BitPay uses zero confirmation. They have their own algo to determine if a transaction looks unlikely to be double spent. I'm not sure but I think it looks like this:
1. Wait for transaction; see it. (they ask you to pay a particular address, so that's all they have to watch.)
2. Look at transaction; see if it has at least a minimum tx fee and inputs are already confirmed.
3. Wait for a few seconds; see if there are any other transactions using the same inputs (double spend)
4. If the above looks good, accept the transaction and credit the user or payer; give them their receipt or whatever.
According to transaction propagation statistics, on average, 5 seconds later your tx has been seen by 50% to 90% of nodes on the network. 10 seconds later 99% of nodes have seen your tx. Blocks take maybe a minute or two to be seen by 90% of nodes.
Even if there are 2 or 3 block orphans, that does not mean your particular transaction is being double-spent or an attempt on it. The only one who can do that is the one who has control of the private keys of the inputs in question. Your transaction or the transaction you are watching will likely be included in the any or all forks or orphans, or will be included in the next block.
I just stick to 1 confirmation. To me, that means a miner included it in that block, and other miners will probably include that particular one I am interested in in the next block if an orphan happens.
I recently constructed a rather large transaction with several inputs worth 50 BTC. Since I was the one doing it, I did not even bother to wait for a confirmation when I was combining all the inputs, I just did it one after the other. (No one is going to double spend my stuff, except me, right?) Turns out the whole thing (4 transactions all together) confirmed in about 20 minutes since I broadcast them.
wait, I know BitPay, it's most secure and many famous companies worked with them. Also once I had experience to integrate their API on one company's website as payment system but I remember that there wasn't any similar things, transactions with zero confirmation. Can you link me the information about that on their website? I can't find it.
So what's about this thread, of course 6 confirmations wins here
Many websites usually need 5-6 confirmation to make transaction, not more than 6. Also you are more secured with 6 transaction than 1 but it depends on how is payment options because some websites give you permission to use bitcoin deposited money once it is registered but you can't withdraw it if's not confirmed because we can remove transactions that has no more than 1-2 confirmation