vantzy-
I can't speak for all of the game manufacturers, but I know on the older WMS games, specifically "Jackpot Party" (where you keep picking presents until you hit a Party Pooper), all of the values were assigned and shuffled, and player interaction did make a difference as to what they'd win (ie. if the party pooper was in present box #1, picking box #1 would end the bonus whether it was the 1st or 10th pick).
You asked a good question about how the machine can maintain its payback percentage if the player has influence over their destiny in the bonus round. Allow me to explain how:
The way the machine is able to maintain its average payback percentage is by figuring the math of the average award in the bonus -- over the long term of the bonus getting hit, the number of picks before hittng a pooper will average out, and the total credit amount won will average out.
You can see how that works with this example: offer people who walk up to you two doors to pick from. One of them has 50 coins behind it, the other zero. Over time, you'd pay out an average of 25 coins for every player who gets to pick a door -- you could expect every player who gets to play vantzy's Fabulous Door Selection Game to win 25 coins. Using that concept, a slot designer can determine how much the "picking" bonus round will pay on average, and make sure that the base game plus the bonus add up to a specified percentage payback.
jjjj21-
That blackjack side bet with the wheel was indeed weighted. Even though it was shaped as a wheel, it was essentially a slot machine with 6 physical stops (6 wedges on the wheel) an unknown number of virtual stops and one reel -- it was not a fair wheel (and that's legal). More on that bonus from the Wizard of Odds website:
http://wizardofodds.com/blackjack/appendix8.html#BonusSpin
