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Gas is a 'sub-currency' which enables the EVM and Ethereum's decentralised computer to run -- with each operation, an amount of gas (proportional to the computational effort required to perform the operation) is consumed.
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How does EIP 150 change the call depth attack?
With the new rules, the call cannot consume more than 63/64 of the gas of the parent. So if your gas is X, then N CALLs in, it will be max X * (63/64)^n. … And to be correct, the gas is even less than that, since 63/64 is defined as "all but one 64th" of N as N - floor(N / 64), so there's also a factor of flooring to integers which has an effect. …