fishhead wrote the following
here:
This is something I don't get about this deck. A lot of people are playing really aggressive land counts like 17 or 16, yet you do want to be able to cast Mana Drain ASAP. (Dont you?!)
Running a little math(*), I find that a 7 card hand has about a 40% chance of not showing UU to start. An 8 card hand is 31%, a 9 card hand is 24%. So:
UU 7 cards 60%
UU 8 cards 69%
UU 9 cards 76%
Now, you have to make your mulligan decision after seeing either 7 or 8 cards depending on whether you won the coin toss; you'll have to make your turn 2 play after 8 or 9 cards; hence these numbers.
Can you afford to keep a hand with one blue source? It's relatively likely you'll have to make that decision in any given game. I don't get how Mana Drain ends up being a valid part of this decks plan given the land count.
(*) Math caveats: There are like 100 caveats to this sort of calculation. I only counted lands and the sapphire as U sources, so no Lotus and no Tolarian. I didn't account for any plays by either player, like you Ancestralling to get more cards or him Wastelanding your land. But the numbers should serve as a decent benchmark for discussion.
I am replying here because the level of intelligence and T1 knowledge in the restricted forum is supposedly far beyond mine, so I can't post there, but I just had to point out that this calculation is wrong, before this wrong math starts to influence people's deck building decisions.
If you calculate the chance for at least 2 blue mana sources in a hand of 7 cards, while you have 17 blue mana sources, this is how it should be done:
43/60 * 42/59 * 41/58 * 40/57 * 39/56 * 38/55 * 37/54 = 8.344%
17/60 * 43/57 * 42/58 * 41/57 * 40/56 * 39/55 * 38/54 = 3.834%
The above chance in the 6 other orders: = 23.002%
Chance of no 2 blue mana sources in 7 cards: 35.179% (Sum of the 3 chances above)
So that's about 35% instead of the 40% previously advocated by fishhead.
Recap: The first line is the chance that you draw no lands at all. You can't just do (43/60)^7, because if a non-land is drawn, the odds for a land increase. The 2nd line is the chance of first drawing a land, then 6 non-land, you have to do this 7 times, for each order in which this can happen. Then you have all the odds added up for not drawing 2 lands.
Some people after the quoted post rightfully pointed out that Brainstorm should improve your chances. I also did the calculation in the case of having 4 Brainstorms (BS) and an Ancestral (A), then the calculation of all the unpleasant scenarios becomes:
No land in 7 cards: 8.344%
1 land, but no BS, no A: 12.152%
1 land, a BS/A, but no land in next 3 cards: 4.870%
This adds up to: 25.366%
Note that this is almost 10 percent points lower! So the addition of Brainstorms is obviously very good. But most people already know that, I hope.
The exact calculation:
8.344%: see above.
17/60 * 38/59 * 37/58 * 36/57 * 35/56 * 34/55 * 33/54 = 12.152%
The calculation of the 4.870% is more complicated:
Chance of just 1 land 3.834% + 23.002% (see above) = 26.836%
The chance of 1 land, but no BS, no A: 12.152%.
The difference between the above 2 chances is the chance that you have a hand with 1 land and at least 1 BS or A. This difference is: 14.684%. Then when you have 1 land and a BS or A, the chance that there is no land in the next 3 cards is:
37/53 * 36/52 * 35/51 = 33.168%
Then: 33.168% * 14.684% = 4.870%
Note that even this is not completely right, as with Ancestral you will see 4 more cards out of which 1 being a land would be sufficient. But well, Ancestrals are more likely to be countered, so you can continue arguing from here endlessly about things like that.
I just wanted to show that Brainstorms help incredibly and that the previous calculations weren't right.
BTW, also a possible play is not Brainstorming eot, but first drawing the 8th card, and then Brainstorming. You will see 4 extra cards then, instead of 3. This can be an option when you estimate having UU open on turn 2 is not absolutely neccessary. The 33% chance of not getting a 2nd land, is then reduced to 22.6%.
Greets,
Koen
