Question 1: How many quest do I need to have in a 60 card deck to get 1 quest card in my starting hand of 7?
(If a percentage is required, use 85%)

Question 2: Substitute the 1 quest card to 2.

Hope some maths guru can help out here... was reading about the quest count post and started thinking about this. Thanks in advance.

Well, the way you work out the chance of drawing a quest is one minus the chance of not drawing it. So, chance of not drawing in the first card x chance of not drawing in the 2nd etc.

But, you don't really need to go that far to work out how many quests to run. If you run a 60 card deck and 15 quests, one in every 4 cards is a quest. Therefore, in an opening hand, you would expect 1 3/4 quests.

Sorry, not willing to do the math right now.

Cheers.

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Come play at C & Js in Newark, CA

888509:

Question 1: How many quest do I need to have in a 60 card deck to get 1 quest card in my starting hand of 7?
(If a percentage is required, use 85%)

Question 2: Substitute the 1 quest card to 2.

Hope some maths guru can help out here... was reading about the quest count post and started thinking about this. Thanks in advance.

Your opening hand is 7 card draws.  So the percent chance of getting 1quest/7card draws should then be compared to a 60 card deck.

1/7=14.3%

14.3% of 60 is 8.5

So to reliably have at least 1 quest in your opening hand you need at least 8.5 quests.

For two quests its different.

2/7=28.5%

28.5% of 60 is 17.1

So to reliably get 2 quests in your opening hand per game you need at least 17 quests.

Do know that this is simply about drawing a quest or two in your opening hand.  Different formulas need to be used if you want to control how many (And how often) you draw a quest throughout a game.

The same formula can be used with non-quests.  "How many removal cards do I need to run to have 4 by turn 4?"

4/7+3(This is the 3 cards you draw during your first 4 turns if you went first)
4/10=40%
40% of 60 is 24

The numbers change even more if you add card drawing, deck thinning and if you first calculate how many cards you want in your opening hand, and then calculate how often you draw the extra cards.  I hope this helps.

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If they take the ship, they'll rape us to death, eat our flesh, and sew our skins into their clothing. And if we're very, very lucky, they'll do it in that order.
--Zoe, Firefly

Lorkac - That math is way off. And he's not asking the chance to get only 1 quest, but at least 1. Then, at least 2.

Cheers.

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Come play at C & Js in Newark, CA

888509:

Your opening hand is 7 card draws.  So the percent chance of getting 1quest/7card draws should then be compared to a 60 card deck.

1/7=14.3%

14.3% of 60 is 8.5

So to reliably have at least 1 quest in your opening hand you need at least 8.5 quests.

This does not seem right.  If you have 8.5 quests you have a 8.5/60 chance of drawing one.  Which is a 14.2% chance of having a quest...not Reliably (>85% chance) having 1 quest in your opening hand to relate to 8.5 quests.

For cards sake, let's just round that to 9.  You have 9 quests in your 60 card deck.  There is a 15% chance that first card will be the first one you draw (1 card of your opening 7, or 9 / 60 = 15%), 15.25% chance it will be the 2nd one if the first didn't net you a card (9 / 59).  And so on and so forth.  It only goes up as you don't hit that quest.

In order to 'reliably' draw a quest in your opening 7, more than 85% of the time.  You need that first draw to be at least 15%.  This would make 9 quests for your 85% of the time.  Of course once you hit one, you are VERY unlikely to hit any others along the way during the game.  IE: You would need to draw ~ 8 cards (or 8 turns - card draw) into the game to see that 2nd quest.  So assuming you dump your hand and even if you use Orders from Lady Vashj, you aren't going to see another quest until turn 6.  That's a lot of top decking in the mean time.

Most decks run roughly 12-14 because in a rush deck, it's easy to run out of gas (have your board wiped off the table), then not draw any more cards, see the example above..it's already too late to get back into the game.  More quests allow you to run the game for a lot longer.

Control decks look for more quests 14-16 (+in deck draw mechanics) so they can answer your cards and continue to have the best options available to themselves come the later game.  Plague Demonsoul is about the only exception, as it runs 12 quests, because like 10 other cards in the deck say draw a card on them somewhere.  So you are using deck draw mechanics to sort of skimp on quests a little.  This allows you to put in more of other cards.  Other typical examples are Paladin with Hammer of Justice (cantrip), and Blessing of Wisdom (deck draw mechanic).  This allows them to run slightly lighter on quests so they can just use their overwhelming draw mechanics to bury you with card advantage.

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I like PIE......Discuss!

The maths gets rather troublesome when it comes to a changing population size. You see, if you have 15 quests in a 60 card deck, yes the first card you draw has a 25% chance of being a quest. But the next card, if the first wasn't a quest, is 15/59, if the first was a quest, 14/59. Then for the next card, if the first two weren't quests, it's 15/58, if one of them was a quest, 14/58, if they were both quests, 13/58 etc...

I tried using this Hypergeometric Distribution Probability Calculator...

http://stattrek.com/Tables/Hypergeometric.aspx

...because its example seemed exactly the type of problem we're dealing with. But the numbers were surprising. According to this, with 16 quests in a 60 card deck, the chance of drawing at least 2 in a 7 card starting hand is approx 0.6 (60%). Answering the OP's questions, according to the above calculator...

1. To have at least 85% chance of drawing at least 1 quest, you need at least 14 quests in your deck.

2. To have at least 85% chance of drawing at least 2 quests, you need at least 24 quests in your deck. (20 gives at least 75%, 14 gives at least 50%)

Seems surprising, but when I think about it, that's probably about right. It's only about 50% of the time that I draw at least 2 quests in my opening hand with my decks (14-16 quests).

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OK, I'll do the math to make sure people get it.

Let's say you have 10 quests in a 60 card deck. You get 7 cards in hand.

Your chances of having at least 1 quest are 1 - chance of none.

Chance of none is 50/60 x 49/59 x 48/58 x 47/57 x 46/56 x 45/55 x 44/54 => .2586

Thus, you have a 74.14% chance of having at least 1 quest.

With 14 quests, you have a 1 - 46/60 x 45/59 x 44/58 x 43/57 x 42/56 x 41/55 x 40/54

which gives a 86.15% chance of having at least 1 quest.

Cheers.

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Come play at C & Js in Newark, CA

The answer is 14 (for 1 quest). Punch this into Excel:

HYPGEOMDIST(1,7,14,60)+HYPGEOMDIST(2,7,14,60)+HYPGEOMDIST(3,7,14,60)+HYPGEOMDIST(4,7,14,60)

It gives me 85.6%, which is off a bit from Lanky's calculations.

I made a post 2 years ago that may be helpful if you want to get a better understanding of probability.

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My entire collection for sale.

Sigh... there is no need to use overly complex calculations like the ones you guys are using.  It is both ineffective when it comes to actual game play and requires you to keep track of things that you should never really have to keep track of.

He asked to get at least 1 quest in the first 7 cards.  the answer to that is 8.5 which rounds up to 9.  The more quests he adds in the better his chances of getting more than one quest in his opening hand.

While yes, you can be more precise by calculating how each successive card draw affects the proceeding card draw, you could also simply it to something that people can actually use without having to use an excel spreadsheet.

If you want X% of your hand to contain Y, then have X% of your deck contain at least that many Y.

This is because the two variables are absolutes in the game of WoW.  It isn't like you'll all of a sudden have a starting hand of 6 like when you mulligan in Magic.  The fact that you can mulligan means that if you want your calculations to be accurate you need to figure out what the chances of drawing the quests are within 14-15 card draws depending on who goes first and second.

If he was the type of person to enjoy using spreadsheets, probability graphs and outlier correlation to means; he wouldn't be going online asking us how many quests he should run to get at least one in his opening hand, he'd just calculate it out himself.

Don't ever forget the demographic that you are speaking to.  If a 10 year old asks you how many quests he should play, you don't show him excel, you tell him an arbitrary number that's close enough to correct.

Like I said in my post, if you want to add variables into the question, you'll need different formulas.  But all he really needs are basic percentage correlations.

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If they take the ship, they'll rape us to death, eat our flesh, and sew our skins into their clothing. And if we're very, very lucky, they'll do it in that order.
--Zoe, Firefly

Wall of Text + Being Wrong = Wall of Fail

The answer is 14 (without accounting for mulligan). If you're going to lecture me about how to respond properly, at least be right. Unless you think 8.5 is a good approximation of 14.

LankyBrit already provided the answer. My post was to add additional information if anyone wanted to delve into the subject deeper.

If I wanted to confuse the OP, I would have just made a huge wall of fail.

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My entire collection for sale.

1279444:

If he was the type of person to enjoy using spreadsheets, probability graphs and outlier correlation to means; he wouldn't be going online asking us how many quests he should run to get at least one in his opening hand, he'd just calculate it out himself.

Actually, I am looking for a detailed calculation with a formula given, rather than a simplified estimation. Also, its just that I am rather lazy and do not have the capability to do all the maths.

Anyway, thanks guys for the help here. Appreciated. : )

don;t you multiply(or add) the results together because of the mulligan?

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1284658:

LankyBrit already provided the answer.

Hey, so did I :(

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1279444:

Sigh... there is no need to use overly complex calculations like the ones you guys are using.  It is both ineffective when it comes to actual game play and requires you to keep track of things that you should never really have to keep track of.

He asked to get at least 1 quest in the first 7 cards.  the answer to that is 8.5 which rounds up to 9.  The more quests he adds in the better his chances of getting more than one quest in his opening hand.

While yes, you can be more precise by calculating how each successive card draw affects the proceeding card draw, you could also simply it to something that people can actually use without having to use an excel spreadsheet.

If you want X% of your hand to contain Y, then have X% of your deck contain at least that many Y.

This is because the two variables are absolutes in the game of WoW.  It isn't like you'll all of a sudden have a starting hand of 6 like when you mulligan in Magic.  The fact that you can mulligan means that if you want your calculations to be accurate you need to figure out what the chances of drawing the quests are within 14-15 card draws depending on who goes first and second.

If he was the type of person to enjoy using spreadsheets, probability graphs and outlier correlation to means; he wouldn't be going online asking us how many quests he should run to get at least one in his opening hand, he'd just calculate it out himself.

Don't ever forget the demographic that you are speaking to.  If a 10 year old asks you how many quests he should play, you don't show him excel, you tell him an arbitrary number that's close enough to correct.

Like I said in my post, if you want to add variables into the question, you'll need different formulas.  But all he really needs are basic percentage correlations.

Here is someone who really doesn't understand Statistics.

"If you want X% of your hand to contain Y, then have X% of your deck contain at least that many Y."

My hand is 2 cards. I want 50% of it to contain Y. So, you're saying that 50% of my deck should be Y to assure that. Now, tell me, what is the actual percentage that I will have at least 1 Y in my hand. The answer is 1 - chance it will contain none => 1 -  30/60 x 29/59 => 75.43%.

Not bad, but not the 85% that he wanted.

I don't think we're going to persuade you that your approach is way off, but it is.

Cheers.

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Come play at C & Js in Newark, CA

I've never seen someone type so much and then want to make things even simpler.

Its not like you need to figure out these odds in the middle of a game.

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Has made top8 of some events