Anonymous I have more than double the amount than my opponent. " Anonymous There is a better chance that he doesn't have it than he does have it. " That's how I would rephrase these examples, but I'm sure there are other ways.
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AnonymousI have more than double the amount than my opponent."I have more than double the amount [of ...] as my opponent does."
AnonymousThere is a better chance that he doesn't have it than he does have it."There is a better chance of him not having it, than of him having it."
AnonymousHow must I make the sentences symmetrical?The term you are looking for is 'parallel.' I agree with DoNotPassGo's suggestions.
DoNotPassGoI have more than double the amount [of ...] as my opponent does.That doesn't sound right to me. I'd go for I have twice/double the amount (that) my opponent has/does.
fivejedjonI have twice/double the amount (that) my opponent has/does.This sounds more common to me than DoNotPassGo's version.