Quote from: BlackHatCoiner on Today at 09:41:12 AM

Alice opens a channel to node Bob.
Charlie opens a channel to node Bob.
They both deposit 10 mBTC and they wait for the required confirmations.

In the first channel, Alice has 10 mBTC and Bob 0 mBTC. In the other channel, Charlie has 10 mBTC and Bob 0 mBTC. Bob is an intermediary between Alice and Charlie, so theoretically both of them should be able to send payments between each other through Bob. However, it's not going to work in this case.

Quote from: BlackHatCoiner on Today at 09:41:12 AM

So now Alice and Charlie can both send ~10 mBTC to each other by none of them can receive. In order to do that they'll have to increase their receiving capacity. Can you continue this sentence further?

The only way to do that is to pay Bob for something. Let's say Bob has a coffee shop. Alice and Bob went there together. Alice bought a coffee for 3 mBTC and Bob bought a cake for 2 mBTC. Now, the balance sheet looks like this: Alice (7 mBTC) -> Bob (3 mBTC). Charlie (8 mBTC) -> Bob (2 mBTC). Now, let's say Alice owed Charlie 1 mBTC. She doesn't have a direct channel with Charlie, but she can route her payment through Bob. Alice sends her transaction and the balances change again. Alice (6 mBTC) -> Bob (4 mBTC). Charlie (9 mBTC) -> Bob (1 mBTC).

If Alice owed Charlie 3 mBTC, she wouldn't be able to send him that much because Bob has only 2 mBTC in a channel opened by Charlie.

Quote from: BlackHatCoiner on Today at 09:41:12 AM

15 mBTC to Alice and 5 mBTC to Charlie. So now the current, signed from both sides, transaction can be broadcasted to the blockchain. Charlie has signed that he'll transfer 5 mBTC from his multi-sig address to Alice's.

You need to make sure that all payments are enforceable on the blockchain in an efficient way. Neither is achieved here. Let's say Charlie transacted this way with a couple more people. The final transaction would have the same amount of outputs as the number of people Charlie transacted with. Also, why would he need to transfer his funds to a multi-signature address since you didn't even mention Bob? How would Alice be sure if Charlie is not going to cheat?

The trick is that Alice updates the balance of the channel with Bob and Bob updates his channel with Charlie the moment he routes the payment. This way, Alice needs only to ensure that Bob is not cheating. She doesn't have to think about Charlie anymore.