You have been captured for the crime of making a rude comment on Puzzling Stack Exchange and sent to Puzzlcatraz, a special prison for perfectly logical logicians. The warden is fair and decides to play a game with you, as is standard for this prison. Failure to win the game results in death.
1: You are in a group of 10 prisoners. Each prisoner has a number on their head. These numbers are RANDOM, from 1 to 100.
2: To win the game, you must guess if your number is even or odd. If you are correct, you will immediately be freed from prison. If you are incorrect, the warden will throw you into a pit of sharp objects, killing you.
3: You have a 50/50 chance of survival if you simply guess, but the warden, who is a terrible person, will kill all prisoners if he finds out you are guessing. Thus, you must make a strategy.
4: If less than 6 prisoners survive, then all prisoners will die because the warden assumes you are guessing.
5: Prisoners can see other prisoners numbers.
What is the optimal strategy to free as many prisoners as you can?