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Many gambling services (and p2p exchanges) do not wait for confirmations before exchanging value (many realize their customers will not wait 6+ hours for a confirmation).

What's to stop someone from sending 10 BTC they don't have, assuming that the party they're sending it to will not wait for confirmations?

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They don't wait for confirmations, but they check if a transaction has appeared in mempools of some miners. They could also just check if the preceeding transaction (the source of 10 BTC) exists on the blockchain.

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You can't send money you don't have. If you want to show someone a transaction to an address they specified and have given to no one else, and want that transaction to be over 10 BTC, you actually need to have at least 10 BTC. You might not actually have lose those 10 BTC to them if you double-spend and the transaction to the gambling service doesn't make it into the blockchain but you do have to control UTXOs worth at least 10 BTC in order to make a transaction which looks like you're sending that much to the gambling service.

They'll probably wait a few seconds until that transaction made it to virtually all nodes. After that, you'll have a hard time double-spending as nodes which have a transaction A (your transaction to the gambling service) will in most cases reject a transaction B conflicting with transaction A as they notice the conflict.

If you double-spend quickly, you can actually get both conflicting transactions out there, but in that case, they'll know that you're double-spending and not recognize your payment until the transaction to them made it into the blockchain, because then they know that you're trying to cheat them.

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