If you take them to the very last minute on Game A, they just have to take you to the very last minute on game B when it's their turn and they've unwound any advantage you might have gained.
I'm saying in every state where each player has 1 running clock, the times can be defined by [my time remaining] and [his time - time it took him to relay] and he will always have less time as he waits for my next input.
I don't understand when they will be able to take me to the very last minute. I'm never waiting on their input. Furthermore I never have both my clock's running. At every point I do have a clock running, they have a clock running that has less time.
As I said, in order to break the chain you need to get the clocks out of synch by more than the amount of time alotted for a single move, something they can prevent you from doing.
Chess.com measures it down to the minute though right? As long as the relay takes longer than a minute, it's enough of a difference to force them to lose time waiting on your next move.
Thriller : That doesn't work either. He simply does the same. Whatever time you take , he will do too . You are basically playing 1 game , against yourself. It is a symmetrical situation , unless there is a difference in vacation time.
The problem is : You want him to move first in his White-game , where he won't be able to copy your move ( because you haven't moved in the other game yet). It is only the clock that can force him to do his move.
This is not totally true:
Think about it - Let's say you have already played 1.e4 e5 2.Nf3 Nc6 Bb5, and he has done the same. In one of the two games, it's his move, and since you played Bb5 before he did, the game where it's his move there is a SHORTER amount of time left on the clock. It may only be 4 minutes, but it's shorter.
Think about it, if I made the move 3.Bb5 at 10:34 today, and he "copied" me at 10:38 today, I have until 10:38 tomorrow, he has until 10:34 tomorrow. What if I wait until 10:36 to make my move, where I have 2 minutes left on the clock?
He better have made his move already. If he played 3...a6, I play 3...Nf6. If he didn't play 3...a6, I play 3...a6.
If he let his clock run out, I play whatever I feel like at that time!