- (11011..01000)(10000...00100)....
- ^attempt 1 ^attempt 2
You have to try, on expectation, quite a few times to win this game! Now, you could easily get lucky for sure. But on average, your chance of winning per attempt is roughly 0.5^128! So, how many times do you have to try to win this game? Something like 2^128 times - and you have to consider that each attempt uses 128 bits as well. So more like 2^135. But you don't have to start fresh in each attempt, you can see it as like this: - 11011................00100...
- ( 128 flips )
- ( another 128 )
- ( )
- ... so on and so on
That's where the 2^128 number came from.