Is bughouse a win for a team with excess time?

Question

In bughouse it is a huge advantage during the game to have more time on your clocks than your opponents.
So I wonder what happens if one team starts with a time advantage (from now on called the time lords).
Say, the time lords have 10 mins, while their opponents have only 5 mins.
This way the time lords can move on either board, and their opponents must always move on the same board.

Does this guarantee a win for the time lords, assuming perfect play?

This is an entirely theoretical question! No musings on weaknesses and skills, please.
For example, assuming that chess is a win for white (or for black), the answer to my question is yes, as the time lords can enforce the whole game to be played on one board, they can sit on the other.
But I expect some simpler argument that doesn't use any unproven hypothesis.
Maybe the time lords can even win in a dozen moves or so, no matter what the other team does.

ps. Note that this also gives an asymmetric way to play bughouse without a clock.

Answer 1

If both your clocks are ticking down you lose regardless of how much time advantage you have. So, if the "timelords" refuse to move on both of their boards this is how they will lose.

A team can only afford to let one of the two clocks tick down to have any chance to win.

If the timelords refuse to move on one game they need to move on the other and their opponents have to make them use more time than the difference between their (total) time and opponents time. Your example of 10min vs. 5min is not ideal to show this mechanism. Instead, let the time be:

Timelords: 8min
Opponents: 5min

Now, the clocks are started and the timelords don't play on one board. On the other board the opponent has to make the timelord think for 3min+ more than he himself has thought to win the game. Once the timelord has less than his opponents time + 3min on his clock the opponent could also refuse to play and the timelord will lose on time first.

Start (first board TLs refuse to play):

Timelords: 8min / 8min
Opponents: 5min / 5min

After, say, 4 minutes of play:

Timelords: 4:00 / 5:00 (-3min)
Opponents: 5:00 / 4:00 (-1min)

Once the opponent can make the timelord use more time than himself he can let the time run out.