cool idea. i was imagining storing state on relays but this is an interesting, more robust spin.
You could roll up all entries into OTS. Bets for next block go in OTS merkle tree for current block.
Discussion
You just want proveable time anchors so there's less cheating. OTS provides that.
nostr events are signed, if you trust the signer.
Signatures are just one part. Timestamping is the other.