Quantum Entanglement (A Love Story)

mom always told me to "turn it into a game" when things got difficult.

thats where i learned virtue number 3 - the most important one.

geezerchess would say, "but i love eating dinosaur nuggets, yet i dont want to eat dinosaurs"

I've gotta think of a family vacation spot for a week or less trip next year.

It has to be warm, it should be 420 friendly.

Constant Readers, any ideas??

A game is a system of rules that structures playful or competitive activity, typically with goals, challenges, constraints, and outcomes that engage participants for enjoyment, skill-testing, social interaction, or reward.Mathematical Definitions: Two Major BranchesMathematics formalizes "game" in two largely separate but overlapping traditions: classical game theory (strategic interactions, possibly with imperfect information or chance) and combinatorial game theory (perfect-information, usually deterministic, recreational games). Below are the deepest, most rigorous definitions in each.1. Classical Game Theory (von Neumann–Morgenstern–Nash Framework)The foundational object is a game in normal (or strategic) form😃efinition (Finite Normal-Form Game)
A finite normal-form game is a tuple
Γ = ⟨ N, (S_i){i∈N}, (u_i){i∈N} ⟩
where:N = {1, 2, …, n} is a finite set of players.
For each player i ∈ N, S_i is a finite nonempty set of pure strategies (complete plans of action available to i).
For each player i ∈ N, u_i : S → ℝ (where S = ∏_{j∈N} S_j is the set of pure-strategy profiles) is the payoff (or utility) function, assigning a real number representing i’s payoff when the strategy profile s = (s_1, …, s_n) ∈ S is played.

When players can randomize, we extend to mixed strategies:
Let Δ(S_i) be the set of probability distributions over S_i.
A mixed-strategy profile σ = (σ_i){i∈N} yields expected payoff
u_i(σ😉 = ∑{s∈S} (∏_{j} σ_j(s_j)) u_i(s).Key extensions:Infinite games: S_i can be arbitrary measurable spaces, u_i measurable, with mixed strategies as probability measures.
Games with chance: Add a fictitious player "Nature" who chooses moves according to a fixed probability distribution.
Bayesian games (incomplete information): Add type spaces Θ_i for each player, beliefs p_i(θ_{-i} | θ_i), and type-dependent payoffs u_i(s, θ😉.

Extensive-Form Games (capturing sequence, timing, and information)
An extensive-form game is a game tree with:A set of nodes V, partitioned into decision nodes and terminal nodes.
Edges representing moves.
A player partition function p: (non-terminal nodes) → N ∪ {Nature}.
Information sets: Partitions of each player’s decision nodes into sets where the player cannot distinguish between nodes (imperfect information).
Payoffs defined only at terminal nodes.

Kuhn (1953) showed that every extensive-form game with perfect recall has a strategically equivalent normal-form representation (though exponentially larger).Solution Concepts (what "rational play" means):Nash equilibrium: σ* such that ∀i ∀σ_i', u_i(σ*i, σ*{-i}) ≥ u_i(σ_i', σ*_{-i}).
Subgame-perfect equilibrium, perfect Bayesian equilibrium, etc., for dynamic games.

2. Combinatorial Game Theory (Conway’s Framework)This branch studies short games of perfect information, no chance, and usually two players (Left and Right). The deepest formalism is Conway’s surreal numbers construction.Definition (Combinatorial Game, Normal Play)
A game G (under normal play: last move wins) is defined recursively:
G = { L | R }
where:L is a set of games (options for Left player).
R is a set of games (options for Right player).

The notation means: Left may move to any G^L ∈ L, Right to any G^R ∈ R.
The terminal position (no moves) is 0 = { ⋅ | ⋅ } (empty options).Key derived concepts:Negation: -G = { -R | -L } (swaps players).
Sum (disjunctive sum: play in one component at a time):
G + H = { G^L + H, G + H^L | G^R + H, G + H^R }.
Outcome classes:G > 0 if Left wins no matter who starts.
G < 0 if Right wins.
G = 0 if second player wins.
G ∥ 0 (fuzzy) if first player wins.

Grundy number (nimber) for impartial games (L = R):
mex (minimum excluded value) of Grundy numbers of options.
G + H = 0 iff Grundy(G) ⊕ Grundy(H) = 0 (XOR).
Surreal numbers: Every game G has a birthday (transfinite recursion depth) and is eventually equal to a surreal number (dyadic rational extended transfinitely). Examples:
0 = { ⋅ | ⋅ }
1 = { 0 | ⋅ } = { 0 | 0 } (nim-heap of size 1)
↑ = { 0 | * } (very hot game).

Conway’s On Numbers and Games (1976) proves that the class of all games under + forms an ordered field (the surreals) plus infinitesimal "nimbers."Connections and Broader ViewsStochastic games (Shapley 1953): Markov decision processes with multiple players; state-dependent normal-form games plus transition probabilities.
Evolutionary game theory: Replicator dynamics on strategy distributions.
Algorithmic game theory: Computational complexity of finding equilibria.
Category-theoretic views: Games as objects in symmetric monoidal categories (e.g., for compositional reasoning).

In the most abstract mathematical sense, a "game" is any formal structure that models interactive decision-making under rules, with outcomes depending on the joint choices of agents. The two major mathematical theories provide complementary, extremely rich universes: one built on utility and probability, the other on recursive positions and ordinals. Together they cover nearly every rigorous notion of "game" that mathematics has developed.

Come to central Florida and we can make a pilgrimage to the Mecca of Old Man Coffees at the Oxford Downs Poker Palace where on a Monday morning the average age will be close to double your own. The friday-sun games are totally different beast.Florida has a lot more to offer than beaches and the "attractions", lots of pine trees and cows.

Artemis mission is slated to pop off soon, I can see the rockets launch from Kennedy Space center out here pretty well especially since there's very little light pollution something like 100 miles away

This applies to me. More of a feature than a bug.

So here'es your holidayyyyyyyyyy
Hope you enjoy it this time
You gave it all awayyyyyyyyyy