul reaper.

    Follow-up comment
    Yup, this perspective works best for cards that is a) only cast 1 per game b) typically cast late, say T10. As i mentioned, it works for cards like resurrection and ER.

    Cards like Tidal wave or WoTF, which you NEED by a specific turn, you better off include more of the card.

    The implication of my post for me is that for a priest deck or elemental deck, instead of cutting down 2 cards to put in 2x Resurrection/ ER, it's actually worthwhile to just include it in. Cos I'm not so worry abt % for those cards.
    Last edited by Atomzed; 11-17-2011 at 01:55 PM.
    A1's Mustard-Seed Knight of Hope (IGN:A1 atomzed)
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  2. #2
    DP Visionary Atomzed's Avatar
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    An online version of the hypergeometric calculators can be found here

    http://www.shadowera.com/showthread....r-deck-designs
    Last edited by Atomzed; 11-17-2011 at 04:43 PM.
    A1's Mustard-Seed Knight of Hope (IGN:A1 atomzed)
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  3. #3
    Senior Member bicin's Avatar
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    nice one atomzed..

    i'm thinking about going beyond 40..
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    Senior Member Nickey293's Avatar
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    Were you a math or stats major? Excellent article btw.
    Team Juggernaut FTW!!

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    Devoted Fan Gondorian's Avatar
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    Of course, the larger the deck, the chances of getting a good start diminish. If you are not running 1cc/2cc allies, you can risk bigger deck for little penalty. If you do want to get early board presence, then your extra cards above 40 should probably be 1cc and 2cc allies.

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    Senior Member Dima's Avatar
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    lol yesterday played against 130+ elementalis with my Gwen who just had like 4 armor of ages and 4 novas so i just killed against the wall;P

    i think good balanced big decks can work great for elementalis and priests and warriorrs(especially boris)
    Last edited by Dima; 11-17-2011 at 02:44 PM.

  7. #7
    Senior Member Cruxx's Avatar
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    2 short comments at this point:
    • Don't forget that any additional card de-values your chance of drawing every other card / goal (supported by different cards) already present in the deck.
    • A point of percentage isn't equal to another point of percentage.
      Example:
      Increasing your draw chance by 5% from 47,5% to 52.5% still leaves you with about a 50/50 chance to draw that card.
      Increasing your draw chance by 5% from 90% to 95% doubles your effective chance of drawing this card. (Previously every 10th game would end in disappointment, now it's only every 20th game.)


    -> Minimising your cards total is still one of your best friends.
    Conceptual stuff
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  8. #8
    DP Visionary Atomzed's Avatar
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    Quote Originally Posted by Cruxx View Post
    2 short comments at this point:
    • Don't forget that any additional card de-values your chance of drawing every other card / goal (supported by different cards) already present in the deck.
    • A point of percentage isn't equal to another point of percentage.
      Example:
      Increasing your draw chance by 5% from 47,5% to 52.5% still leaves you with about a 50/50 chance to draw that card.
      Increasing your draw chance by 5% from 90% to 95% doubles your effective chance of drawing this card. (Previously every 10th game would end in disappointment, now it's only every 20th game.)


    -> Minimising your cards total is still one of your best friends.
    Hi crux,

    Comments abt your comments:-
    Point 1: my point is related to deck construction. In a actual game, the actual card probability changes with every turn. Say I'm top decking, with no allies on board and desperately trying to get my allies. I might get the scenario of getting 2 consecutive resurrection and I'm screwed. It can happen, which is why I ended by saying that a smaller deck is still better bec it's more consistent. But I will argue that additional loss of % (aka consistency) I worth it bec I have more options in every game (aka adaptability in using a key card say resurrection).

    Point 2: I don't get it when you mean by percentage point differs, though the point abt card draw affecting % is absolutely spot on. Example, the perfect Santa Bomb. It increases the no of cards drawn by 3 cards. That increases the % of drawing a crucial 5cc card (say MC which you have 4 copies) by 71% to 81%. That is also same effect if you cast BF at T2; the reason why warriors feel the game is tougher if they don't have T2 BF is bec BF increased the probability of drawing their key cards across all turns.

    I think to summarize my article, certain cards are worth having just additional 2 copies stack on to our current deck. Example like eternal renewal. If you have a great 39 card elementalis deck without ER, you *might* consider just adding 2 ER into the deck. The probability change is minimal, but the adaptability improvement may be well worth it.
    A1's Mustard-Seed Knight of Hope (IGN:A1 atomzed)
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    Meltdown Tier and Payout Analysis

  9. #9
    DP Visionary Atomzed's Avatar
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    @Nickey and bicin, thanks for the compliment! I don't major in stats but my profession requires some amt of stats knowledge. But in this case, you can just use the hypergeometric calculators to do the maths. Shannong had a sticky page on the strategy section.
    A1's Mustard-Seed Knight of Hope (IGN:A1 atomzed)
    Also a member of PFG1 and PFG2
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    "Rapid analysis, accurate judgement, and superb powers of concentration...That is all we need." - Lezard Valeth

    Proud member of A1 - Evolution in Theory
    Project Omega - Card Analysis and Strategy Guide

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    Deck size and Probability - A case for (slightly) bigger deck
    Meltdown Tier and Payout Analysis

  10. #10
    Senior Member Cruxx's Avatar
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    Quote Originally Posted by Atomzed View Post
    I think to summarize my article, certain cards are worth having just additional 2 copies stack on to our current deck. Example like eternal renewal. If you have a great 39 card elementalis deck without ER, you *might* consider just adding 2 ER into the deck. The probability change is minimal, but the adaptability improvement may be well worth it.
    Sure, as a good old min/maxer I still would argue the point that there might be 2 cards you do not need that desperately to make room for those you mentioned.

    I might agree in cases where your deck only supports say 2 or 3 overall goals, supported by 20 to 13 cards each. In such a case it's less important to keep to the absolute card minimum since your chances of drawing your goals are still very high, but most decks don't work this way in my experience.

    €dit:
    I don't get it when you mean by percentage point differs, though the point abt card draw affecting % is absolutely spot on.
    It just means that the 2 points decrease from 93% to 91% mentioned in your example shouldn't be neglected (It's almost 30% more likely to draw the card going from 91% to 93%). That's why I gave the example of 5 points around the 50% mark not having the same value as the 5 points around the 90% mark.
    Last edited by Cruxx; 11-17-2011 at 04:25 PM.
    Conceptual stuff
    The Rule of Six - Building and reviewing a deck.

    Behold my Wulven decks
    Wrath of the Wulven - Making the most of your Moonstalker!

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