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game show paradox (money in 1 1/3 (choose 1 1/3 (reveal 2 1/2 (stay (win),…
game show paradox
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clarification:
when moving along the branches, we multiply.
example 1: if we go "money in1-player choose 1- host reveal 2":
(1/3)(1/3)(1/2)=1/18
example 2: if we go "money in 2- player choose 3- host reveal 1":
(1/3)(1/3)(1/1)=1/9
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if you stay, you win in cases a+b+f+g+k+l=
1/18+1/18+1/18+1/18+1/18+1/18=
6/18=1/3=33%
if you switch, you win in cases
c+d+e+h+i+j=
1/9+1/9+1/9+1/9+1/9+1/9=
6/9=2/3=66%
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