It's not clear why one wouldn't just use the label "chance" in these examples. Casino-goers would actually say that roulette has more chance than blackjack. Action or intervention producing a particular effect is descriptive of all the cases, given the differing lusory means. When I play 500, I decide what I will call and play. When I play Roulette, it's down to me what numbers I bet on.
Because chance is only relevant to the examples due to removing the GM-control angle. In absence of a controlling figure like a GM, dice or other random-number generators are the most common choice for producing fictional states without simply authoring the whole thing yourself. Many truly single-player games work this way. Something like
Dogs in the Vineyard can also achieve something kinda-sorta like this via players wagering against one another for what they want to have happen, and I'm sure there are other systems besides.
Also, I don't think Pemerton was even remotely trying to imply that roulette is higher agency than blackjack. Almost certainly the reverse. There is no way to meaningfully predict roulette without actively cheating (e.g. controlling the board.) You can count cards in blackjack (though Nevada casinos will ask you to stop playing if they think you are doing so, and it is actually illegal to use a device to
help you count cards.)
Unless the thesis is that agency equates with reduction in chance, in which case to fear that a GM reduced agency would be to suppose a GM's decisions were random. As we don't typically think of human choices as random (and to do so would hard-conflate agency with chance) any mechanic that invokes a dice roll reduces agency more than a GM call does. That is if agency is equivalent to chance.
No. It equates an increase of agency with a decrease in
influence. You cannot influence anything in roulette, and cannot realistically do so in blackjack. (I mean, you
could try by intentionally busting to drain the deck of cards! But that's a losing strategy.) To continue using games that mix chance and skill (quite appropriate, given D&D's mechanics), poker would be yet higher on the agency spectrum, because of the ability to bluff and the betting mechanics. Conversely, we get the phrase "a crapshoot" because the player has little influence over the actual results in craps, it's all on the dice.
Lacking information is one of the ways to lose influence, and chance is a prominent way of not having information, but far from the only way. Another way is illusionism, where facts that were true yesterday are no longer true today. A third is having unreliable sources of information, e.g. a GM secretly determining the result of a Perception check and then saying, "You see nothing out of the ordinary." Is that a "nothing out of the ordinary" because there is nothing to see, or because there IS something to see but you missed it? That's a lack of information, and can affect influence. (And, to be clear since I know I will get jumped on for this if I'm not extremely explicit every single time:
Players not being omnicient is absolutely fine; it is when they are not given even the opportunity to learn that things become a problem.)
But an absence of information is not the only cause of an absence of influence. Lacking tools, or having tools that are mostly useless, also results in an absence of influence. This is what a lot of people bring up in conversations about "mundane vs magic" or, to use the D&D version of that conflict, "Fighter vs Wizard." And why it's so frustrating to be told "well the Fighter can just get
creative!" ANYONE can do that! Anyone can apply creativity to their surroundings! Wizards can be creative AND warp reality.
Some players feel more empowered when the outcomes of what they attempt are up to them ("say yes") or mechanically determined ("or roll the dice")... even if rolling the dice introduces chance that is absent when GM decides. Others players feel more empowered when they can make any play they can think of, because someone has been appointed to make rulings.
Of course, I myself am skeptical of the "tactical infinity" so often discussed, as I find far, far too many GMs are rather more interested in tactical
subfinity: "only those things I, the GM, think are possible, regardless of how poorly that reflects either actual IRL possibility, fun gameplay, or engaging narrative." The possibilities are actually
more limited than they would be for an appropriately-talented IRL person attempting to do things. The problem of iterative probability is a good demonstration of this. (GMs failing to understand that asking for 5 checks in a row, even if you have an 80% chance to succeed each time, is actually a two thirds chance to fail.) The problem of perverse incentives is another. (GMs
saying how annoying they find murderhobos and how much they
wish players would just be heroic, only to
actually run a world where mercy is "rewarded" with enemy reinforcements and "allies" are consistently just itching to betray the PCs.)
Reflecting on that, and on my Chess and other examples, perhaps one can define agency like this: the extent to which the agreements I made entering the magic circle are binding on all participants.
I don't think that really equates to agency--more like the foundation thereof. That is, it would be a bit like saying that modern science
is statistics, and nothing more. It would be absolutely correct if you meant that only in the sense that the science of statistical analysis is the beating heart of modern scientific study. It would be absolutely
wrong if you meant it in the sense that science is
nothing more than statistical analysis, since experimental design, data collection, theoretical modeling, and post-analysis interpretation are all critical parts of science that are not part of statistical analysis.
I do expect that the agreements made before entering the magic circle are binding. If they aren't, then the magic circle is pointless and the exercise is simply one of dancing to someone else's tune. We may as well not even bother with the pretense.