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# Tyrant + Splinter Twin combo
# https://twitter.com/Flusterstorm/status/639356812270174208
# my opponent says "make a million dudes" with twin, I vial in tyrant of discord. How do we handle this?

# Math: # Lands = # of land permanents # Exarchs = # of attacking Deceiver Exarchs # Rest = # of other non-lands permanents (ignored because doesn't change asymptotic probabilities) # Life = player's life # probability of hitting a land P_stop = Lands/(Lands + Exarchs + Rest) probability of sacrificing N Exarcs = (1-Lands/(Lands+Exarchs+Rest))*(1-Lands/(Lands+Exarchs+Rest-1))*...*(1-Lands/(Lands + Exarchs + Rest-N))Lands/(Lands + Exarchs + Rest) # Expected number of permanents to be sacrificed: sum for i 1-Lands/(Lands + Exarchs + Rest - i) asymptotically, only x=number of exarchs matter probability of sacrificing N Exarcs = 1/(x) * product 1-1/(x- i), i = 0..n-1 = (1 - n/x)/x expected surviving: x - sum n * (1 - n/x)/x, n=0..x = x-(x^2-1)/(6 x)



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# Simulation
lands = 10
exarchs = 10^6
rest = 1 #(splinter twin)

while lands == 10: