"Two people enter into a series of transactions, and both have the same probability of winning some amount of wealth from the other, just as in a free-market transaction."

I don't really think this is a great description of free market transactions at all. Do you regret the decision anywhere close to 50% of the time when you buy groceries, pay rent, or buy new boots? Does the grocer, landlord or shoe store owner regret it anywhere close to 50% if the time? The answer is no in both cases.