游戏获胜者之间利润的对数分布

Question

我有一个赠品，完成后，有一张玩家和他们的得分表。 另一方面，我有一个虚拟的钱罐，我想分配给这些获胜者。我正在寻找一个 SQL 查询或一段 C# 代码来执行此操作。

降序排列的表格如下所示：

UserId | Name | Score | Position | % of winnings | abs. winnings $
00579  | John | 754   | 1        |  ?            | 500 $    
98983  | Sam  | 733   | 2        |  ?            | ?    
29837  | Rick | 654   | 3        |  ?            | ?    <- there are 2 3rd places
21123  | Hank | 654   | 3        |  ?            | ?    <- there are 2 3rd places
99821  | Buck | 521   | 5        |  ?            | ?    <- there is no 4th, because of the 2 3rd places
92831  | Joe  | 439   | 6        |  ?            | ?    <- there are 2 6rd places 
99281  | Jack | 439   | 6        |  ?            | ?    <- there are 2 6rd places 
12345  | Hal  | 412   | 8        |  ?            | ?    
98112  | Mick | 381   | 9        |  ?            | ?    
and so on, until position 50 
98484  | Sue  | 142   | 50       |  ?            | 5 $ 

注意双第 3 和第 6 名。

现在我想在前 50 个职位中分配（虚拟）资金总额（10,000 美元）。 （如果分配的位置（现在是 50）可以是一个变量，那就太好了）。

最大和最小数量（对于 nr 1 和 nr 50）固定为 500 和 5。

是否有人对 SQL 查询或一段 C# 代码有一个好主意来正确地用 % of bonuss 和 absolutewinnings$ 填充列？

我更喜欢这样一个看起来有点对数的分布：（这使得较高的位置相对于较低的位置获得更多）。

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Answer 1

自 1994 年以来我没有使用过 SQL，但我喜欢 C# :-)。以下可能适合，根据需要调整DistributeWinPot.DistributeWinPot(...)的参数：

private class DistributeWinPot {

    private static double[] GetWinAmounts(int[] psns, double TotWinAmounts, double HighWeight, double LowWeight) {
        double[] retval = new double[psns.Length];
        double fac = -Math.Log(HighWeight / LowWeight) / (psns.Length - 1), sum = 0;
        for (int i = 0; i < psns.Length; i++) {
            sum += retval[i] = (i == 0 || psns[i] > psns[i - 1] ? HighWeight * Math.Exp(fac * (i - 1)) : retval[i - 1]);
        }
        double scaling = TotWinAmounts / sum;
        for (int i = 0; i < psns.Length; i++) {
            retval[i] *= scaling;
        }
        return retval;
    }

    public static void main(string[] args) {
        // set up dummy data, positions in an int array
        int[] psns = new int[50];
        for (int i = 0; i < psns.Length; i++) {
            psns[i] = i+1;
        }
        psns[3] = 3;
        psns[6] = 6;
        double[] WinAmounts = GetWinAmounts(psns, 10000, 500, 5);
        for (int i = 0; i < psns.Length; i++) {
            System.Diagnostics.Trace.WriteLine((i + 1) + "," + psns[i] + "," + string.Format("{0:F2}", WinAmounts[i]));
        }
    }
}

该代码的输出是：

1,1,894.70
2,2,814.44
3,3,741.38
4,3,741.38
5,5,614.34
6,6,559.24
7,6,559.24
8,8,463.41
9,9,421.84
10,10,384.00
11,11,349.55
12,12,318.20
13,13,289.65
14,14,263.67
15,15,240.02
16,16,218.49
17,17,198.89
18,18,181.05
19,19,164.81
20,20,150.03
21,21,136.57
22,22,124.32
23,23,113.17
24,24,103.02
25,25,93.77
26,26,85.36
27,27,77.71
28,28,70.74
29,29,64.39
30,30,58.61
31,31,53.36
32,32,48.57
33,33,44.21
34,34,40.25
35,35,36.64
36,36,33.35
37,37,30.36
38,38,27.64
39,39,25.16
40,40,22.90
41,41,20.85
42,42,18.98
43,43,17.27
44,44,15.72
45,45,14.31
46,46,13.03
47,47,11.86
48,48,10.80
49,49,9.83
50,50,8.95

Answer 2

那么这个怎么样？

Select userid, log(score),
   10000 * log(score) / 
      (Select Sum(log(score)) 
       From TableName
       Where score >=
            (Select Min(score) 
             from (Select top 50 score     
                   From TableName
                   Order By score desc) z)) 
From TableName
Order By score desc