One thing in the pic is not clear about the game whether the coin is flipped by a human or a machine.

But the best strategy would in terms of mathematics be Fibonacci series 1 3 5 7 9 11 because doubling down can make you zero easily and Fibonacci is the strategy that is used in most of the investments and gambling which makes it slow for you to lose the money and win a minimum amount.

While coming to the game strategy if they are showing you the coin before flipping you can bet on the opposite side because it has maximum chance.