I came up with a probability sheet for how likely it is to draw a specific card given the number of cards drawn. This table assumes that the deck size is 60 and the deck contains 4 copies of the specific card. The table starts at 7 because your opening hand is 7.

So for those who's wondering, the likelihood of a hunter playing a turn 1 Bloodclaw (given that he has 4 in his deck), is the sum of the first row (39.9%). This does not account for mulligan.

The table doesn't illustrate this, but if you have 3 copies, then this probability decreases to 31.5%, for 2 it's 22.1%, and for 1 it's 11.7%.

	P(drawing N specific cards given total cards drawn)
Cards Drawn	1	2	3	4
7	0.336	0.059	0.004	0.000
8	0.363	0.076	0.006	0.000
9	0.384	0.094	0.009	0.000
10	0.402	0.113	0.012	0.000
11	0.416	0.133	0.017	0.001
12	0.426	0.153	0.022	0.001
13	0.432	0.173	0.028	0.001
14	0.436	0.193	0.034	0.002
15	0.436	0.213	0.042	0.003
16	0.435	0.233	0.051	0.004
17	0.430	0.252	0.060	0.005
18	0.424	0.270	0.070	0.006
19	0.415	0.288	0.081	0.008
20	0.405	0.304	0.094	0.010
21	0.394	0.319	0.106	0.012
22	0.381	0.333	0.120	0.015
23	0.366	0.346	0.134	0.018
24	0.351	0.357	0.149	0.022
25	0.336	0.366	0.165	0.026
26	0.319	0.374	0.181	0.031
27	0.302	0.380	0.198	0.036
28	0.285	0.384	0.215	0.042
29	0.267	0.387	0.232	0.049
30	0.250	0.388	0.250	0.056
31	0.232	0.387	0.267	0.065
32	0.215	0.384	0.285	0.074
33	0.198	0.380	0.302	0.084
34	0.181	0.374	0.319	0.095
35	0.165	0.366	0.336	0.107
36	0.149	0.357	0.351	0.121
37	0.134	0.346	0.366	0.135
38	0.120	0.333	0.381	0.151
39	0.106	0.319	0.394	0.169
40	0.094	0.304	0.405	0.187
41	0.081	0.288	0.415	0.208
42	0.070	0.270	0.424	0.230
43	0.060	0.252	0.430	0.253
44	0.051	0.233	0.435	0.278
45	0.042	0.213	0.436	0.306
46	0.034	0.193	0.436	0.335
47	0.028	0.173	0.432	0.366
48	0.022	0.153	0.426	0.399
49	0.017	0.133	0.416	0.434
50	0.012	0.113	0.402	0.472
51	0.009	0.094	0.384	0.512
52	0.006	0.076	0.363	0.555
53	0.004	0.059	0.336	0.601
54	0.002	0.044	0.305	0.649
55	0.001	0.030	0.269	0.699
56	0.000	0.019	0.227	0.753
57	0.000	0.010	0.180	0.810
58	-	0.003	0.127	0.870
59	-	-	0.067	0.933
60	-	-	-	1.000

For you math freaks, I used the hypergeometric distribution as illustrated here. Let me know if there are other probabilties of interest and I'll try to impliment it. Or, if I've erred in this calculation, let me know.

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My entire collection for sale.

So I have about a 44% chance of getting my searing totem (assuming the rush deck opponent is going first).  That's not so bad.  If you assumed I got no searing totems then the probability would be about (1-.399)(.44) + (.44) = .70

That's pretty damn good. 

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The hands of the King are the hands of a Healer

Bay Area Organized Play Calendar

That's why shaman is king =)

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My entire collection for sale.

You really had nothing else to do that day didnt you? :P

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http://entertainment.upperdeck.com/WOW/COMMUNITY/forums/721706/ShowThread.aspx#721706 -- this is my HAVE WANTS LIST!

You forgot to mention how broken warriors are.

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*

Wasn't relevant to the topic ;-)

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http://entertainment.upperdeck.com/WOW/COMMUNITY/forums/721706/ShowThread.aspx#721706 -- this is my HAVE WANTS LIST!

In what way are warriors broken?

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-Vio
Retired Tauren Warrior
Have/Want List here

Its mainly Warrax Warriors, the others aren't so bad coz they go for aggression sacrificing turtling tactics.

(1) Mass armour damage reduction with not enough cards to destroy Armour unless ur a Rogue
(2) Stoneform if ur Warrax
(3) Defensive Stance - negates all DOT's, mini allies and gives protector all for 3 mana
(4) Demorilizing Shout

Basically the turtle warrior can just sit there un damagable whilst it pings you each turn. Now assuming the opponent hasn't spent £150 on their deck obtaining all the epics, they're screwed.

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http://entertainment.upperdeck.com/WOW/COMMUNITY/forums/721706/ShowThread.aspx#721706 -- this is my HAVE WANTS LIST!

If you mulligan how does that effect the chance of getting a card you have 4 of on the first turn?

Damnit, Kyusuke, you beat me to it. I'd love to see your formula for the probabilities, I've got a different table in mind.

To the above, mulliganing would affect it in the following way:

Take the probability you would get the card in your first hand. Subtract it from 1. So in the case of having 4 copies, this would be 60%. This is the chance you would have to mulligan it. Multiply that by itself, again the chance you would not draw the card  in your second hand. .60*.60 = .36 This is the chance you will not draw the card in either of your opening hands. Again, subtract this from 1, and you get approximately a 64% chance that you will draw the card in one of your two opening hands.

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WoW Rules Knowledge Lvl 1
Player Management Lvl 1
Tournament Organizer Lvl 1

God this thread brings back warm memories. Whatever happened to FarmerGiles?

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Level 1 Judge

Here's that other table I had in mind:

This table represents the probability of having a card in your opening hand, given how many cards are in your deck and how many copies of that card are in your deck, for both Opening Hand and Mulliganned Hand.

First Hand            60             61            62           63             64            65
              4    39.95%    39.40%    38.86%    38.34%    37.83%    37.33%
              3    31.54%    31.08%    30.63%    30.20%    29.77%    29.36%
              2    22.15%    21.80%    21.47%    21.15%    20.83%    20.53%
              1    11.67%    11.48%    11.29%    11.11%    10.94%    10.77%
                       
After Mulligan       60            61            62            63             64            65
              4    63.94%    63.27%    62.62%    61.98%    61.35%    60.73%
              3    53.14%    52.50%    51.88%    51.27%    50.68%    50.10%
              2    39.39%    38.85%    38.33%    37.82%    37.33%    36.84%
              1    21.97%    21.63%    21.31%    20.99%    20.68%    20.38%

Here's how to read this chart: Lets say you're playing Paladin, up against a Rush deck. You really want Avenger's Shield in your hand. Ideally, you have 4 of them, and your deck is only 60 cards. This gives you about a 40% chance that you'll have one at the start of the game. If you don't, you can mulligan which will give you a second 40% chance, bringing your total chance up to about 64%. So including Mulligan, with 4 copies of the card, you can expect to see an Avenger's Shield in your hand in just about 2 of every 3 games you play.

Now lets say you're no longer up against a rush deck. Avenger's Shield becomes less useful, so you decide to pull a couple out. You now only have a 22% chance to draw it, which means you'll only see it in your opening hand in about 1 in 5 games. Not bad, since you might be able to draw it later when larger creatures are out and you can use it then.

Statistics continue to change as you add more cards to the size of your deck. If you're running the same deck, but now with 65 cards, your opening hand chance drops slightly. Not an amazing amount, but enough to probably screw with your mechanics.

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WoW Rules Knowledge Lvl 1
Player Management Lvl 1
Tournament Organizer Lvl 1

1812975:

Here's that other table I had in mind:

This table represents the probability of having a card in your opening hand, given how many cards are in your deck and how many copies of that card are in your deck, for both Opening Hand and Mulliganned Hand.

First Hand            60             61            62           63             64            65
              4    39.95%    39.40%    38.86%    38.34%    37.83%    37.33%
              3    31.54%    31.08%    30.63%    30.20%    29.77%    29.36%
              2    22.15%    21.80%    21.47%    21.15%    20.83%    20.53%
              1    11.67%    11.48%    11.29%    11.11%    10.94%    10.77%
                       
After Mulligan       60            61            62            63             64            65
              4    63.94%    63.27%    62.62%    61.98%    61.35%    60.73%
              3    53.14%    52.50%    51.88%    51.27%    50.68%    50.10%
              2    39.39%    38.85%    38.33%    37.82%    37.33%    36.84%
              1    21.97%    21.63%    21.31%    20.99%    20.68%    20.38%

Here's how to read this chart: Lets say you're playing Paladin, up against a Rush deck. You really want Avenger's Shield in your hand. Ideally, you have 4 of them, and your deck is only 60 cards. This gives you about a 40% chance that you'll have one at the start of the game. If you don't, you can mulligan which will give you a second 40% chance, bringing your total chance up to about 64%. So including Mulligan, with 4 copies of the card, you can expect to see an Avenger's Shield in your hand in just about 2 of every 3 games you play.

Now lets say you're no longer up against a rush deck. Avenger's Shield becomes less useful, so you decide to pull a couple out. You now only have a 22% chance to draw it, which means you'll only see it in your opening hand in about 1 in 5 games. Not bad, since you might be able to draw it later when larger creatures are out and you can use it then.

Statistics continue to change as you add more cards to the size of your deck. If you're running the same deck, but now with 65 cards, your opening hand chance drops slightly. Not an amazing amount, but enough to probably screw with your mechanics.

Your "After Mulligan" table is misleading. If you first see a hand with no Avenger's Shield and decide to mulligan, you still only have a 39.95% chance of getting Avenger's Shield in your new hand.

The two hands are independent, so the 63.94% is actually the probability of getting an Avenger's Shield in one hand, the other, or both. However, it's not like you can draw two sets of opening hands and then decided whether or not to keep the first or the second.

That is correct, I should have made it a little more clear. I attempted to explain it in the paragraph below the chart, but it may not have come across as clearly as I would have liked.

To re-iterate: The After Mulligan chart is the probability that you will get at least one copy of the card in either of your two opening hands. Which means that you have, at best, a 64% chance of having the card you want in your hand at the beginning of a match unless it is an (Unlimited) card.

I'm working on publishing a spreadsheet so you can easily see based on the number of a type of card you have in  your deck what the probability of drawing one is. For instance, a friend of mine will scoop if he doesn't get a weapon in either of his opening hands. How many weapons must he have in his deck to minimize the number of times he scoops?

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WoW Rules Knowledge Lvl 1
Player Management Lvl 1
Tournament Organizer Lvl 1

knowing the odds of drawing a certain card int his game is very important....here it is in order or importance the 5 top things u need to know to win at this game.

1. know your deck well and every little trick in it.
2. know your opponents deck and every little trick in it
3. know how to read the back of your opponents cards...in other words try to figure out whats in his hand, and learn how to read his moves, play his turn for him b4 he does.
4.learn to bluff noob.  talking up your opponent during a game and influencing his descisions through your words,bluffs, or fake actions are critical in confusing your opponent.
5. know the odds of card x in his hand and card x is always the worst case scenario.  in other words, dont always play conservative but know the odds of what your doing when u play and minimize each moves risk.  in many games it all comes down to well if i do this this turn and he doesnt have that card in his hand, he loses, but if he does he wins, or i can do this, play 2 more turns and win then.  you have to know when to push all your chips on the table.


hope this puts the odds table in perspective

jewbacca

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2010 poty and world champion