1287275:

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

Sort of.  To make it easy, if you have an 85% chance of a quest, it means you have a 15% chance of no quest.  If you mulligan 15% of the time, 15% of the time you mulligan you will still have no quest.  So there is a 2.25% chance of no quest (.15*.15) if you are mulliganing for it.

Lorkac, as others have said you are completely wrong.  This is a fairly straight-forward example of combinations and permutations from basic statistics.  If 14% of your deck is quests and you draw an infinite number of opening hands then, on average, you will end up with 1 quest every time.  However that isn't what the OP asked.  He wants to have an 85% chance of having at least 1 quest in his opening hand each time he draws one.  These are two completely different questions.

1279444:

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.

How long have you been screwing over people trying to get in the game with this awful, awful reasoning.

And yes I created an account just to figure this point out.

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Why has the car stopped?

It's frightened.

1287275:

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

Multiplying the answer will give you the probability that both hands will contain at least 1 quest card with 14 quests in the deck, which is around 75%.

After you mulligan it is still 86%, just like if we flipped a coin, it is still 50% that it will be tails regardless of how many times it was heads previously.  Las Vegas makes bank off the Roulette tables from this misconception alone, I know people that believe that if they track the colors previously it gives them a better chance of guessing the right color...meh.

If your asking what the probability is that you will have an opening hand of no quests and then mulligan into a hand with 1 quest, that is about 12% that this event occurs as a whole. 

The probability that neither hand will have a quest is about 2% as JW pointed out.  So if you put 14 quests in your deck, about 2% of the time you won't have at least one quest.

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Trains, Planes, or Automobiles...you better have my DOUGHnuts.

Regarding mulligans...

There are three possibilities. For argument's sake, I'll use 85% as your chance, even though 14 quests is 86.1%.

1. First hand has at least 1 quest - 85%

2. First hand has no quests -15% Second hand has at least 1 quest - 85%
3. First hand has no quests -15% Neither does second. - 15%

Total chance of option 2: 15% x 85% = 12.75%
Total chance of option 3: 15% x 15% = 2.25%

(Which totals 100% for all possibilities, as required)

So the chance of not drawing any quests, for both hands, is 2.25%. Which means the chance of drawing at least 1 quest, factoring in mulligan, is 100% - 2.25% = 97.75%. (Or, chance of first or second possibility is 85% + 12.75% = 97.5%)

So with 14 quests in deck, you've got slightly better than 97.5% to draw at least 1 quest in opening hand.

Let's go a bit further for curiosity's sake and check for at least 2 quests, in a 14 quest deck.

Chance of drawing at least 2 quests is 52.2%. (Therefore, chance of not getting at least 2 quests is 48.8%) Using the above working, chance of neither hand having at least 2 is 47.8% x 47.8% = 22.8%. Therefore, chance of drawing at least 2 quests is 100% = 22.8% = 77.2%. Not too bad really.

Of course, what creamstout said above still stands. If you've got 85% chance to draw at least 1 quest in your first hand, and you don't, then you've still only got 85% chance to draw at least 1 quest if you mulligan. All depends on how you view it.

Edit: Just did some extra working, to answer the second question in the OP, 16 quests gives approximately 85% chance to draw at least 2 in opening hand when mulligan is factored in.

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1473012:

Lorkac, as others have said you are completely wrong.  This is a fairly straight-forward example of combinations and permutations from basic statistics.  If 14% of your deck is quests and you draw an infinite number of opening hands then, on average, you will end up with 1 quest every time.  However that isn't what the OP asked.  He wants to have an 85% chance of having at least 1 quest in his opening hand each time he draws one.  These are two completely different questions.

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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

If you enjoy writing you must love reading too. I recommend this.

While you're at it go grab a stats book.

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My entire collection for sale.

If short cutting to some random numbers is fine what is wrong with people saying other decks run 16 so they are probably right.

To get to 16 I played other numbers 14,15,17,18 and played a number of games saw if I had too many or too few quests. After this I ended up with 16, other decks might run less if after playing a number of games with 14 you feel it is the right number.

I don't see how playtesting a large number of games isn't good enough but dividing by osme random numbers and saying you want 27 card draw effects. Count invocation and arcane shot as both one is utterly meaningless.

Also I'd like more than one quest in my opener please.

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Has made top8 of some events

1279444:

1473012:

Lorkac, as others have said you are completely wrong.  This is a fairly straight-forward example of combinations and permutations from basic statistics.  If 14% of your deck is quests and you draw an infinite number of opening hands then, on average, you will end up with 1 quest every time.  However that isn't what the OP asked.  He wants to have an 85% chance of having at least 1 quest in his opening hand each time he draws one.  These are two completely different questions.

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.

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If it is required, you can try impressing him with your math skills.  His actual question is how many quests does he need to get 1 quest in his starting hand.  The minimum is 8.5 and the chances increase as you add more.  14 only matters if you add in the 85%.  If he was simply given that number it would imply that you need at least 14 quests to get 1 quest in your opening hand consistently which isn't true.

Now, if it makes you feel better, yes, with the 85% chance you are correct, you need 14.  However, that was not his question; as you can see he asked *if* and in truth, the percentage is not necessary unless of course you wish to put to use your statistics skills.  Overall, in the long term, is both faster and more practical.  For example, you're in a tournament and you're trying to figure out how many turns it would take for you to conceivably draw the burn spell you need to win on end of match procedures.  You could try calculating with statistics, or you could count your hand, graveyard, resources and permanents and know how think your library is.  You can then keep track of how likely you can draw it, and if its helpful you can aim for that mode of victory.  If the chances are still slim to none such as you only have 2-3 burn spells left in a 40 card library because you drew your burn early, then you can switch gears and aim for a more realistic game scenario.  Statistics wouldn't be useful because it would take too much effort and energy to do it.  Unless of course you actually do statistics graphs while you play in tournaments; if you do kudos.  Personally I'd rather just spend my energy playing the game and its easier to do that with shortcuts.

You do realize that with only 1 quest in the deck he can get 1 quest in his hand, right?  Therefore, there's no need to run more than 1 quest since you can get 1 in your opening hand if you only have 1 in your deck.  After all, he only said if the percentage matters, so I decided to ignore it entirely...

You clearly don't grasp the logic here, so let me explain it to you...

OP has 7 chances to draw 1 quest out of however many he has in his 60 card deck and wants an 85% chance of doing so.  Let's say for a minute that we think your 8.5 might be right (and realize that nobody does) the chance of getting 1 quest in your opening hand is:
The chance of drawing one with your first card (1-(51.5/60)) plus the chance of drawing one on your second card assuming you did not draw it on your first (1-50.5/59)*(1-(1-(51.5/60))) plus the chance of drawing one on your third card assuming you didn't draw one on the first 2, etc...  I stopped writing out the equations for the chance of each card because they become very complicated to write out without using the combination/permutations formulae and functions which you clearly don't understand anyway, but it works out to be approximately a 73% chance of having at least one quest in your opening hand with 8.5 quests in your deck, which means that 1 game out of every 4 you will have a zero quest hand.  If you factor in the mulligan, and you can only do this if you are specifically mulliganing a zero quest hand to get a hand with at least one quest, you will end up with a quest in your hand roughly 92.7% of the time - I don't think this is what the OP had in mind, but if it was your 8.5 quest deck would actually be overkill to achieve an 85% hit rate.

Your example, I have 3 burn spells in my 40 card deck, is very easy - your chance of drawing any one of them on your next draw is 3/40.  That is straight probability and is very different from wanting 1 of the 14 quests in your 60 card deck to appear in an opening hand consisting of 7 draws.

Just accept that you're wrong on this issue and move on. 

 

TL/DR - Lorkac failed basic stats

1279444:

If it is required, you can try impressing him with your math skills.

If by that you mean giving him the CORRECT answer, then yes that is what we are doing.

1279444:

His actual question is how many quests does he need to get 1 quest in his starting hand.  The minimum is 8.5 and the chances increase as you add more.

Actually, the minimum is 1 quest to get 1 quest in your opening hand, and the chances increase as you add more, until they get to 86.14% at 14 quests. Also, I will note that nobody is asking you what you mean by 1/2 a quest. I'm guessing there's a good reason for that ;).

It's actually not particularly impressive math to get that figure, here's the formula for the chance of getting at least 1 quest in your opening 7:

f(x) = 1 - nCr( 60 - x, 7 ) / nCr( 60, 7 ) where X is the number of quests in the deck. As you might imagine, this takes about 12 button presses on a calculator to figure out, which is probably about the same as your method with the additional benefit of being correct rather than having a 40% margin of error.

1279444:

If he was simply given that number it would imply that you need at least 14 quests to get 1 quest in your opening hand consistently which isn't true.

Since he definited "consistently" as 85%, it is absolutely true unless you fail to propertly randomize your deck.

1284658:

If you enjoy writing you must love reading too. I recommend this. While you're at it go grab a stats book.

I do love writing.  I also love reading.  Though reading about writing gets kind of boring.  Grammar books, for example, are interesting for the first half but quickly becomes monotonous for the next half.  This is mostly because sentence and phrase construction is, at its core, an attempt to maintain a level of clarity that is, more often than not, hindered by the walls of grammar; as well as self help books on writing.

This is because in the fluid world of word concatenation, people like making up new rules, new words, new lingo, etc...

As for your second sentence, are you suggesting that you *do* perform excel type calculations during your casual and tournament WoW TCG playing?  If so, how do you manage that level of calculation?  Do you bring graphing paper so you can keep track of the changing means?  I'll be curious to know.

As for statistics books, do you have a suggestion?  The statistic book that you read maybe.  Which one did you study?

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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

1279444:

As for your second sentence, are you suggesting that you *do* perform excel type calculations during your casual and tournament WoW TCG playing?

No, I (and plenty others) are suggesting that we answer the OP's question correctly. Facts cannot be argued.

If you want to argue whether the OP is wasting his time making a post about stats that he cannot do practically during tournament play, then I'm sure the OP appreciates your condescending attitude.

I find it funny that you, Mr. Wall of Fail, are suggesting we should be taking shortcuts.

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My entire collection for sale.

Somewhere I read an article on the amount of lands needed (yes, it was a MtG article but may still be relevant) being worked out according to the casting cost of your cards - with tweaks being made if you had any non-land mana sources and/or extra card-drawing
If someone happens to know where that could be found, a link would be of use (I would but I seriously need sleep right now)

The basic theory runs that the easier it is to play the bulk of your cards, the fewer resources you'll need in order to do so.


There is also around a very good probability checker for CCGs. Stick in number of cards in deck, number of a given card in that deck, number of cards in opening hand.....& it will give you the percentage chance of drawing that card at any chosen point (opening hand, within first 5 draws etc)

(did a bit of digging- http://faculty.gvsu.edu/goldenj/MagicProbability2.xls" target="_blank" title=" http://faculty.gvsu.edu/goldenj/MagicProbability2.xls"> http://faculty.gvsu.edu/goldenj/MagicProbability2.xls looks like a useful little program)

1576609:

Also I'd like more than one quest in my opener please.

If my posts would stop getting filtered out by... other things... then you'd have your answer for two. I'll post it again anyway...

52.2% is the chance of drawing at least 2 quests in a hand of 7 from a 60 card deck containing 14 quests. 60.9% for 16, you need at least 24 quests in your deck to get at least 85%. Factoring in mulligans I suggest you read up because I'm not doing that again :P

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1999699:

Somewhere I read an article on the amount of lands needed (yes, it was a MtG article but may still be relevant) being worked out according to the casting cost of your cards - with tweaks being made if you had any non-land mana sources and/or extra card-drawing
If someone happens to know where that could be found, a link would be of use (I would but I seriously need sleep right now)

The basic theory runs that the easier it is to play the bulk of your cards, the fewer resources you'll need in order to do so.

I think in this case, being WoW TCG, we wouldn't benefit much from this article. As has been argued on another thread I believe, number of lands is very different to number of quests. If I was to give a reason, it'd be; how many quests you draw is irrelevant of how many resources you place, essentially. But really, it's just a very different scenario to MtG land.

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