If I purchase a game on a Steam account, can I play that game on a second account?

If you are confused i will clear it up...

Account 1 (mine) I purchased --> Left 4 Dead

Then I made a new account,

Account 2 (also mine) I didn't purchase anything yet.

Can I play Left 4 Dead with account 2?

Solution 1:

Yes and no. Game licenses are tied to an account, so your new account will not own the game.

However, using Steam Family Sharing, you can set up your new account to play games from your old account. Once that is set up, yes, you will be able to play Left 4 Dead from your new account on that computer.

Note that this will not allow you to use one copy of Left 4 Dead to play with two people. Only one person can be playing games from the old account at a time. You also need to keep access to the old account so you can set family sharing up again on any future computers.