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Samsung Note 7 recall over exploding batteries

Genetic art?

Nim

Make k piles of any number of coins

Take turns taking any number (>0) of coins from a single pile

Player that takes the last coin wins

Nim Strategy?

Simple Nim

Make 2 piles of coins- One pile has a single coin- Other pile has two coins

Play a couple of rounds

Would you rather go first or second?

Nim Game Tree Pile #1 Pile #2

Take 1pile #1

Take 1pile #2

Take 2pile #2

Nim Game Tree Pile #1 Pile #2

Take 1pile #1

Take 1pile #2

Take 2pile #2

Take 1pile #2

Take 2pile #2

Take 1pile #2Take 1

pile #1

Take 1pile #1

Nim Game Tree Pile #1 Pile #2

Take 1pile #1

Take 1pile #2

Take 2pile #2

Take 1pile #2

Take 2pile #2

Take 1pile #2

Take 1pile #2Take 1

pile #1

Take 1pile #1

Take 1pile #2

Take 1pile #1

Nim Game Tree Pile #1 Pile #2

Take 1pile #1

Take 1pile #2

Take 2pile #2

Take 1pile #2

Take 2pile #2

Take 1pile #2

1

Take 1pile #2Take 1

pile #1

Take 1pile #1

Take 1pile #2

Take 1pile #1

Player1 wins

Nim Game Tree Pile #1 Pile #2

Take 1pile #1

Take 1pile #2

Take 2pile #2

Take 1pile #2

-1

Take 2pile #2

Take 1pile #2

1

Take 1pile #2Take 1

pile #1

Take 1pile #1

-1

Take 1pile #2

1

Take 1pile #1

1

All winning values in leaves

Nim Game Tree

1

Pile #1 Pile #2

Take 1pile #1

Take 1pile #2

Take 2pile #2

Take 1pile #2

-1

Take 2pile #2

Take 1pile #2

1

Take 1pile #2Take 1

pile #1

Take 1pile #1

-1

Take 1pile #2

1

Take 1pile #1

1

Propagate best moves up:Player1 does the

maximum value move

Nim Game Tree

1

-1

Pile #1 Pile #2

Take 1pile #1

Take 1pile #2

Take 2pile #2

Take 1pile #2

-1

Take 2pile #2

Take 1pile #2

1

Take 1pile #2Take 1

pile #1

Take 1pile #1

-1

Take 1pile #2

1

Take 1pile #1

1

Propagate best moves up:Player2 does the

minimum value move

Nim Game Tree

1

-1

Pile #1 Pile #2

Take 1pile #1

Take 1pile #2

Take 2pile #2

Take 1pile #2

-1

Take 2pile #2

Take 1pile #2

1

1

Take 1pile #2Take 1

pile #1

Take 1pile #1

-1

Take 1pile #2

1

Take 1pile #1

1

Propagate best moves up:Player1 does the

maximum value move

Nim Game Tree

1

-1

Pile #1 Pile #2

Take 1pile #1

Take 1pile #2

Take 2pile #2

Take 1pile #2

-1

Take 2pile #2

Take 1pile #2

1

1

Take 1pile #2

1

Take 1pile #1

Take 1pile #1

-1

Take 1pile #2

1

Take 1pile #1

1

Propagate best moves up:Player1 does the

maximum value move

Nim Game Tree

1

-1 1

Pile #1 Pile #2

Take 1pile #1

Take 1pile #2

Take 2pile #2

Take 1pile #2

-1

Take 2pile #2

Take 1pile #2

1

1

Take 1pile #2

1

Take 1pile #1

Take 1pile #1

-1

Take 1pile #2

1

Take 1pile #1

1

Propagate best moves up:Player2 does the

minimum value move

Nim Game Tree

1

-1 1 -1

Pile #1 Pile #2

Take 1pile #1

Take 1pile #2

Take 2pile #2

Take 1pile #2

-1

Take 2pile #2

Take 1pile #2

1

1

Take 1pile #2

1

Take 1pile #1

Take 1pile #1

-1

Take 1pile #2

1

Take 1pile #1

1

Propagate best moves up:Player2 does the

minimum value move

Nim Game Tree

1

1

-1 1 -1

Pile #1 Pile #2

Take 1pile #1

Take 1pile #2

Take 2pile #2

Take 1pile #2

-1

Take 2pile #2

Take 1pile #2

1

1

Take 1pile #2

1

Take 1pile #1

Take 1pile #1

-1

Take 1pile #2

1

Take 1pile #1

1

Propagate best moves up:Player1 does the

maximum value move

Nim Game Tree

1

1

-1 1 -1

Pile #1 Pile #2

Take 1pile #1

Take 1pile #2

Take 2pile #2

Take 1pile #2

-1

Take 2pile #2

Take 1pile #2

1

1

Take 1pile #2

1

Take 1pile #1

Take 1pile #1

-1

Take 1pile #2

1

Take 1pile #1

1

Value of the game tree:Player1 wins.

Minimax Algorithm

Each player should select the move that minimizes the other player's maximum (best) move

Problems with Minimax?

Our old friend: tree size

Let's minimax again...

Player2 wants a minimum value.

Player2 wants a minimum value.

Player2 wants a minimum value.

WAIT! 4 is less than Player1's other option of 5.

Player1 will always pick 5.

Since Player2 wants a minimum value, we know that C will be 4 or less

without checking G and H.

Prune away node C.

Don't bother checking any of its entire subtree!

Alpha-Beta Pruning Key Idea

If a player has a better move further up the tree than the best move further down, then prune!

Alpha-Beta Pruningalpha: maximizing player's best (highest) value yet seen

beta: minimizing player's best (lowest) value yet seen

Alpha-Beta Pruningalpha: maximizing player's best (highest) value yet seen

beta: minimizing player's best (lowest) value yet seen

Do DFS and when alpha gets bigger than beta, prune by ending that recursive path

Alpha-Beta Code

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