2012/09/10 by Sebastian Böcker, Böcker, Sebastian
Computer Science · Mathematics · #Artificial Intelligence in Games #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #F.2.2 #FOS: Computer and information sciences #G.2.1 #K.8.0 #Optimization and Search Problems #Probability and Statistical Research #cs.DM #cs.DS
paper · pdf · doi:10.48550/arxiv.1209.1977
10 pages
arxiv created 2012/09/10 · openalex publication_date 2012/09/10 · arxiv updated 2012/09/11 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
We consider the following simple game: We are given a table with ten slots indexed one to ten. In each of the ten rounds of the game, three dice are rolled and the numbers are added. We then put this number into any free slot. For each slot, we multiply the slot index with the number in this slot, and add up the products. The goal of the game is to maximize this score. In more detail, we play the game many times, and try to maximize the sum of scores or, equivalently, the expected score. We present a strategy to optimally play this game with respect to the expected score. We then modify our strategy so that we need only polynomial time and space. Finally, we show that knowing all ten rolls in advance, results in a relatively small increase in score. Although the game has a random component and requires a non-trivial strategy to be solved optimally, this strategy needs only polynomial time and space.