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What happens if the 'High' risk option (one confirmation) was chosen and then the TX turns out to be a double spend in the end? Would the value deposited be revoked? Would the user be notified somehow?

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    You've put the tag bitpay on this. Do you mean to ask this specifically from the perspective of a merchant using BitPay to accept payments? If yes, you might want to clarify that in your question. :) I've also added the tag doublespend. – Murch Dec 15 '14 at 20:20
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The order will never be confirmed, and depending on what wallet your using, it should be reflected as never having been confirmed and won't show up in your balance.

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The appearance of a double-spend on the network throws the status of the earlier payment into doubt. The doubt is only resolved when one of the payments is confirmed. As always, the more confirmations, the more certainty that the payment will be permanent.

The recipient of the payment that was double-spent is NOT notified very quickly. The bitcoin network itself tries not to propagate double-spends. Therefore, the earliest that recipient reliably learns of the problem is when the double-spend is actually confirmed in a block.

Even then, most wallets are not very vocal about notification. This is an area where bitcoin could improve. A bitcoin core improvement request initiated by Gavin Andresen does exist.

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With one block confirmation, problems can occur when there is a blockchain fork. Say if two miners simultaneously mined a blocks B1 and B2. Network gets split into two groups Group 1 (using Block B1) and Group 2 (using Block B2). If the next block gets mined by Group 1, then Block 2 gets rejected and vice versa. So, here comes a chance for the double spent transaction. If same transaction was spent in Blocks B1 and B2, but sent to 2 different outputs, only one will get confirmed finally. As a merchant, if you happen to accept B2 and B1 gets confirmed, you will be at risk. Waiting for 6 confirmations, reduces the risk to 0 (almost).

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