My Math Forum Probability of drawing certian cards...

 February 15th, 2014, 09:06 AM #1 Newbie   Joined: Feb 2014 Posts: 5 Thanks: 0 Probability of drawing certian cards... Hi there.. I am not a math student or anything.. just a card game player and would really like help with this as I have no idea where to even start to try and solve it, I have a deck of 50 cards. I am allowed a max of 3 of any single card in my deck. At the start of the game I draw 6 cards, and have the option to discard all 6, reshuffle and then redraw 6 (You can only do this once), then I draw a 7th card. So.. what is the chances of drawing a given card in my opening hand of 7 cards if the card I want has 1,2 or 3 copies in the deck? Thanks I hope someone can help!
February 16th, 2014, 10:39 AM   #2
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Re: Probability of drawing certian cards...

Quote:
 Originally Posted by Jynks I have a deck of 50 cards. I am allowed a max of 3 of any single card in my deck. At the start of the game I draw 6 cards, and have the option to discard all 6, reshuffle and then redraw 6 (You can only do this once), then I draw a 7th card. So.. what is the chances of drawing a given card in my opening hand of 7 cards if the card I want has 1,2 or 3 copies in the deck?
Very unclear.
IF you want a 1 and only 1 copy in deck, then same as deck containing one 1 and 49 2's ?

Why draw a 7th card if the 1 is one of the 6 cards?

When/why discard all 6 at first round?

 February 16th, 2014, 02:00 PM #3 Newbie   Joined: Feb 2014 Posts: 5 Thanks: 0 Re: Probability of drawing certian cards... because those are the rules of the game. You start the game with a 50 card deck. You draw 6 cards. If you do not like your hand you can mulligan and shuffle those 6 back in and draw another 6. (you can only do this once) Then you draw a 7th card You can only have 3 copies of a given card in the deck. BUT you can have 1 or 2 copies. So.. If i have 1 copy of a card what is the chance of drawing it in my opening hand with those 13 draws? If I have 2 copies of a card what is the chance of drawing it in my opening hand with those 13 draws? If I have 3 copies of a card what is the chance of drawing it in my opening hand with those 13 draws?
February 16th, 2014, 02:04 PM   #4
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Re: Probability of drawing certian cards...

Hello, Jynks!

Would you please explain this strange deck of cards
and the rules of this weird game.

Quote:
 I have a deck of 50 cards. I am allowed a max of 3 of any single card in my deck.

There are some duplicate cards in this deck?

Suppose the cards are numbered: 1, 2, 3, ...

We could have 50 different cards (from 1 to 50).

Or we could have: three 1's, three 2's, three 3's, . . . three 16's, and two 17's.

Is this true?
Do we know this distribution at the start?

Quote:
 At the start of the game I draw 6 cards, and have the option to discard all 6, reshuffle and then redraw 6. (You can only do this once), then I draw a 7th card.

You are seeking a particular card.
I assume you select it at the beginning of the game.

If it is not included in the initial 6 cards, discard the 6 cards,
[color=beige]. . [/color]and draw 6 more from the remaining 44 cards.
Then draw a 7th card anyway,

Quote:
 What is the chance of drawing a given card in my opening hand of 7 cards [color=blue]if the card I want has 1, 2 or 3 copies in the deck?[/color][color=beige] .[/color][color=red]Why?[/color]

You already said that every card has 1, 2 or 3 copies.

We can't find the probability of, say, getting a "5"
[color=beige]. . [/color]without knowing how many 5's are in the deck.

February 16th, 2014, 02:29 PM   #5
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Re: Probability of drawing certian cards...

Quote:
 Originally Posted by soroban Hello, Jynks! Would you please explain this strange deck of cards and the rules of this weird game.
The game is called "Lord of the Rings" The Card Game" is is kind of like Magic the Gathering but it is a Co-Op game that can be played solo. You can read the rules here if you like LoTR-LCG Rules.pdf.. or check out this video some dude made.

Quote:
Originally Posted by soroban
Quote:
 I have a deck of 50 cards. I am allowed a max of 3 of any single card in my deck.
[size=7]
There are some duplicate cards in this deck?

Suppose the cards are numbered: 1, 2, 3, ...

We could have 50 different cards (from 1 to 50).

Or we could have: three 1's, three 2's, three 3's, . . . three 16's, and two 17's.

Is this true?
There is a card pool of about 1000 cards or so (and growing). When you build a deck you have to make it 50 cards large form the 1000ish card available at this time. You can only have 3 copies of any given card BUT you do not have to put in 3, you can put in 1 copy or 2.

So each deck has a very different make up of cards and quantity of cards. Some cards will have 3 copies, some 2 copies and some 1 copy.

Though I no nothing about maths, I thought the type of card didn't matter beyond how many of the one you were looking for.

Quote:
Originally Posted by soroban
Quote:
 At the start of the game I draw 6 cards, and have the option to discard all 6, reshuffle and then redraw 6. (You can only do this once), then I draw a 7th card.

You are seeking a particular card.
I assume you select it at the beginning of the game.

If it is not included in the initial 6 cards, discard the 6 cards,
[color=beige]. . [/color]and draw 6 more from the remaining 44 cards.
Then draw a 7th card anyway,
Yes I am trying to work out the chances of drawing a named card in my opening hand of 7.

You draw 6. If you do not have the card you want you shuffle those 6 back into the deck and draw again from 50... then you draw 1 extra card. So at the start of the game you have 7 cards in hand and 43 in your deck. Remembering that with the mulligan you can draw 12 in total (draw 6, mulligan to shuffle those 6 back in, draw 6, draw 1)

Quote:
Originally Posted by soroban
Quote:
 What is the chance of drawing a given card in my opening hand of 7 cards [color=blue]if the card I want has 1, 2 or 3 copies in the deck?[/color][color=beige] .[/color][color=red]Why?[/color]

You already said that every card has 1, 2 or 3 copies.

We can't find the probability of, say, getting a "5"
[color=beige]. . [/color]without knowing how many 5's are in the deck.
I am not sure I understand you here. You can only have 1,2 or 3 copies of any given card.

So say I wanted a the card "5". I know there are 3 copies of that card... so what is the chance of drawing it in the opening hand?
So say I wanted a the card "8". I know there are 2 copies of that card... so what is the chance of drawing it in the opening hand?
So say I wanted a the card "10". I know there are 1 copies of that card... so what is the chance of drawing it in the opening hand?

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

Here is an example of a deck...

Wall of Gondor
Total : 50

Heroes

Hero 1 : • Thalin ( Core Set 6 )
Hero 2 : • Éowyn ( Core Set 7 )
Hero 3 : • Beregond ( Heirs of Númenor 1 )

Allies

3 x • Bofur ( The Hobbit - Over Hill and Under Hill 8 )
3 x Imladris Stargazer ( Foundations of Stone 106 )
3 x Gondorian Spearman ( Core Set 29 )
3 x Knights of the Swan ( The Steward's Fear 4 )
2 x • Arwen Undómiel ( The Watcher in the Water 58 )
3 x Ethir Swordsman ( The Steward's Fear 6 )
3 x • Gandalf ( Core Set 73 )

Attachments

3 x Dwarrowdelf Axe ( Khazad-dûm 7 )
3 x Spear of the Citadel ( Heirs of Númenor 9 )
3 x Ancient Mathom ( A Journey to Rhosgobel 56 )
2 x Blood of Númenor ( Heirs of Númenor 13 )
3 x Unexpected Courage ( Core Set 57 )
2 x Resourceful ( The Watcher in the Water 62 )

Events

3 x Swift Strike ( Core Set 37 )
3 x Goblin-cleaver ( The Hobbit - Over Hill and Under Hill 16 )
3 x A Test of Will ( Core Set 50 )
3 x Dwarven Tomb ( Core Set 53 )
3 x The Galadhrim's Greeting ( Core Set 46 )

(ignore the Heores they start on the table and are NOT part of the 50 card deck)

So for example... what is the chance of getting Ethir Swordsman (3) in your opening hand. or Resourceful (2)in your hand. There isn't any cards with a single copy here.. but if there was.. what would be the chance of that?

 February 17th, 2014, 07:33 AM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Re: Probability of drawing certian cards... Still makes no sense... like, why reshuffle the 1st 6 when they don't contain your target card? You're better off not to. Anyhoo, poor question = poor answer; out of 13 cards: 1 copy: ~25% 2 copies: ~45% 3 copies: ~60%
February 17th, 2014, 06:11 PM   #7
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Re: Probability of drawing certian cards...

Quote:
Originally Posted by Denis
Why reshuffle the 1st 6 when they don't contain your target card?
You're better off not to./quote]

Why do you say that? If the target card is not in the first 6 you draw.. don't you have a better chance of drawing it after a re-shuffle and drawing another 7 rather than just drawing 1 card with out a reshuffle?

Quote:
 Originally Posted by Denis Anyhoo, poor question = poor answer; out of 13 cards: 1 copy: ~25% 2 copies: ~45% 3 copies: ~60%
This doesn't seam correct to me? Could you please explain how to came to this?

February 17th, 2014, 10:47 PM   #8
Math Team

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Posts: 14,597
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Re: Probability of drawing certian cards...

Quote:
Originally Posted by Jynks
Quote:
 Originally Posted by Denis Anyhoo, poor question = poor answer; out of 13 cards: 1 copy: ~25% 2 copies: ~45% 3 copies: ~60%
This doesn't seam correct to me? Could you please explain how to came to this?[/quote]
"If i have 1 copy of a card what is the chance of drawing it in my opening hand with those 13 draws?
If I have 2 copies of a card what is the chance of drawing it in my opening hand with those 13 draws?
If I have 3 copies of a card what is the chance of drawing it in my opening hand with those 13 draws?"

In other words (using 1 copy as example), if you're dealt 13 cards out of 50, then probability
of getting your card is ~25%.

 March 2nd, 2014, 02:42 PM #9 Newbie   Joined: Feb 2014 Posts: 5 Thanks: 0 Re: Probability of drawing certian cards... So reshuffling doesn't affect the ods?

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