I think you're confusing two hashes. There's:
* The hash of the day's secret number. It was published months ago and won't change.
* The hash of your bet transaction, also known as the transaction ID. It is created (by your client, not by SatoshiDice) when you make a payment. It doesn't change.
You get to pick your transaction ID if you want to, as follows:
1. back up your wallet.dat file
2. turn off your Internet connection
3. tell your wallet to send a bet to SD
4. check the transaction ID
5. if you don't like it, quit the wallet program, restore your wallet.dat from the backup, restart the wallet program, and go back to step 3, but add 1 satoshi to the bet amount. that will cause a completely different transaction ID to be used
6. turn your Internet connection back on
7. wait for the wallet to send the transaction (only the most recent one, whose txid you liked) out to the network
There's no point doing any of this if you don't know the daily secret, because you can't tell with txid values to "like" - you would want to like just the ones that are going to win, but you can't tell that without the secret, which you won't know until tomorrow. You usually just create a transaction and instantly broadcast it, but using the steps above it's possible to check the txid before broadcasting it, and delete (by restoring a backup) the transaction so nobody but you ever knows you made it.