Understanding Lightning Network in practice

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I'm trying to understand how Lightning Network will work in practice. As I understand it, there are three benefits: (1) Fast transactions; (2) reduced transaction fees (enabling micro-transactions); and, (3) reduced impact on the blockchain since there are fewer actual blockchain transactions. Please let me know if I'm missing something there.

My question is this: Isn't it the case that LN only works well if there are lots of transactions in a channel? That is, if Alice sends 0.00001 BTC to Carol via Bob, and that's the only transaction in that channel in, say, a month, then benefits #2 & #3 above don't really apply since you effectively have a 1-to-1 relationship between a LN transaction and a blockchain transaction. Is that correct?

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[DannyHamilton]

My question is this: Isn't it the case that LN only works well if there are lots of transactions in a channel? That is, if Alice sends 0.00001 BTC to Carol via Bob, and that's the only transaction in that channel in, say, a month, then benefits #2 & #3 above don't really apply since you effectively have a 1-to-1 relationship between a LN transaction and a blockchain transaction. Is that correct?

Correct.

However, there isn't necessarily any reason for Alice and Bob to close their channel, nor for Bob and Carol to close their channel.

Therefore, the channels could be left open for many years, allowing additional opportunities for Alice, Bob, and Carol to use the channels.

Additionally, if Alice, Bob, or Carol are well connected enough, then all three of them could continue to use those same channels for other payments to other Lightning Network users elsewhere on the network.

[aleksej996]

My question is this: Isn't it the case that LN only works well if there are lots of transactions in a channel? That is, if Alice sends 0.00001 BTC to Carol via Bob, and that's the only transaction in that channel in, say, a month, then benefits #2 & #3 above don't really apply since you effectively have a 1-to-1 relationship between a LN transaction and a blockchain transaction. Is that correct?

Well, apart from the fact that LN channel would still be beneficial here if it stays open for 2 months, it still has transitive properties.
When you open a channel with someone, it is not just that you can use LN with them, but with anyone they have an open channel with, as well.
So there is obviously more to it than that.