Talk:Black Lotus

Chance of getting a first turn kill with Black Lotus in Alpha era

"Originally, Magic did not limit the number of copies of a card you could play in a deck; this allowed constant first-turn wins with decks comprised of twenty Black Lotus, twenty Channel, and twenty Fireball."

It could not be constant first-turn wins with this deck. What if you get 7 BL in your as starting hand?

The only way that would work is if you went second and drew and had a hand of 7 Black lotus and a fireball for 21 damage. 63.163.213.249 23:17, 28 September 2011 (EDT)

"Constant" is a bit rhetorical here but fair enough I think. Don't forget Channel first of all. You only need 2 lotuses, 1 Channel, and 1 Fireball to win first turn. The 2 lotuses give you 6 red + green mana which funds the colored part of the Channel and Fireball costs with 3 mana left over. Then you spend 17 life for 17 more mana, a total of 20 mana for X=20 on your fireball.

To be honest my probability skills are failing me at coming up with an exact number, but regardless, it's at least close to 50/50, if not a fair amount higher, to draw the pieces first turn. (I suspect my "under 50/50" calculation is wrongly set up and it's actually much higher.) And given that the games would go so fast, I'm pretty sure it would FEEL like a constant stream of first turn wins haha.

I've included my notes of 2 different approaches with conflicting answers below if anyone cares to tell me where I've been foolish :)

Combinatoric approach:

P(drawing 2 out of 20, 1 out of 20, and 1 out of 20 with those 4 cards arranged any order in a 7 card hand)

= 20/60*19/59*20/58*20/57*(7!/4!/3!) = 45.5% chance of success?

Composition approach:

P(drawing no lotuses) = P(drawing no fireballs) = P(drawing no channels)

= (40*39*38*37*36*35*34) / (60*59*58*57*56*55*54) = 4.8%

P(drawing exactly 1 lotus) = 7 * (40*39*38*37*36*35) / (60*59*58*57*56*55) * 20/54 = 19.9%

P(drawing 1 or less lotus) = (40*39*38*37*36*35) * (7*20 + 34) / (60*59*58*57*56*55*54) = 24.7%

P(drawing no fireballs AND no channels) = P(drawing all lotuses)

= (20*19*18*17*16*15*14) / (60*59*58*57*56*55*54) = 0.02%

P(drawing no fireballs OR no channels) = P(no balls) + P(no channels) - P(none of either)

= ((40*39*38*37*36*35*34)*2 - (20*19*18*17*16*15*14)) / (60*59*58*57*56*55*54) = 9.6%

P(drawing 1 or less lotus AND no fireballs) = P(drawing 1 or less lotus AND no channels) = P(drawing 1 or less lotus AND no Xs)

= P(drawing 1 lotus and 6 Ys) + P(drawing 7 Ys)

= (20*19*18*17*16*15) / (60*59*58*57*56*55) * 20/54 * 7 + (20*19*18*17*16*15*14) / (60*59*58*57*56*55*54)

= (20*19*18*17*16*15) * (7*20 + 14) / (60*59*58*57*56*55*54) = 0.2%

P(drawing 1 or less lotus AND either no fireballs or no channels) = 2*P(drawing 1 or less lotus AND no Xs) = 0.4%

P(drawing 1 or less lotus OR no fireballs OR no channels) = P(<=1 lotus) + P(no balls or no channels) - P(<=1 lotus AND no balls or no channels)

= (40*39*38*37*36*35) * (7*20 + 34) / (60*59*58*57*56*55*54)

+ ((40*39*38*37*36*35*34)*2 - (20*19*18*17*16*15*14)) / (60*59*58*57*56*55*54)

- (20*19*18*17*16*15) * (7*20 + 14)*2 / (60*59*58*57*56*55*54)

= ((40*39*38*37*36*35) * (7*20+34*3) - (20*19*18*17*16*15) * (2*7*20 + 14*3)) / (60*59*58*57*56*55*54)

= 33.9% chance of failure?

- jerodast (talk) 22:17, 17 January 2021 (UTC)