Monty Hall 模拟仅 44%

Question

我刚刚为 Monty Hall 问题创建了一个模拟，但我的结果（即使有 10,000,000 次测试）还是很奇怪。对于策略 1（保持），命中率为 1/3，而策略 2（转换）为 44.44%。代码有错吗？

谢谢大家！

var hits1 = 0
var hits2 = 0
let testsNumber = 1000

for i in 0..<testsNumber {

    var doors: [Int] = []

    for i in 0..<3 {
        doors.append(0) // Append closed door
    }

    doors[Int(arc4random_uniform(UInt32(doors.count)))] = 1 // Here's the car...        
    var selection = Int(arc4random_uniform(UInt32(doors.count))) // Select door


    if doors[selection] == 1 {
        hits1 += 1
    }

    // Open first closed door
    for i in 0..<doors.count {
        if doors[i] != 1 {
            doors[i] = -1 // Open door
            break
        }
    }

    // Switch to next closed door
    repeat {
        selection = (selection + 1) % doors.count 
    } while(doors[selection] == -1)

    if doors[selection] == 1 {
        hits2 += 1
    }

}

print("Hits: \(hits1), quote: \((Double) (hits1) / (Double) (testsNumber))")
print("Hits: \(hits2), quote: \((Double) (hits2) / (Double) (testsNumber))")

Answer 1

Monty Hall 问题说 "pick a door; before I open it, I'll show what's behind one of the other doors (one that doesn't have a car) and let you stay with your initial selection or switch to the other closed door"。

但请考虑：

for i in 0 ..< doors.count {
    if doors[i] != 1 {
        doors[i] = -1 // Open door
        break
    }
}

这实际上是说 "show the contestant what's behind the first door that doesn't have a car"。

但是，您没有考虑这扇门可能是参赛者已经选择的那扇门的可能性。那就是改变游戏的参数。

你的意思是"open a door that does not have a car and is not the door the contestant picked."

for i in 0 ..< doors.count {
    if doors[i] != 1 && i != selection {
        doors[i] = -1 // Open door
        break
    }
}

当你这样做时，你总是改变你的选择（已经显示其他两扇没有车的门之一）的几率上升到 2/3。

Monty Hall 模拟仅 44%

Monty Hall simulation only 44%

simulation

math

swift