From what I understand, that would just be overcomplicating the matter, because most modern video gambling machines just use a set number of wins per time interval.
If you like, add a bit of skill that gives the primates the feeling of control (video poker) or when you let loose of the handle or press a button (which simply grabs a number).
Stir in a bit of marketing pizzazz (off-by-one on slots, enormous number of simultaneous smaller bets, low payoff better odds vs. high payoff worse odds) and you can get the mark to stand there for a bit longer.
Networking, recognition and databases on players, etc. add more wrinkles.
In any case, I don't doubt that a Monty Hall bet could be wrappered into the game somehow to give the appearance of better odds than really exist.
(hopefully I got this somewhat right, I've never designed any gaming stuff. I'll bet that a gig at Bally or IGT would be a real eye-opener.)
The machines are random, with no enforcement on wins per time interval.
Source: I work in the industry.
Oh, and fwiw, I know several people who always win when they come to Las Vegas. I know because they've told me so. This proves that you don't actually work in the industry.
(I really hate that I have to disclose that I don't really have a Ph.D. is slot machines.)