This video shows a gamified version of Bell's Theorem called the "CHSH Game".

The theorem proves the nonlocal nature of quantum physics, known sometimes as "Spooky action at a distance". The gamified version further shows that quantum entanglement can be useful.

See more about the usefulness of quantum entanglement in this video about the relation of such games and interactive proofs, and a recent result related to the halting problem:
   • Halting Problem & Quantum Entanglemen...  

Some history:
Bell's Theorem is due to John Stuart Bell in 1964.
The CHSH inequality, by John Clauser, Michael Horne, Abner Shimony, and Richard Holt, improved on it in 1969.
The CHSH game by R. Cleve, P. Hoyer, B. Toner and J. Watrous in 2004.


About "Bell Locality":
The formal statement of it is this requirement of the probability distribution:
P(x,y|a,b,particle1,particle2)=P(x|a,particle1)P(y|b,particle2)
This means that the outcomes are independent given the input bits and the respective particle statements.
Another way to say that is as stated in the video: that given the particle the top player has, we can specify the table P(x|a,particle1), and it makes no difference what happens with the bottom player (or the other way around of course).
Bell's theorem proves this is not what's happening.

As stated in the closing slide, this conclusion relies on a few more background assumptions:
* Each measurement has one outcome. According to the "manyworlds" theory a measurement can have multiple outcomes, and Bell locallity may still hold with this interpretation.
* The referee can choose random bits. According to "superdeterminisim" world view, there's no such thing as randomness, and it might be that the referee chooses bits somehow predetermined to match the particles held by the players.

Some more links:
A primer on quantum physics:    • Visualization of Quantum Physics (Qua...  
A more rigorous explanation of quantum spin (Physics Videos by Eugene Khutoryansky):    • Quantum Spin  Visualizing the physic...  

Chapters:
0:00 Part 1: Decision problems
1:56 Part 2: Classical bound
6:20 Part 3: Quantum spin
13:44 Part 4: A Quantum Strategy
16:10 Part 5: Local realism
18:48 Part 6: No signaling
22:45 Part 7: Bell locality