He didn't say contingent bias, you did. Nothing he's written is in any way related to prior individual rolls.

He said he knew how to place a winning bet, he never said it was because the previous results were exactly 1, 2, and 3 and no other numbers. Those results can indicate something other than a "contingent" bias; because they landed on 1, 2, and 3, the wheel is leaning more towards that half of the wheel, meaning he could therefore assume bets on that half of the wheel were more likely to hit, which would then allow him to accurately say he knew what to bet next (a complex bet) that would pay out (win more than wagered).

You're thinking about this mathematically, when the edge comes from mechanical physics.

1 2 and 3 are distributed around the wheel, there is no "that half"

Not perfectly evenly distributed, which is the point.

You could think of the statement as being about knowing the actual bias as a function of only being able to look at the previous rolls. In other words, it is “contingent” on the specific roulette wheel being observed, not “contingent” on which exact rolls were seen recently, per se. But language and thinking on these subjects has evolved since 1969, so the way to frame it to a layman would obviously evolve as well. It’s been over 50 years, after all! Trying to understand the statement in the context of 1969 makes the framing much more reasonable.

Edit: I can also see how this framing might have been important to funding ongoing research, ie, perhaps you are right that there was some degree of unethical framing here.

Recall the quoted passage:

> “If numbers 1, 2, and 3 won the last 3 rounds, [I could determine] what was most likely to win the next 3.”

That is unambiguously claiming not just a contingent bias, but a bias contingent on the previous three rounds. My math was based on a one-round contingent bias. That is already in the realm of extremely unlikely. Three-rounds is just flat-out impossible.

I don't think it's unambiguous. I think the parent's interpretation is also quite possible (even probable, given your point that the contingent interpretation is impossible).

Would a bias contingent on the previous 3 be considered Markovian in this case?

> That is unambiguously claiming not just a contingent bias, but a bias contingent on the previous three rounds.

No it isn't, only that three rounds may be enough to predict the bias. Whether the bias actually depends on previous results is irrelevant to the quote.

> three rounds may be enough to predict the bias

That is an even more absurd claim.

Wouldn't this be a very simple example (simple to the point that it's obviously exaggerated and wouldn't happen in a real casino): each spin of the wheel takes it exactly one whole rotation plus one number, which if the dealer always picks up the ball and spins starting from the previous winner would mean the next winner is always the next number around on the wheel?

It's pretty clear that you've never actually seen a roulette wheel in action. Introducing a bias intentionally (i.e. trying to control where the ball drops) would take extreme skill. Doing it unintentionally is impossible.

I've played roulette many times, and yes I agree that doing it with skill on a fair wheel would be impossible. I thought we were talking about potentially rigged games, and just as I couldn't roll fair dice to the same number 20x in a row I'm aware that dodgy dice can be made, so why couldn't a dodgy wheel (or accidentally dodgy by being so old that a noticeable pattern emerges) be made?