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Is it possible to get randomness in a smart contract? E.g. I would like the validator to randomly choose between two conditions to use to validate a transaction. Such a capability could be used for example to implement a lottery smart contract.

If so, what are the mechanics of the randomness?

If not, how could the lack of randomness be circumvented to implement something like a lottery smart contract?

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Validation is deterministic, so decidedly non-random. And this is a desirable feature, because it means you can validate a transaction off-chain before ever submitting it, thus being sure you'll never have to pay fees for a transaction that will turn out to be invalid.

In order to get randomness, one could for example use an oracle that provides entropy.

Alternatively, one could use a commitment scheme: In your example, the lottery operator publishes the hash of the random draw up-front, then later, after players have signed on, reveals it. The operator can't cheat, because he has committed already (by publishing the hash up front).

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