After the first lottery and first shop, Stacy has \[2d - 1024\]dollars. After the second lottery and second shop, Stacy has \[2(2d - 1024) - 1024 = 2^2 d - (1 + 2) 1024\]dollars. After the third lottery and third shop, Stacy has \[2(2^2 d - (1 + 2) 1024) - 1024 = 2^3 d - (1 + 2 + 2^2) 1024\]dollars. More generally, after the $ n $th lottery and $ n $th shop, Stacy has \[2^n d - (1 + 2 + 2^2 + \dots + 2^{n - 1}) 1024 = 2^n d - 1024 (2^n - 1)\]dollars. In particular, for $ n = 10, $ Stacy has \[1024d - 1024 (1023)\]dollars, which is also 0. Hence, $ d = \boxed{1023} $.