AI Advantage

If we take any game (chess for example) with a deterministic steps and all opponent data that is known to a computer at the time a game is played, then it simple to determine the AI's advantage. It could be written as the differential equations based on the optimization of the current state of the game, in any given step (\( t_x \)). Given data terms \( D_1 \) and \(D_2 \) and where \(O() \) and \(h() \) are the optimization and heuritic functions respectively. In the case of computer vs. player playing chess, there is not much of a strategy so the heuristic strategy function can be ignored there. \(C_H\) is also the computer-human handicap factor, when the data of the game is not fully know. In the case of chess, all data to make decisions at a given step \( t_x \) is on the board at any given time so a computer-human handicap is not a factor.

AI (CA=Computer Advantage) Eq1: \[ O(D_1) + h(t_x) = CA \]

Player (HA=Human Advantage) Eq2: \[ O(D_2 \times C_H) + h(t_x) = HA \]

For any given step \( t_x \), in a deterministic game like chess, the relative game theory win conditions are simple:

\(  if  CA > HA  then  C  wins  \)

\(  if  HA > CA  then  H  wins  \)

In non-deterministic games, where we have randomness and unknown data in any given step of time, it is possible to introduce an error rate into CA: \( O(D_1 \times E_t) \)

Proposition: If the human player is able to introduce an error rate into optimization function of CA by introducing random noise into \( D_1 \) then the human player is able to increase the effectiveness of his heuristic strategy in the term \( h(t_x) \) in any give step. The interesting thing is that if \( h() \) term is able to create the error term introduced then human-player handicap can disappear in many non-deterministic random games.

Our equations become:

AI (CA=Computer Advantage) Eq1: \[ O(D_1 \times E_t) + h(t_x) = CA \]

Player (HA=Human Advantage) Eq2: \[ O(D_2 \times C_H) + h(t_x) = HA \]

Error Heuristic Eq3: \[ E_t = h_e(t_x) \]

The proposition is based on an assumption that CA optimization \( O(D_1 \times E_t) \) is not able to change from step to step fast enough to optimize for correction due to the introduction of the human-created error noise.

The opposite is also true, if CA can introduce its own noise into the HA optimization function, then the human-player handicap becomes even larger.

The question now is, when does the game become unplayable because of too much noise and fake data introduced into the game by the two players (the human and the computer). But even if the optimizations \(O()\) of CA and HA become unreliable and useless, we are back to who has the best heuritic functions \(h(t_x) \). Even if the rules remain the same for the non-deterministic game, are we still playing the same game then or has the game changed too? :)

The next step is to decompose \( O() \) and \( h() \) into their respective partial differential differential equations with learning rates. Maybe in the end, only the most efficient strategies and simple efficient optimization functions win.

Next proposition:

The learning rate as time reaches infinity of computers and humans is inherently known to be different. Our brains are biological systems. Biological systems are trained through millions of years allowing us to make very optimized decisions even with very limited data in any given step.

In a world where all non-deterministic games have so much random noise that they are virtually unplayable, which player will be able to adapt quicker?