Vincent Ciarcia | Searcharxiv

arXiv2026

Limit Cases And Strategy In Chutes and Ladders

We analyze what happens to the average duration of a game of Chutes and Ladders as the probability of rolling $δ\in \{ 1,2,3,4,5,6\}$ approaches 100%. We utilize Markov models, and Monte Carlo simulations in Python. We also introduce strategy to the board game by allowing the player to choose whether or not they flip a coin after each die roll where if they get heads they will advance one square and if they get tails they will go back one square. The strategy the player employs to decide when to flip the coin has a significant impact on the average duration of the game. We analyze six different non-trivial strategies.

math.GM↗

arXiv2021

Markov models for the tipsy cop and robber game on graphs

In this paper we analyze and model three open problems posed by Harris, Insko, Prieto-Langarica, Stoisavljevic, and Sullivan in 2020 concerning the tipsy cop and robber game on graphs. The three different scenarios we model account for different biological scenarios. The first scenario is when the cop and robber have a consistent tipsiness level though the duration of the game; the second is when the cop and robber sober up as a function of time; the third is when the cop and robber sober up as a function of the distance between them. Using Markov chains to model each scenario we calculate the probability of a game persisting through $\mathbf{M}$ rounds of the game and the expected game length given different starting positions and tipsiness levels for the cop and robber.

math.CO↗