Primer for Old School D&D
With so few definite "rules" in the game, OD&D relies heavily on Rule Zero: the DM has the final say in rulings at the table.
This requires a lot of trust. The players have to trust that the DM isn't "cheating" or trying to kill the PCs on purpose.
To foster this trust, I will try to be up front with House Rules, clear about potential consequences of certain actions (and not play "Gotcha!" with traps, etc.), and roll my dice in the open, so you can see I'm not fudging.
(Earned) Success and Failure
OD&D is more firmly a game than a story. This means the game is designed to provide a challenge to the players. It is not "balanced" to give the characters a fair chance of survival.
This doesn't mean I want you to fail. On the contrary, I want you to succeed. But I want you to succeed because you actually succeeded, not because I let you.
Failing in fun
The best Old School D&D stories are not about the time you defeated a big bad without taking any damage. They're about the time you all hatched a terrible plan, everything about it went wrong, and it was an unmitigated, but wildly entertaining, disaster.
How My Character Died is probably the best genre of Old School D&D story. By contrast, How My Character Reached Level 20 and Lived Happily Ever After is a pretty boring story.
So try crazy things, embrace Plan B, and take a failed dice roll as a opportunity to go out in a blaze of glory. There's always another character waiting to be rolled up.