Combinatorial Games
What's the name for the type of game where the last person to move wins?
A normal-play game
What type of game is Hackenbush?
Combinatorial, partizan, normal-play
Here's the payoff matrix for the row player in a zero-sum game. What is the column player's payoff matrix?
[-1 3
5 7]
[1 -3
-5 -7]
General strategic.
What is Aly's favorite sport to watch?
Baseball
What does Zermelo's Theorem say?
In any combinatorial game, exactly one player has a winning strategy or both players have drawing strategies.
What is the binary expansion of 137?
128+8+1 or 10001001
What is a Nash equilibrium?
A pair of strategies such that each is the best response to the other.
What are Dr. Thurber's cats named?
Raven and Pipit
What is a strategy?
A set of decisions indicating which move to make at each node where you have a choice.
What are the requirements for a combinatorial game?
You're the first player in this Nim game. What is your best move?
*6 + *5 + *2
Take one from the pile of 5.
Create a payoff matrix to go with the game tree on the board.
[ (1,0) (0,1)
(0,1) (1,0) ]
Create a game tree for a four-kitten position in pick-up-kittens with Richard moving first (like pick-up-bricks, but with kittens).
(picture on board)
As of Monday afternoon, Alex L. holds the world record in the milk-and-bog-water chug. What was his world record time? Answers within two seconds are acceptable.
41.83 seconds (accept answers between 39.83 and 43.83 seconds)
Draw a type R position in Domineering that uses exactly three squares.
What does the Sprague-Grundy Theorem say?
Every impartial, normal-play game is equivalent to a nimber.
Remember the payoff matrix for 2-finger Morra:
[ 0 2 -3 0
-2 0 0 3
3 0 0 -4
0 -3 4 0]
What is the payoff when R plays [0, 2/3, 1/3, 0] and C always plays C3?
0 for both players
Cat story
Nash equilibrium at (-5, -5), when they both tattle.
Find the best pure strategies for the matrix
[ 0 6 1
2 5 0
6 4 3 ]
R3, C3
Use position notation to represent a 2x3 position in Cut-cake.
(On board)
What is the value of the Hackenbush position with one blue line pointing straight up with one red line on top of it?
1/2
Find all Nash equilibria in the following payoff matrix:
[(3,-1) (-2,-3)
(2,5) (0,6)]
Two pure Nash equilibria: R1C1 and R2C2
One mixed Nash equilibrium: row player uses [1/3, 2/3] and column player uses [2/3, 1/3]
Classify the Hackenbush position (on the board) as L, R, N, or P.
Type P
1.5 million