It applies to what you put in the circle for your initial bet. You should be able to double, split, etc.
Of course, there may be a jurisdiction with crazy rules that prohibit this. For example, in Colorado, back in the $100 max bet days, it was OK on table games, however, if you were playing a BJ machine, you weren't permitted to exceed a total of $100. Also, this example wouldn't apply to BJ, but on some carny game tables, there may be a table maximum payout per hand, which is less than what's theoretically possible. For example at Mississippi, if you hit a Royal, the payment may be capped at something like $25K. This should be on a sign on the table.
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