-1
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lets consider the outcomes to get 2 heads followed by 2 tails:
T, probability 1/2, wasted one attempt
HT, probability 1/4, wasted 2 attempts
HHH, probability 1/8, wasted one attempt
HHTH, probability 1/16, 2 attempts
HHTT probabilty 1/16
let x be expected rolls to get HHTT
x = 1/2(x+1) + 1/4(x+2)...