Analyzing Transition Matrices of Chutes and Ladders Game Variant

Imagine each directional chute and ladder in the classic board game replaced with bidirectional portals. How does the game change? Expected game play and probabilities of each position are determined by the location and type of eigenvalues. We analyzed the transition matrix and discovered Gershgorin eigenvalue bounds for each board layout were constructed from a limited set of Gershgorin disks. Further, we discovered a minimum bounding region for the eigenvalues, independent of location and number of portals on the board.