While You're reviewing the motif of the game, let's ask why and how sometimes the producers add 1 strike to the mix or and sometimes 3 to the mix. Much of Bob's closing years it was only 1 but went back to 3 when Drew come on the Scene.
They weren't quite getting as much winners as they wanted, and they decided taking out two of the strikes was the simplest way to get the win rate back up to where they wanted it.
Drew's second season was a bit of a mess and the new showrunners couldn't figure out what they wanted to do; they tried all sorts of rules tinkering with games that really didn't need it. Who knows why. Eventually decided to go back to playing it with three strike chips after much on-air experimentation.
If there actually was a study done, cool. It's always nice for the show to reciprocate good earned publicity and make an example for others who may have been watching. But I'm sure they all knew that already--you really don't need to run a study to know that starting the game with 5/6 odds of drawing a number will produce more wins than than 5/8.
Another question: Was the game changed from regular cars to luxury cars to make the game a rare occurrence? Early playings showed the game was played more often.
Like most of the show's early car games, 3 Strikes was originally designed around four-digit cars. With four chips in the bag, it was more or less in line with the difficulty of other car games. When the game permanently expanded to 5 digits and added an additional chip in the bag, it became quite a bit more difficult, since it shrank the odds of both pulling all the numbers and placing each one correctly. They made up for the added difficulty by playing it for something really special.
Also, 3 Strikes is a loooong game. As the 90's went on, the show's running time began to slowly be cut down to make room for more commercials. Since 3 Strikes was going to have to cut back on playings no matter what, might as well make an event of it and ensure it's always played for something really special.