I can point to a lot of lotteries like that, but they are all out of business now since the laws got tighened up! Typically they worked in reverse -- see these numbers they won't come up!
Sure, the DM can be influenced, negotiated with, and otherwise influenced -- that's using player agency in a less formal manner.
You are engaged in affecting the world in a way your character (despite the number of prayers he may utter) cannot.
I think agency is just a particular type of narrative control. You find narrative control distributed differently around the table depending on the rpg, and sometimes group, you're looking at.
As I stated upthread, it's nonsensical to define narrative control as total control, because then no one at the table (not even the DM) possesses it! Not even the DM can tell me without cause that my human is a dwarf. He can't tell me that my mage memorized fireball instead of divination this morning. He needs a reason to deny my fighter an attack roll.
IMO, this is because the rules create a framework for shared reality, and a DM who violates those boundaries without the consent of his players will find himself with justifiably irate players. If you step outside the framework set by the rules without approval from the participants you're playing cowboys and indians in the back yard, not a role playing
game.
Players certainly have
less narrative control in most games than the DM. Since the DM acts as a referee, that makes sense. However, even though 1 is both less than 2 and less than infinity, you would be in error assuming that this implies that 2 equals infinity:
1 < 2 && 1 < infinity
2 =/= infinity
The DM, players, and even dice all share narrative control of the game. I believe that this is a big part of the reason that railroading has such a bad reputation; without consent from the players, a railroading DM oversteps the limits placed on his share of narrative control and steals that which belongs to the players. It's also why railroads work for some groups; those players consent to surrendering a portion of their control to the DM in exchange for a better experience (from their perspective). That it works for some and not for others isn't really relevant beyond that some players are willing to surrender more narrative control than others.
It's similar in some respects to the government of certain republics. The DM is akin to the president. He wields great authority, but not without limits. Players are like congressmen, guiding the game in the direction they'd like to see it go. Both the president and the congress are granted different political powers by law (the rules).
Stories abound of players who ignored the Dungeon of the Week in order to explore something the DM never anticipated. You can't tell me that that isn't a significant degree of control in regard to the narrative. The DM planned for this week's story to be about exploring the dungeon. Instead, the players made it about exploring the intricacies of wenching. The story completely changed, not because of the DM but rather the
players! The DM, of course, still acts in his role as guide for the narrative of the wenching story, but this new narrative is nothing like what he intended.
Granted, in the above example, it may be the DM who feels slighted. After all, he presumably spent time and effort preparing the Dungeon of the Week for the players but now that material is useless and he's being forced to improvise. Other groups, including my own, love this sort of thing. Not wenching, but rather taking the game completely off the track. Some of our best sessions were 99% improvised.
All narrative control in rpgs is a matter of degrees. What degree that control is shared, is admittedly a matter of personal preference. However, assuming that the DM is the only one in control is a mistake. If that were the case, the DM would be telling the "players" story rather than arbitrating a game.