掷骰直到出现相邻相等：总和为偶的概率
What is the probability that this sum is an even number?
题目详情
A standard six- sided die is rolled until two consecutive outcomes are equal. All the numbers obtained up to that point are summed. What is the probability that this sum is an even number?
解析
把状态按“上一掷的奇偶”和“当前总和奇偶”归类，利用对称性可写成 4 状态马尔可夫链并解线性方程。
解得最终总和为偶数的概率为