You cannot use timestamps if you want to be provably fair. There is no fixed timestamp at bitcoin transactions. There can be a 0 - 10 second delay EASILY between when a bitcoin node gets the transaction. You could maliciously change the timestamp to 1,2,3,4.. seconds later to make the player lose. There is no way for the player to verify if you did this. Therefor it's impossible to generate a provably fair outcome with this.
I replied to your PM already too:
I never really looked into secondstrade. It is possible that some of their games are not provably fair too.
LuckyBit uses a correct way to calculate provably fair bet results for on-chain games. They just use a hash of:
::
vout_id is the output index, in case of multiple bets in 1 transaction. Secret key is a daily secret,
all hashes of future secrets are published already. Then after midnight they release the secret so people can verify the hash and also the bet outcomes. More details on LuckyBit.
This could work for your ODD / EVEN game as well.
Of course there wouldn't be any relation with the bitcoin price anymore though.