NLNico is spot on. One extra benefit of going nonceless is that it is hugely easier to verify each bet with a script (or verify the script) as there's no history (bet direction, bet size, result) to accumulate, you can just on-demand verify each bet.

Or if you're planning on releasing something like a userscript or a browser plugin that automatically verifies bets, I'd definitely go nonceless (it can check immediately, as you play). Or if you're expecting people to verify batches themselves by hand, I'd go with a JD-style nonce.