If it's in open time, you can't pick it up as a reserve. It can be ASSIGNED to you , but I don't think you can grab it. Open time goes to lineholders first, and they have (I think) up to 72 hours before the shift begins to try to grab it. After that, it's generally assigned to a reserve guy. In reality, it normally gets assigned to a reserve guy much earlier than that. Back when I was on reserve, I generally knew what I was flying a week or so in advance. There was ONE day where I got a call saying "you're flying XXXX today."
And if you DO get assigned a trip, scheduling can change it at any time. Since you're on reserve, you don't "own" any of those trips. If you check your schedule the night before and see you have a sweet 4 day with 14 hour layovers, you might wake up in the morning with 4 high speeds.