VBA 模拟中的随机数

Question

我正在尝试创建一个棒球季后赛模拟器，以了解糟糕的投手对球队的冠军赔率有多大影响。所以我基本上为季后赛创建了一个模拟器（3轮，第一轮是5局3胜，接下来的两轮是7局3胜）。我可以看到，如果 SP 每三场比赛就投球一次，并且他将获胜的机会减少 10%，那么他会对球队造成多大的伤害。

为了确保我写了这篇文章，我首先在没有任何调整的情况下运行模拟，这样每场比赛两支球队都有 50% 的获胜机会......（因此，一支球队有 12.5% 的机会赢得世界大赛） 3 轮季后赛）然而，我一直高于 12.5。

我感觉问题出在 Rnd 函数上，所以我玩了一下（添加了一个函数，尝试改变时间等），现在我的模拟结果是 <12.5%. I then tried to trouble shoot and noticed that in each round was not being won 50% of the time... which was the case each time I re-ran the simulation (Like round 1 would have a 47% success then round two 51% then round three 58%... then the next run would return 46%, 52%, 59%.

我做错了什么，还是这只是 rnd 函数不擅长处理的事情？

Public Function wRandomNumber(lowerbound, upperbound, Optional rndType = 1) As Double
Dim rndVariable As Double
'Const ms As Double = 0.000000011574

Randomize Timer
'Application.Wait Now + ms * 1
rndVariable = Rnd
If rndType = 1 Then
    wRandomNumber = Int((upperbound - lowerbound + 1) * rndVariable + lowerbound)
ElseIf rndType = 2 Then
    If (upperbound - lowerbound + 1) * rndVariable + lowerbound <= upperbound Then
        wRandomNumber = (upperbound - lowerbound + 1) * rndVariable + lowerbound
    Else
        Do While (upperbound - lowerbound + 1) * rndVariable + lowerbound > upperbound
            rndVariable = Rnd
            If (upperbound - lowerbound + 1) * rndVariable + lowerbound <= upperbound Then
                wRandomNumber = (upperbound - lowerbound + 1) * rndVariable + lowerbound
            End If
        Loop
    End If
End If
End Function

Public Sub Playoff_sim()

Dim game_num As Integer
Dim lds_wins_stros As Integer
Dim lds_loss_stros As Integer
Dim lcs_wins_stros As Integer
Dim lcs_loss_stros As Integer
Dim ws_wins_stros As Integer
Dim ws_loss_stros As Integer
Dim p As Double
Dim outcome1 As Single
Dim outcome2 As Single
Dim outcome3 As Single
Dim i As Double
Dim iter As Double
Dim CHAMPS As Double
Dim Loser As Double
Dim p_bad As Double
Dim p_norm As Double
Dim lds_champs As Double
Dim lcs_champs As Double
Dim r As Double
Const ms As Double = 0.000000011574

iter = 100000
CHAMPS = 0
Loser = 0
lds_champs = 0
lcs_champs = 0
p_bad = 0.5
p_norm = 0.5
r = 0
For i = 1 To iter

game_num = 1
lds_wins_stros = 0
lds_loss_stros = 0
lcs_wins_stros = 0
lcs_loss_stros = 0
ws_loss_stros = 0
ws_wins_stros = 0

Do Until lds_wins_stros = 3 Or lds_loss_stros = 3

outcome1 = wRandomNumber(0, 1, 2)
    If game_num = 3 Then
        p = p_bad
    Else
        p = p_norm
    End If

    If p > outcome1 Then
        lds_wins_stros = lds_wins_stros + 1
    Else
        lds_loss_stros = lds_loss_stros + 1
    End If
    r = r + 1
    'Worksheets("Playoff_Sim").Cells(r, 15).Value = outcome1

game_num = game_num + 1
Loop

If lds_wins_stros = 3 Then

    outcome2 = wRandomNumber(0, 1, 2)
    lds_champs = 1 + lds_champs
    Do Until lcs_wins_stros = 4 Or lcs_loss_stros = 4

    If game_num = 3 Or 6 Or 9 Or 12 Or 15 Or 18 Or 21 Then
        p = p_bad
    Else
        p = p_norm
    End If

    If p > outcome2 Then
        lcs_wins_stros = lcs_wins_stros + 1
    Else
        lcs_loss_stros = lcs_loss_stros + 1
    End If

    game_num = game_num + 1

    Loop

    If lcs_wins_stros = 4 Then
        lcs_champs = lcs_champs + 1

        outcome3 = wRandomNumber(0, 1, 2)
        Do Until ws_wins_stros = 4 Or ws_loss_stros = 4

            If game_num = 3 Or 6 Or 9 Or 12 Or 15 Or 18 Or 21 Then
                p = p_bad
            Else
                p = p_norm
            End If

            If p > outcome3 Then
                ws_wins_stros = ws_wins_stros + 1
            Else
                ws_loss_stros = ws_loss_stros + 1
            End If
        'r = r + 1
        game_num = game_num + 1
        'Worksheets("Playoff_Sim").Cells(r, 15).Value = outcome3
        Loop

        If ws_wins_stros = 4 Then
            CHAMPS = CHAMPS + 1
        Else
            Loser = Loser + 1
        End If

    Else
        Loser = Loser + 1
    End If

Else
    Loser = Loser + 1
End If

Next i

Worksheets("Playoff_Sim").Cells(2, 1).Value = CHAMPS
Worksheets("Playoff_Sim").Cells(2, 2).Value = Loser
Worksheets("Playoff_Sim").Cells(2, 3).Value = lds_champs
Worksheets("Playoff_Sim").Cells(2, 4).Value = lcs_champs

结束子

Answer 1

问题不仅在于随机数（可以通过@A.S.H的建议使用

Application.RandBetween

来解决），还在于模拟的逻辑。重复两次的代码片段

If game_num = 3 Or 6 Or 9 Or 12 Or 15 Or 18 Or 21 Then
    p = p_bad
Else
    p = p_norm
End If

相当于单行

p = p_bad

。这是因为条件

game_num = 3 Or 6 Or 9 Or 12 Or 15 Or 18 Or 21

始终评估为

True

，因为您仅将

game_num

与

3

进行比较，然后强制 VBA 将剩余数字 (6,9,15,18,21) 解释为

True

通过与它们一起使用

Or

运算符。相反，只需这样做：

If game_num Mod 3 = 0 Then
    p = p_bad
Else
    p = p_norm
End If

可能还有其他问题，但这应该足以让您开始。

Answer 2

我一直在探索随机数生成器，我注意到频繁重新随机化（我认为这就是随机计时器在这里所做的）实际上是有害的。

我一直在做一个简单的：

随机化 如果rnd

代码，随机化使数字偏向较低的值，使用此代码，我的测试成功率为 15%，统计上应该有 5% 的成功率。

我对模拟器进行了很多次运行，事实上，比我想要的还要多，因为这样的结果分布得更好，然后不断地重新随机化。