is the price for opening a channel fixed? doesn't it vary with the number of available channels?

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oh wait yes

for every channel that needs to be opened you pay a minimum of 3k sats +1% of fees

so it's a good idea to topup your wallet with a big fat stack at first, then send 50% back to another wallet of yours

this creates enough inbound liquidity to last for a good while

it all depends on your own estimate of how much you're planning to earn / receive wrt how many big channels you want to open

i think.