Hearthpwn

Scenario:

• 4 cards, coin
• hard mulligan for Keleseth
• Keleseth in opening hand: hard mulligan for Shadowstep

First case (86,66%):

Keleseth not in opening hand, mulligan for 4.

Probability that this case occurs: 29/30*28/29*27/28*26/27=0.8(6).

I will have 5 random cards at the start of turn 1. There is a 1/30 chance to draw Keleseth in the first card and a 2/29 chance to draw a Shadowstep in the second. There are 3276 ways to choose the other 3 cards. 1/30*2/29*3276=7,53%.

Second case (13,33%):

Keleseth in opening hand, mulligan for 3.

Probability that this case occurs: 4/30=0.1(3).

I already have Keleseth and I am going to calculate what is the chance that I get a Shadowstep in the next 4 cards. Probability of failure (that I miss both Shadowsteps): 27/29*26/28*25/27*24/26=73,89% -> Probability of success: 26,1%.

Overall probability:

86,66% * 7,53% + 13,33% * 26,1% = 10,00% to have Keleseth and Shadowstep on turn 1 given you started second.