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4 points

Because the max blocksize of BTC is heavily crippled, max transactions per block is around 3,500ish. That puts us at about 500k transactions max per day (1 block every 10 min). So divide 500k by how many seconds are in a day (86,400) and you get slightly under 6 TPS. Whoever came up with 7 TPS probably did more accurate math than me.

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3 points

Different transactions use different amounts of space so it’s always going to be a rough estimate.

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4 points

Yep. That 3.5k I pulled out of my ass was just by looking at a graph of max transactions per block thus far. It highly depends on the efficiency of the transactions and size of each.

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2 points

So what happens if a lot of people want to make transactions at the same time? Do they have to queue? Also, this sounds like anyone can cripple the system by scheduling a few thousand tiny transactions.

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4 points

Yes, there’s a queue called mempool.
Clogging up the network is possible, but costs money (BTC), because transaction fees need to be added to the transactions and those fees need to be higher than those of the highest not yet processed transactions if “regular” users’ transactions shall be delayed.
Miners prefer transactions with higher fees (to be precise: higher fees per occupied block space), because they earn them when creating the block successfully - together with the BTC that get issued when a block gets created.

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3 points

There’s a transaction fee, the higher you pay the more priority you have (since miners get a cut).

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