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Holding ether/usd price constant, how does the amount of gas for a transaction scale as more ethereum nodes are added? Does it become more expensive to execute the same transaction, since there are many more miners trying to do the same thing -- or is it constant, since only one can include it?

If it's the former, isn't that an extremely large barrier to entry? If I make a gambling dapp that only my community of 100 people would ever care about, would using it cost something on the scale of n=world_population (variable) rather than n=100 (fixed)?

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Holding ether price constant, how does gas price scale as more ethereum nodes are added?

if the ether price is constant, gas price will be the same when more transaction or mining nodes will be added

Does it become more expensive to execute the same transaction, since there are many more miners trying to do the same thing -- or is it constant, since only one can include it?

it's the same price for the same ether price

If it's the former, isn't that an extremely large barrier to entry? If I make a gambling dapp that only my community of 100 people would ever care about, would using it cost something on the scale of n=world_population (variable) rather than n=100 (fixed)?

More people will use your dapp, more gas they will spend and it's a linear dependency. You can set-up a private ethereum network to run your contracts and make payout in the main network with some interledger dapp. Or you can set-up a hybrid network with trustfull validators but much cheaper gas price. I'm working on a project which will help to set-up that type of hybrid network. Please let me know if you'd like to know more.

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