here are some thoughts on your presentation slides. hopefully this is a better articulation of the brief criticism I gave earlier.

“games are things we play”

we can think of games as: networks of signs, spaces of possibility, mechanical signifiers
games are an expression of ^the constituent parts^ within an “acceptable” range of mathematical complexity
(so say the slides)

let me propose a slight re-thinking:
games are imposed structures (yes: signs, spaces, mechanisms—also, logics (ideologies//”cultural orientations,” subject/verb/object constructions, materialism, etc)) on which we shape “play” into a rehearsal (yes: an mathematically complex expression) that reinforces or maintains the structure itself.*

so, an acceptable “rehearsal” is temporally contingent on
an ability to understand and execute a performance on command,

and the heuristics (provided or borrowed from elsewhere)
serve to functionally guess (as you said) the
complexity and formulation of the “win.”

how long we attempt to win and how we react to losing are also both contingent on how we’ve rehearsed “attempting” and “losing” in the past.

winning itself can also be a rehearsed performance.

humans sometimes “impose” games upon other games
such that that “losing” becomes “winning.”
these “impositions” are rehearsed, too.
every imposition is “mapped” for a reason
(why lose? altruism, humility, honor, grace, affection, etc.)

we can have games within games within games—so many games. they tend to map on to each other. each game a person plays can affect their performance in other games, and some games are valued as more important than others.

some of the games are structured to “feel” designed (artifacts) and others are structured to seem natural.

for example: sex discrimination.
sexism is a game. the practice of discrimination is a performance. the game space=everywhere, the mechanics=[numerous], signs=[numerous], logics=patriarchal, matriarchal, etc. (pick a hegemonic dominant class that then defines all other classes as “less” [valued, powerful, material, etc.]) it is done for oneself and for other people. it is recognizable. it is a “win” if the performance yields a desired result.
the naturalness of sex discrimination is built into the logic of the game; acknowledging the design of this game breaks it. 

if we are only concerned with “artifacts”—games that exist within games that are within other games, etc.—that are designed to provide a player with some kind of freedom to move//behave, then a designer needs to think about the relationship between her artifact and the other games (alt.read: social constructs) that players will map onto it.

for example, a devout and longstanding Halo fan sits down to play the next installment in the series: what does she anticipate? how are designers forced to negotiate their vision for the next installment with the previous iterations in the series?

for example, a game designer wants to make a game with a single humanoid avatar but wants the space to feel inclusive, so he renders the avatar aesthetically ambiguous in terms of race and gender. are aesthetics all that define the gender binary? (no, obviously)

when you talk about choice architecture, you glide over the fact that choice architecture is where all the possibilities are—this is where the edges of the sandbox are made. the theoretical infinite space is only a narratological one; it is not just where interpretability is. the space between the borders of your sandbox and the limits of the imagination is where a designer obfuscates as much of the game as possible. the player (armed with a sense of discovery or serious entitlement complex) probes that space to discover the limits of the sandbox. [henceforth: discovery = [verb] + obfuscated space] “fun” might derive from “learning” a new or unexpected performance, but the fun dissipates when a person has:

1) fully mastered the performance; there is nothing new to discover within the rehearsal of a performance

2) discovered (or concluded) the limitations of a space; no mystery pertaining to the choice architecture exists.

thus, the place//sandbox defines one’s ability to discover, to interpret,
but not necessarily one’s play.

game + discovery + fun = play

it’s not that I don’t believe in the word “agency”—
it’s just that I don’t find it useful.

just because I can “run” in a game
doesn’t mean that I’m learning, having fun, or playing
[by my definition]

similarly, “play” being defined by possible outputs
doesn’t assume discovery. are games without
discovery any fun to play?

so,
play is not dependent on space, and especially not sandboxes

the sandbox is an insincere space 

the sandbox game would like players to believe that
they are free agents within the sandbox
but the reality is:
the sandbox has already delineated all possibilities of
existence within it. there is no fantasy within a sandbox

again: if the original purpose is to design an artifact that provides a player with the freedom to move or behave, then we need to start thinking outside the sandbox.

IMO, a designer can either:

1) focus on obfuscating the edges of the box (basically keep doing what the industry has been doing for a really long time)

or

2) work on creating a game that generates procedurally. create a game that doesn’t rely on a player being able to interpret a designer’s signs. a game with sufficient complexity and capacity to make games within itself.

I hope these thoughts were of some use.

Sincerely,

i