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Am I allowed to redeposit after my initial deposit, so that I have more money to play with, without increasing my wagering requirements?

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Don't do that, just make smaller bets.

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Also, does "doubling down" count for two bets when it comes to wagering requirements?

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Yes, and so does splitting.

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Where do I find their terms and conditions?

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It's on the website somewhere, just look for it. If you can't find it, just ask the live help people what you need to know.