hmmm...but when the sum is 4,5,6,8,9,10 the gain is not $0...rather the whole process is repeated again.
my solution: let the expected gain = $x
$x = (8/36 x +$1) + (4/36 x –$1) + (24/36 x $x)
explanation of the last term : (24/36 x $x)
When the sum is 4,5,6,8,9,10 then the dice are...