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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 by Jan. 15, 2014. The winner, chosen randomly from correct answers, will receive a Magic 8 Ball. Past questions can be found at

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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