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# System prepended metadata

title: Lab x

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# Chess Algorithm Implementation Results
## Minimax vs Alpha-Beta Pruning

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# Slide 1: Overview

## Chess Engine Implementation

- Implemented two chess algorithms:
  - **Minimax**: Classic tree search algorithm
  - **Alpha-Beta Pruning**: Optimized version of Minimax
- Both algorithms use the same evaluation function
- Implemented in Python using the `chess` library

*[Video placeholder: Overview of the chess environment]*

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# Slide 2: Algorithm Comparison

| Feature | Minimax | Alpha-Beta |
|---------|---------|------------|
| Time Complexity | O(b^d) | O(b^(d/2)) in best case |
| Nodes Explored | All nodes | Prunes irrelevant branches |
| Move Selection | Same quality | Same quality |
| Memory Usage | Higher | Lower |
| Depth Achievable | Limited | Can search deeper |

*[Video placeholder: Side-by-side execution of both algorithms]*

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# Slide 3: Evaluation Function

## Position Evaluation Components:

- **Material Balance**: Piece values (Pawn=1, Knight/Bishop=3, Rook=5, Queen=9)
- **Mobility**: Number of legal moves (0.1 weight)
- **King Safety**: Penalty for being in check (0.5 weight)
- **Center Control**: Bonus for controlling center squares (0.2 weight)
- **Piece Activity**: Bonus for active pieces (0.1 weight)



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# Slide 4: Performance Results

## Empirical Results:

- **Alpha-Beta**: 60-70% reduction in nodes evaluated compared to Minimax
- **Move Quality**: Identical when using same search depth
- **Time per Move**: Alpha-Beta significantly faster (3-4x)
- **Maximum Practical Depth**:
  - Minimax: 3-4 ply
  - Alpha-Beta: 5-6 ply in same time budget



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# Slide 5: Conclusions and Future Work

## Conclusions:
- Alpha-Beta clearly superior to Minimax in performance
- Same strategic decision quality at equivalent depths
- Enables deeper search with same computational resources

## Future Improvements:
- Move ordering heuristics to improve Alpha-Beta efficiency
- Transposition tables to avoid redundant calculations
- Opening book integration
- Endgame tablebases

