[Legend Series] Drawing Those Cards

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    DuelLegend

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    [Legend Series] Drawing Those Cards

    Post by DuelLegend on Sat Jun 09, 2012 1:47 am

    Article Name: Drawing Those Cards
    Author: DuelLegend
    Copyright (use permitted if attributed): DuelLegend

    15%

    That's the chance of drawing one specific card from a 40-card deck, with a 6-card starting hand. This is illustrated by the following table:


    Click for Source

    This is why many duelists stick to a maximum of 40 or 42 cards in their deck. The more cards you have in your deck, the more this probability goes down. In fact, with a 45-card deck, this 15% goes to 13%. In a 50-card deck, this is 12%. 4 turns are worth 1%. Whilst this may not sound like much of an increase, every card counts. Every turn counts.

    Specific Cards in a Hand
    Now let us consider the likelihood of drawing specific cards. If your deck relies on a One-Turn-Kill, how likely is it that the OTK will work?
    A Chimeratech OTK consists of:
    • Future Fusion (FF)
    • Overload Fusion (OF)
    • Heavy Storm (HS)

    This is assuming we have the cards we need in our deck, extra deck and graveyard, including:
    • 2x Chimeratech Overdragon (CO)
    • 1+ Cyber Dragon (CD)

    Now, the cards we need in our hand (FF, OF, HS) have to be drawn from our deck. In our deck, there are:
    • Future Fusion (FF) x2
    • Overload Fusion (OF) x3
    • Heavy Storm (HS) x1

    The chances of drawing these cards from your deck on turn 1 is:

    1.07%

    See how small that is? That could get even smaller if you introduce more cards into your deck.
    The best way to get around these small probabilities is to try to introduce cards that draw more cards in place of other cards that may not otherwise contribute, such as Cardcar D or Cyber Valley in place of Effect Veiler (side Veiler instead).

    Multiple Cards in a Deck
    Having multiples of the same card in a 40-card deck can help immeasurably. Let us illustrate why, with examples.

    • 3 of the same card:

    Turn 1: 45%
    Turn 2: 8.3%
    Turn 3: There will only be 33 cards in the deck at the draw phrase of turn 3. Thus, 9.09%.
    For the remaining turns, the equation is: (3/cards in deck) * 100

    • 2 of the same card:

    Turn 1: 33.3%
    Turn 2: 5.5%
    Turn 3: There will only be 33 cards in the deck at the draw phrase of turn 3. Thus, 6.06%.
    For the remaining turns, the equation is: (2/cards in deck) * 100

    • 1 of the same card:

    Turn 1: 15%
    Turn 2: 2.9%
    Turn 3: There will only be 33 cards in the deck at the draw phrase of turn 3. Thus, 3.03%.
    For the remaining turns, the equation is: (1/cards in deck) * 100

    NOW FOR THE IMPORTANT PART.

    Look at the numbers:

    3: Turn 3: There will only be 33 cards in the deck at the draw phrase of turn 3. Thus, 9.09%.
    2: Turn 3: There will only be 33 cards in the deck at the draw phrase of turn 3. Thus, 6.06%.
    1: Turn 3: There will only be 33 cards in the deck at the draw phrase of turn 3. Thus, 3.03%.
    Do you notice something here? Yes, that's right. The chances of you drawing a specific card from your deck on the third turn TREBLE if you put another of the same card in it. Your challenge is to find out how this affects later turns, and you will soon understand the value of using multiples of the same, necessary card!

    However, be cautious. There are some cards you don't want to have clogging up your hand, like Future Fusion when you already have a Chimeratech on the field, for example. In this case, it would be wise to minimise the probability of you drawing such cards. Something I found on the internet that was quite useful was a Deck Builder Toolkit. Have a look. It helps you to work out the likelihood of drawing a specific hand, and you could also use it to work out the drawing of a specific card if you're having trouble with your maths.

    To summarise, probability is important to consider when working out what cards should go in your deck and how many. The extra cards you don't put in (as they may become a dead draw if drawn at the wrong time) could be replaced with even more helpful cards, thus making the difference between victory, defeat and whether a deck has been built smartly. Defining probability is often a subconscious thing for many of us, and is what divides the pros from the experts in tournaments.

    Happy deck building!



    Code:

    [b]Article Name:[/b] Drawing Those Cards
    [b]Author:[/b] DuelLegend
    [b]Copyright (use permitted if attributed):[/b] DuelLegend

    [center][size=24]15%[/size][/center]

    That's the chance of drawing one specific card from a 40-card deck, with a 6-card starting hand. This is illustrated by the following table:

    [center][img]http://img28.imageshack.us/img28/367/40card.jpg[/img]
    [url=http://www.shadowera.com/showthread.php?8898-Odds-of-drawing-cards-at-30-and-40-card-deck-size]Click for Source[/url][/center]

    This is why many duelists stick to a maximum of 40 or 42 cards in their deck. The more cards you have in your deck, the more this probability goes down. In fact, with a 45-card deck, this 15% goes to 13%. In a 50-card deck, this is 12%. 4 turns are worth 1%. Whilst this may not sound like much of an increase, every card counts. Every turn counts.

    [b]Specific Cards in a Hand[/b]
    Now let us consider the likelihood of drawing specific cards. If your deck relies on a One-Turn-Kill, how likely is it that the OTK will work?
    A Chimeratech OTK consists of:
    [list][*]Future Fusion (FF)
    [*] Overload Fusion (OF)
    [*] Heavy Storm (HS)[/list]
    This is assuming we have the cards we need in our deck, extra deck and graveyard, including:
    [list][*] 2x Chimeratech Overdragon (CO)
    [*] 1+ Cyber Dragon (CD)[/list]
    Now, the cards we need in our hand (FF, OF, HS) have to be drawn from our deck. In our deck, there are:
    [list][*]Future Fusion (FF) x2
    [*] Overload Fusion (OF) x3
    [*] Heavy Storm (HS) x1[/list]
    The chances of drawing these cards from your deck on turn 1 is:

    [center]1.07%[/center]

    See how small that is? That could get even smaller if you introduce more cards into your deck.
    The best way to get around these small probabilities is to try to introduce cards that draw more cards in place of other cards that may not otherwise contribute, such as Cardcar D or Cyber Valley in place of Effect Veiler (side Veiler instead).

    [b]Multiple Cards in a Deck[/b]
    Having multiples of the same card in a 40-card deck can help immeasurably. Let us illustrate why, with examples.

    [list][*]3 of the same card:[/list]
    Turn 1: 45%
    Turn 2: 8.3%
    Turn 3: There will only be 33 cards in the deck at the draw phrase of turn 3. Thus, 9.09%.
    For the remaining turns, the equation is: (3/cards in deck) * 100

    [list][*]2 of the same card:[/list]
    Turn 1: 33.3%
    Turn 2: 5.5%
    Turn 3: There will only be 33 cards in the deck at the draw phrase of turn 3. Thus, 6.06%.
    For the remaining turns, the equation is: (2/cards in deck) * 100

    [list][*]1 of the same card:[/list]
    Turn 1: 15%
    Turn 2: 2.9%
    Turn 3: There will only be 33 cards in the deck at the draw phrase of turn 3. Thus, 3.03%.
    For the remaining turns, the equation is: (1/cards in deck) * 100

    [center]NOW FOR THE IMPORTANT PART.[/center]

    Look at the numbers:
    [quote]
    3: Turn 3: There will only be 33 cards in the deck at the draw phrase of turn 3. Thus, [b]9.09%.[/b]
    2: Turn 3: There will only be 33 cards in the deck at the draw phrase of turn 3. Thus, [b]6.06%.[/b]
    1: Turn 3: There will only be 33 cards in the deck at the draw phrase of turn 3. Thus, [b]3.03%.[/b]
    [/quote]
    Do you notice something here? Yes, that's right. The chances of you drawing a specific card from your deck on the third turn TREBLE if you put another of the same card in it. Your challenge is to find out how this affects later turns, and you will soon understand the value of using multiples of the same, necessary card!

    However, be cautious. There are some cards you don't want to have clogging up your hand, like Future Fusion when you already have a Chimeratech on the field, for example. In this case, it would be wise to minimise the probability of you drawing such cards. Something I found on the internet that was quite useful was a [url=http://www.brianritchson.com/toolkit/index.php]Deck Builder Toolkit[/url]. Have a look. It helps you to work out the likelihood of drawing a specific hand, and you could also use it to work out the drawing of a specific card if you're having trouble with your maths.

    To summarise, probability is important to consider when working out what cards should go in your deck and how many. The extra cards you don't put in (as they may become a dead draw if drawn at the wrong time) could be replaced with even more helpful cards, thus making the difference between victory, defeat and whether a deck has been built smartly. Defining probability is often a subconscious thing for many of us, and is what divides the pros from the experts in tournaments.

    [center]Happy deck building![/center]















    Guest
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    Re: [Legend Series] Drawing Those Cards

    Post by Guest on Tue Jun 12, 2012 5:41 am

    Ok thanks now i will know my chance of drawing card ^_^ Razz
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    StalkerSam

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    Re: [Legend Series] Drawing Those Cards

    Post by StalkerSam on Sun Jun 24, 2012 10:24 am

    9/10.
    that was helpful and full of rich calci....info!
    still a probability is just a probability it mainly depends on the shuffle of the deck Very Happy




    ^^ credits: DL , songy :3

    Guest
    Guest

    correction

    Post by Guest on Mon Jun 25, 2012 4:40 am

    this table is good. it is 15% at start. but it for a deck that has all diferent cards. the math for a deck with multiple card copys is difrent so thats just a special case. Trust me i know. Shocked
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    DuelLegend

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    Re: [Legend Series] Drawing Those Cards

    Post by DuelLegend on Mon Jun 25, 2012 5:45 am

    The second half of the article covers multiple copies of a card.















    Guest
    Guest

    math

    Post by Guest on Mon Jun 25, 2012 6:52 pm

    The second part is correct to but it onli looks for the cards that you by that time have in your deck. In this case you didnt include the probability that in your previos draws didnt got the card. For solving that you use something calld conditional probability. Im not saying your wrong in fact its pure logical. Im just saying you have more aspects to look at it. In your math you use classic probability and that works just in the given moment.
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    DuelLegend

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    Re: [Legend Series] Drawing Those Cards

    Post by DuelLegend on Mon Jun 25, 2012 10:13 pm

    Oh, that's true. I was never a star at maths though! Razz















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