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Anyhow, every share also represents 6% of an island's total financial balance (all 5 shares = 30%).
This means that if you buy a share from someone else, they will lose 6% of the balance of that island, and you will gain 6% of the balance of that island. It also works in reverse, i.e. you will lose 6% of the balance of your island if someone else buys a share.
So, in theory, if you had an island but held no shares in it, that island would only give you 70% of its balance. Conversely, if you held all the shares of an enemy island, you'd get 30% of that island's total balance without actually owning it.
If you own all shares of an enemy island, you also get the option to buy out the island. A buyout costs a large sum of money, destroys every building on the island except the trading post, and then gives control over the island to you. This also works for the AI, so you should try to keep at least 1 share on every island you own to prevent a buyout.
https://anno1800.fandom.com/wiki/Island_shares