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An AI Game Project

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An AI Game Project

Background

- Fivel is a unique hybrid of a NxM game and a sliding puzzle.
- The goals in making this project were:
- Create an original game experience.
- Create a challenging AI player using optimized calculations.
- Achieve an attractive visual look (cute and funny woodland creatures).
- Accessibility – Easy-to-use UI.
- The Future? The ability to export the game to the web upon completion.

The Game

Each turn, a player puts a piece in an empty slot, and slides a tile to an empty place.

The Game

Each turn, a player puts a piece in an empty slot, and slides a tile to an empty place.

The Game

Each turn, a player puts a piece in an empty slot, and slides a tile to an empty place.

The Game

Each turn, a player puts a piece in an empty slot, and slides a tile to an empty place.

The Game

Each turn, a player puts a piece in an empty slot, and slides a tile to an empty place.

The Game

The first player to place 5 pieces in a row, column or diagonal at the endof his turn, wins.

The Game

The first player to place 5 pieces in a row, column or diagonal at the endof his turn, wins.

The Game

The first player to place 5 pieces in a row, column or diagonal at the endof his turn, wins.

The Game

The first player to place 5 pieces in a row, column or diagonal at the endof his turn, wins.

Development

- Problem:Good presentation VS. Strong and reliable computation.

- Flash/AS3
- PROS:
- Allows to create great presentations and GUI’s easily and fast (vector graphics = win).
- WWW Accessibility.

- CONS:
- AS3 is considerably slow.
- Flash is very problematic with deep-recursions (15 seconds limit and render-halting due to its single-threaded nature).

Development

- Problem:Good presentation VS. Strong and reliable computation.

- Java
- PROS:
- Fast and reliable for deep recursions - exactly what is needed for minimax search.
- Everybody knows to develop in Java!

- CONS:
- Harder to achieve the visual look we were looking for.
- Graphical programming in Java is relatively complicated.
- Java is not popular for web gaming since the early 2000’s.

Architecture

Conclusion: Combine them!

HTML

Wrapper

JavaScript

Interface

Flex/AS3 Frontend

GUI

Java Backend

Data Structure, Logic and AI

Data Structure

- The board is based on simple data structures called “Fivlets”.
- These are sets of indices that form a winning row, column or diagonal.
- The board statically stores all the 32 Fivlets in the game.

Example for Row Fivlets

Data Structure

- Each Fivlet knows the status of the 5 slots it contains.
- This structure allows to perform various calculations faster than other methods:
- Moves are easy to perform (bounded by number of Fivlets the modified slots are in).

Example for Column and Diagonal Fivlets

- Iterataions over all Fivlets [O(1)] in order to check for winning conditions and base the heuristics upon their state.

AI and Heuristics

- Automatic players in Fivel use α&β pruning algorithmto search for an optimal move.
- The depth of the search is determined by the user when choosing a difficulty level through the GUI. We supply 4 different levels of difficulty which are different from each other by a few factors:
- MAXIMUM SEARCH DEPTH - The search depth the automated player will use after a few turns.
- AGGRESSION and DEFENSE RATES- Used in the heuristic scoring. Determine how much importance the player will pay for playing aggressively or defensively.

AI and Heuristics

- The difficulty levels in Fivel are:

AI and Heuristics

- Fivel’s branching factor is high - Bounded by 128.
- 32(slots) x 4 (moveable tiles) = 128
- Thus, the search algorithm works reasonably only with a maximum search depth of 3:
- Search depth 3 returns an optimal move in approximately 7-8 seconds.
- In comparison, search depth 4 returns an optimal move in approximately 5 minutes - not reasonable for a game played against a human opponent…

AI and Heuristics

- As the search algorithm deepens, Move objects are generated and performed on the data structure. Each Move objects has an Undo method in order to restore the board.
- These operations are low-cost due to the use of Fivlets.
- Although moves in Fivel consist actually of two different operations (piece placement and then tile sliding), they are considered as a single move when generating moves during the search.

AI and Heuristics

- When a terminal board node is reached (either a board at an end state or when the algorithm reached its designated depth) it is rated according to the following algorithm:
- For each Fivlet in Board
- For each Slot in Fivlet
- If Slot is Mine then mine += 1
- Else if Slot is Opponent then opp += 1
- If mine == 5 then score = BIG_CONST
- Else if opp == 5 then score = -BIG_CONST
- Else if mine == 0 and opp > 0 then score -= -opp^AGG
- Else if opp == 0 and mine > 0 then score += mine^DEF
- Return score

AI and Heuristics

- Basically, the algorithm iterates over all Fivlets and rates each one. Eventually it sums up all the scores and returns it as the board’s heuristic score.
- For each Fivlet in Board
- For each Slot in Fivlet
- If Slot is Mine then mine += 1
- Else if Slot is Opponent then opp += 1
- If mine == 5 then score = BIG_CONST
- Else if opp == 5 then score = -BIG_CONST
- Else if mine == 0 and opp > 0 then score -= -opp^AGG
- Else if opp == 0 and mine > 0 then score += mine^DEF
- Return score

AI and Heuristics

- The algorithm counts how many pieces the current player and his opponent placed in each Fivlet. Empty (no piece) or Void (no tile) slots are not counted and treated the same.
- For each Fivlet in Board
- For each Slot in Fivlet
- If Slot is Mine then mine += 1
- Else if Slot is Opponent then opp += 1
- If mine == 5 then score = BIG_CONST
- Else if opp == 5 then score = -BIG_CONST
- Else if mine == 0 and opp > 0 then score -= -opp^AGG
- Else if opp == 0 and mine > 0 then score += mine^DEF
- Return score

AI and Heuristics

- The Fivlet score is now calculated according to various cases: if The current player has a full Fivlet, the Fivlet is rated with a high score.
- For each Fivlet in Board
- For each Slot in Fivlet
- If Slot is Mine then mine += 1
- Else if Slot is Opponent then opp += 1
- If mine == 5 then score = BIG_CONST
- Else if opp == 5 then score = -BIG_CONST
- Else if mine == 0 and opp > 0 then score -= -opp^AGG
- Else if opp == 0 and mine > 0 then score += mine^DEF
- Return score

AI and Heuristics

- Similarly, if the opponent of the current player has a full Fivlet, the Fivlet is rated with a negative high score.
- For each Fivlet in Board
- For each Slot in Fivlet
- If Slot is Mine then mine += 1
- Else if Slot is Opponent then opp += 1
- If mine == 5 then score = BIG_CONST
- Else if opp == 5 then score = -BIG_CONST
- Else if mine == 0 and opp > 0 then score -= -opp^AGG
- Else if opp == 0 and mine > 0 then score += mine^DEF
- Return score

AI and Heuristics

- If a player has pieces in a Fivlet without an interference from his opponent, the Fivlet is exponentially scored based on the number of pieces in that Fivlet.
- For each Fivlet in Board
- For each Slot in Fivlet
- If Slot is Mine then mine += 1
- Else if Slot is Opponent then opp += 1
- If mine == 5 then score = BIG_CONST
- Else if opp == 5 then score = -BIG_CONST
- Else if mine == 0 and opp > 0 then score -= -opp^AGG
- Else if opp == 0 and mine > 0 then score += mine^DEF
- Return score

AI and Heuristics

- Why BIG_CONST and not INFINITY?If more than one Fivlet is full (which is obviously better than one), the board’s score will still be INFINITY (INF + INF = INF).
- For each Fivlet in Board
- For each Slot in Fivlet
- If Slot is Mine then mine += 1
- Else if Slot is Opponent then opp += 1
- If mine == 5 then score = BIG_CONST
- Else if opp == 5 then score = -BIG_CONST
- Else if mine == 0 and opp > 0 then score -= -opp^AGG
- Else if opp == 0 and mine > 0 then score += mine^DEF
- Return score

AI and Heuristics

- AGG and DEFF? AGG is normally greater than DEF since playing aggressively (striving for full Fivlets) has better priority than playing defensively (preventing opponent’s Full Fivlets).
- For each Fivlet in Board
- For each Slot in Fivlet
- If Slot is Mine then mine += 1
- Else if Slot is Opponent then opp += 1
- If mine == 5 then score = BIG_CONST
- Else if opp == 5 then score = -BIG_CONST
- Else if mine == 0 and opp > 0 then score -= -opp^AGG
- Else if opp == 0 and mine > 0 then score += mine^DEF
- Return score

AI Analysis

Human

AI Analysis

Beginner

- Tested only 1 game due to exact results in all CPU vs. CPU games (due to the lack of a random factor).

AI Analysis

Experienced

- Tested only 1 game due to exact results in all CPU vs. CPU games (due to the lack of a random factor).

AI Analysis

Tough

- Tested only 1 game due to exact results in all CPU vs. CPU games (due to the lack of a random factor).

AI Analysis

Godlike

Enjoy the Game!

woot?