Connect Four

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credit for this assignment: Finn Voichick and Dennis Cosgrove


Minimax is an important concept in game theory and search.

Negamax is a variant which relies on \max(a, b) = -\min(-a, -b)

While this technique is applicable to Chess (as Deep Blue employed to defeat Kasparov), we choose Connect Four as our context since it has a simpler game mechanic.

While the core part of searches like Minimax may be easy to parallelize, critical aspects such as alpha-beta pruning are more challenging.




Solving Connect Four




The Core Questions

  • What are the tasks?
  • What is the data?
  • Is the data mutable?
  • If so, how is it shared?

Code To Use


interface Board

createNextBoard(int column)


class Optional<T>


interface ToDoubleFunction<T>


interface IntPredicate


Mistakes To Avoid

Attention niels epting.svg Warning:Do NOT be lured in be Double.MIN_VALUE. Use Double.NEGATIVE_INFINITY instead.
Attention niels epting.svg Warning:
If you are going to use Double.NaN to indicate an invalid/unsearched column (which as an implementation detail, is not the worst choice) be sure you know what you are doing.
Double.NaN's semantics can absolutely be leveraged, but it can be tricky.

Code To Implement

NOTE: While you should defer to the IntPredicate searchAtDepth for when to continue to search (test returns true) or when to return an evaluation (test returns false), it is up to you to decide when to search in parallel and when to fall back to sequential search.



This private method will do the lion's share of the search. At each invocation either evaluating the board (if appropriate) selecting the evaluation which is worst for the opponent.

For this assignment, there are two conditions when is appropriate to evaluation the board via the specified heuristic:

  1. the board state indicates that the game is over.
  2. the searchAtDepth predicate test fails for the current depth.
class: Java.png
methods: negamaxKernel
source folder: src/main/java

method: private static double negamaxKernel(Board board, ToDoubleFunction<Board> heuristic, IntPredicate searchAtDepth, int currentDepth) Parallel.svg (parallel implementation required)


This public method will leverage negamaxKernel to search, but returns the (optional) column index of the chosen best move rather than the evaluation. If there is no move to make, the method should return Optional.empty().

method: public static Optional<Integer> selectNextColumn(Board board, ToDoubleFunction<Board> heuristic, IntPredicate searchAtDepth) Parallel.svg (parallel implementation required)

Win or Lose Heuristic

class: Java.png
methods: applyAsDouble
source folder: src/main/java

method: public double applyAsDouble(Board board) Sequential.svg (sequential implementation only)

Evaluate the current state of the Board. You should return a negative number if you have lost. You should return less negative numbers for losses that occur later. Put another way, draws should return 0. Losses on the final turn should return -1. Losses on the third to last turn should return -3. Wins should return the analogous positive numbers.

Interestingly (at least to the Professor), if you build your algorithm in an expected way, you will only need to handle draws as well as (wins or losses). Which one is it? Wins? Or losses?

OpenEndedHeuristic (Optional)

class: Java.png
methods: applyAsDouble
package: connectfour.challenge
source folder: src/main/java

method: public double applyAsDouble(Board board) Sequential.svg (sequential implementation only)

Testing Your Solution


class: Junit.png
source folder: src/test/java

Some preliminary tests use a simple end game board, destined for a draw, where the last three searches will end in Optional.of(6).

Simple end game test board.png


class: VIZ
source folder: src/visualization/java