最佳策略是前三层只记住最大尺寸但不拿,第四层起见到比前三层最大的大就拿(若没见到就拿第十层的)。
以下是我的模拟结果:
Number of floors to skip: 1 Number of simulations: 1000000
Number of cases in which biggest diamond is found:283007. Probability: 0.28301
Theoretical probability: 0.2829
Number of floors to skip: 2 Number of simulations: 1000000
Number of cases in which biggest diamond is found:366243. Probability: 0.36624
Theoretical probability: 0.36579
Number of floors to skip: 3 Number of simulations: 1000000
Number of cases in which biggest diamond is found:397734. Probability: 0.39773
Theoretical probability: 0.39869
Number of floors to skip: 4 Number of simulations: 1000000
Number of cases in which biggest diamond is found:398637. Probability: 0.39864
Theoretical probability: 0.39825
Number of floors to skip: 5 Number of simulations: 1000000
Number of cases in which biggest diamond is found:372930. Probability: 0.37293
Theoretical probability: 0.37282
Number of floors to skip: 6 Number of simulations: 1000000
Number of cases in which biggest diamond is found:327176. Probability: 0.32718
Theoretical probability: 0.32738
Number of floors to skip: 7 Number of simulations: 1000000
Number of cases in which biggest diamond is found:265402. Probability: 0.2654
Theoretical probability: 0.26528
Number of floors to skip: 8 Number of simulations: 1000000
Number of cases in which biggest diamond is found:189241. Probability: 0.18924
Theoretical probability: 0.18889
Number of floors to skip: 9 Number of simulations: 1000000
Number of cases in which biggest diamond is found:100030. Probability: 0.10003
Theoretical probability: 0.1