Logarithmic distribution of profits among game winners
I have a gave, which, when it's finished, has a table of players and their scores. On the other hand i have a virtual pot of money that i want to distribute among these winners. I'm looking for a SQL query or piece of C# code to do so.
The descending sorted table looks like this:
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 $
Be aware of the double 3rd and 6th places.
Now i want to distribute the total amount of (virtual) money ($ 10,000) among the first 50 positions. (It would be nice if the positions to distribute among (which is now 50) can be a variable).
The max and min amount (for nr 1 and nr 50) are fixed at 500 and 5.
Does anyone have a good idea for a SQL query or piece of C# code to fill the columns with % of winnings and absolute winnings $ correctly?
I prefer to have a distribution that looks a bit logarithmic like this: (which makes that the higher positions get relatively more than the lower ones).
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I haven't done SQL since 1994, but I like C# :-). The following might suit, adjust parameters of DistributeWinPot.DistributeWinPot(...) as required:
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]));
}
}
}
Output from that code was:
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
那这个怎么样？
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
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