For everyone who thinks there is a problem with this challenge, because "worst possible luck" is ill-defined, there's no problem with that, mathematically speaking. The challenge is "just" to give an strategy for every possible way you and your opponent can shuffle. Many cases will be easy (if you are "lucky"), and there will be some cases which are hard (if you have "bad luck"). There won't be one unique way both players can shuffle which can be called the "most difficult case", so the term "worst possible luck" is indeed not well-defined. There will be different ways to which the players can shuffle, which each bring their own set of complications.
Unfortunately, handling every possible case is quite hard. Giving a separate strategy for every different case is unfeasible. You can group similar shuffles together and give a strategy which works for all of these shuffles. Usually you will lose some efficiency with this, but this might work.
By the way, I'm convinced that you can win 100% of the times against any big money strategy, if the board is strong enough. It should be possible to guarantee to build up a masquerade pin by turn 15 (and it's impossible for big money to get to 8 provinces earlier). If that's not possible, then it should be possible a few turns later, but attacking the big money player enough that he can't get to 8 provinces before that time. It will be very annoying to show that such a strategy will always work, though.