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Analytics Magazine

Thinking Analytically: Mini Chutes and Ladders

November/December 2013

By John Toczek

“Chutes and Ladders” is a popular children’s game where players compete to move along a game board the fastest. It involves both hazard squares that can set you back a few spaces and some helpful squares that can move you forward a few spaces. A mini version of the game is displayed in Figure 1.

Figure 1: On average, how many spins to finish?
Figure 1: On average, how many spins to finish?

A player starts at the red “Start” square and finishes at the green “Finish” square. A player advances along the board by spinning a spinner that results in moving forward one to three squares.

If a player ends his turn on a ladder (depicted by the blue ladder icon) he immediately moves upwards along the ladder. For example, if a player ends his turn on square 6, he would immediately move to square 11.

If a player ends his turn on a chute (depicted by the orange slide) he immediately moves down the slide. For example, if a player ends his turn on square 7, he would automatically move to square 2.
A player wins the game when he lands on or passes the Finish square.

Question: What is the average number of turns needed to finish the game? (Please provide your answer with one decimal place.)

Send your answer to puzzlor@gmail.com by Jan. 15, 2014. The winner, chosen randomly from correct answers, will receive a Magic 8 Ball. Past questions can be found at puzzlor.com.

John Toczek is the director of Decision Support and Analytics for ARAMARK Corporation in the Global Risk Management group. He earned a bachelor’s of science degree in chemical engineering at Drexel University (1996) and a master’s degree in operations research from Virginia Commonwealth University (2005). He is a member of INFORMS.

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