This simulation is based off of the "Don't take the last Teddy" game by Dr. Tim "Dr. T" Chamillard. It is played machine against machine and simulates alternating levels of player difficulty. This "game" is simply for game theory observation and has no controls.
Premise For each game, the number of bins vary as do the number of bears. The player that takes the last teddy bear loses. The goal is to force your opponent into that position. This webGL game runs 100 simulations! Meaning, it will take around 2 minutes, hardware dependant, to finish. In the end you will see the breakdown of games won for each AI player.
https://nohren.github.io/MiniMax-Tree-AI-simulation/
Difficulty level:
Easy - depth 3
Medium - depth 4
Hard - depth 5
Inner Workings:
On player 1's turn, it will look n depth down the tree, it can spot a winning condition through recursion. A winning condition is recursed up from its leaves, depending on if the next node higher likes that condition (maximizing or minimizing), and will transmit the winning condition to the top of the tree. Player 1 will take the path with the greatest value (1).
On player 2's turn, it will look n depth down the new tree that has been generated after the action and result of player 1's move. It will choose the most advantagous decision, the lowest value, since it is minimizing.
Both player 1 and player 2 have heuristics that can infer a winning condition from non winning conditions.
This process continues until there is only one teddy bear left and either player 1 or player 2 loses by taking it.
Example Tree
Player 1's tree as seen printed in the Unity console (No minimax score because it has not been recursed yet)
This is with MiniMax visualization
Results applicable to us 😃
Seize the initiative 🏃 , it's a 1.5x+ advantage 👉: player 1 won 1.5x more than Player 2 of equal skill simply because player 1 goes first. (caveat unless they are both of easy skill- another hint to why forsight is more valueable). Taking the initiative forces player 2 into a corner from the get go. If player 1 is of greater skill forseeing the course of events, this is where the most possible advantage exists.
Practice foresight. This boosts your advantage 3x 🙋 Envision farther out than your opponent 🙈: player 2 beat out player 1 when it possesed greater skill, despite having lost the initiative. Meaning defensive opponents with better crystal balls for seeing the future do better regardless of initiative.
fore·sight - definition /ˈfôrˌsīt/ noun - the ability to predict or the action of predicting what will happen or be needed in the future. "he had the foresight to check that his escape route was clear"
Seeing the future is like looking down the line of choices horizontally as well as their action/results vertically. In other words, forseeing all the breadth and all their depth. Alternatively, it may be easier in life to envision the desired outcome and then recurse back up from the depths to pick the next breadth decision that leads you there. This avoids having to generate many multiples of current choices (breadth) and getting swamped in their depth. The whole reason to generate this tree is because the winning condiiton is unknown. If it's known, just recurse back up to the best decision right now.
Imagine what happens when you seize the initiative and practice forsight! Boom, Check-mate! - the opposing player is out of viable options. 🤘
The enemy always has a say: After your move, the tree of options, breadth and depth is recreated for the other team. And vice versa. A new tree is generated after each action/result cycle. Keep in mind, how you saw something, isn't how it will always be. Things change quickly. Generating a new tree means being open to new conditions existing, seeking them out, and adapting to them. If you stop adapting, you will lose, get boxed up in a corner and be the one out of good options. So keep creating trees after each action/result cycle and practice intentional forsight.
Sample data - Numbers represent wins... Random Range of bins (2-6), random range of bears (1-6), 100 games, 8 different difficulty categories. Results are as expected.
My Crude drawing of forcing the check mate. In this simple scenario, if you go first you win, assuming you know how the game is played!
Any additional insights that you see, just fork it!!