I think flipping the card is a good option
Xplanation:
case 1. if X is 1just flip the card
case 2 X is any no. other than 1
then X must be a power of three lets say X=3^a where ^ : is the power
of function
then Y can be either 3^(a-1) or 3^(a+1) with probability (1/2)^a and
(1/2)^(a+1)
Now u have 2 choice either keep the card or flip the card
if u keep the card
then either u earn 2*3^(a-1) with probabilty (1/2)^a
or u loose 2*3^a with probabilty (1/2)^(a+1)
if u flip the card
then either u earn 2*3^a with probabilty (1/2)^(a+1)
or u loose 2*3^(a-1) with probabilty (1/2)^a
flipping requires a double risks but tripple earning
if the above xplanation seems difficult 2 understand
lats take an xample when X=9
now Y can be either 3 or 27 with probability 1/4 and 1/8
*****************************************************************************************
X=9 probability keep
flip
*****************************************************************************************
Y=3 1/4 earn: 9-3 = 6
loose : 6
*****************************************************************************************
Y=27 1/8 earn: 27-9 = 18
loose : 18
*****************************************************************************************
if u keep then prob of earning 6 is 1/4 but prob of loosing 18 is 1/8
if u flip then prob of earning 18 is 1/8 but prob of loosing 6 is 1/4
flippig have double risks but triple rewards
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