Lightning network channel capacities and gambling site jackpot payouts

Let’s say I want to make some kind of gambling app:

  1. The user creates a channel with the business. (local_amt = 1000, remote_amt = 0, capacity = 1000)
  2. User bets a few times and wins a jackpot of 5000 satoshis which is more than the capacity of existing channel.

How do I transfer the 5000 sats over lightning when the channel capacity is 1000? The only way I can see getting the jackpot money to the user is by me opening a new channel with extra capacity, but obviously that would take an undesirable amount of time.

In other words, I’m curious how a site like accomplishes instant withdrawals.

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