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In 2010 we introduced our formulas for the chances of one item at auction attracting the “most interested bidder” (Alpha) and the “second most interested bidder” (Beta) noting that these are the only two bidders any auctioneer needs.

Our initial treatise on this subject is here: https://mikebrandlyauctioneer.wordpress.com/2010/01/12/auctioneer-looking-for-alpha-and-beta/.

Not long ago we updated and expanded this study in regard to a related court case and that treatise can be seen here: https://mikebrandlyauctioneer.wordpress.com/2019/04/01/auctioneers-alpha-and-beta-and-more/.

Due to some requests, here is a table noting B, X, Y, Y1, Y2 and Y3 for values of B from 0 to 100. Here (again) are the notations for those variables:

B = Number of bidders
X = Chances of having Alpha and Beta
Y = Chances of not having Alpha and Beta
Y1 = Chances of having Alpha and not Beta
Y2 = Chances of having Beta and not Alpha
Y3 = Chances of not having Alpha nor Beta

B
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100

X
0.00%
0.00%
11.11%
25.00%
36.00%
44.44%
51.02%
56.25%
60.49%
64.00%
66.94%
69.44%
71.60%
73.47%
75.11%
76.56%
77.85%
79.01%
80.06%
81.00%
81.86%
82.64%
83.36%
84.03%
84.64%
85.21%
85.73%
86.22%
86.68%
87.11%
87.51%
87.89%
88.25%
88.58%
88.90%
89.20%
89.48%
89.75%
90.01%
90.25%
90.48%
90.70%
90.91%
91.12%
91.31%
91.49%
91.67%
91.84%
92.00%
92.16%
92.31%
92.46%
92.60%
92.73%
92.86%
92.98%
93.11%
93.22%
93.34%
93.44%
93.55%
93.65%
93.75%
93.85%
93.94%
94.03%
94.12%
94.20%
94.29%
94.37%
94.45%
94.52%
94.60%
94.67%
94.74%
94.81%
94.87%
94.94%
95.00%
95.06%
95.12%
95.18%
95.24%
95.29%
95.35%
95.40%
95.46%
95.51%
95.56%
95.60%
95.65%
95.70%
95.75%
95.79%
95.83%
95.88%
95.92%
95.96%
96.00%
96.04%
96.08%

Y
100.00%
100.00%
88.89%
75.00%
64.00%
55.56%
48.98%
43.75%
39.51%
36.00%
33.06%
30.56%
28.40%
26.53%
24.89%
23.44%
22.15%
20.99%
19.94%
19.00%
18.14%
17.36%
16.64%
15.97%
15.36%
14.79%
14.27%
13.78%
13.32%
12.89%
12.49%
12.11%
11.75%
11.42%
11.10%
10.80%
10.52%
10.25%
9.99%
9.75%
9.52%
9.30%
9.09%
8.88%
8.69%
8.51%
8.33%
8.16%
8.00%
7.84%
7.69%
7.54%
7.40%
7.27%
7.14%
7.02%
6.89%
6.78%
6.66%
6.56%
6.45%
6.35%
6.25%
6.15%
6.06%
5.97%
5.88%
5.80%
5.71%
5.63%
5.55%
5.48%
5.40%
5.33%
5.26%
5.19%
5.13%
5.06%
5.00%
4.94%
4.88%
4.82%
4.76%
4.71%
4.65%
4.60%
4.54%
4.49%
4.44%
4.40%
4.35%
4.30%
4.25%
4.21%
4.17%
4.12%
4.08%
4.04%
4.00%
3.96%
3.92%

Y1
0.00%
22.22%
44.44%
37.50%
32.00%
27.78%
24.49%
21.88%
19.75%
18.00%
16.53%
15.28%
14.20%
13.27%
12.44%
11.72%
11.07%
10.49%
9.97%
9.50%
9.07%
8.68%
8.32%
7.99%
7.68%
7.40%
7.13%
6.89%
6.66%
6.44%
6.24%
6.05%
5.88%
5.71%
5.55%
5.40%
5.26%
5.12%
5.00%
4.88%
4.76%
4.65%
4.54%
4.44%
4.35%
4.25%
4.16%
4.08%
4.00%
3.92%
3.84%
3.77%
3.70%
3.64%
3.57%
3.51%
3.45%
3.39%
3.33%
3.28%
3.22%
3.17%
3.12%
3.08%
3.03%
2.98%
2.94%
2.90%
2.86%
2.82%
2.78%
2.74%
2.70%
2.67%
2.63%
2.60%
2.56%
2.53%
2.50%
2.47%
2.44%
2.41%
2.38%
2.35%
2.33%
2.30%
2.27%
2.25%
2.22%
2.20%
2.17%
2.15%
2.13%
2.11%
2.08%
2.06%
2.04%
2.02%
2.00%
1.98%
1.96%

Y2
0.00%
4.44%
8.89%
15.00%
16.94%
17.09%
16.55%
15.75%
14.89%
14.05%
13.26%
12.52%
11.85%
11.24%
10.68%
10.16%
9.69%
9.26%
8.87%
8.50%
8.17%
7.85%
7.56%
7.29%
7.04%
6.81%
6.59%
6.38%
6.18%
6.00%
5.83%
5.66%
5.51%
5.36%
5.22%
5.09%
4.97%
4.85%
4.73%
4.63%
4.52%
4.42%
4.33%
4.24%
4.15%
4.06%
3.98%
3.91%
3.83%
3.76%
3.69%
3.62%
3.56%
3.50%
3.44%
3.38%
3.32%
3.27%
3.22%
3.17%
3.12%
3.07%
3.02%
2.98%
2.93%
2.89%
2.85%
2.81%
2.77%
2.73%
2.70%
2.66%
2.63%
2.59%
2.56%
2.53%
2.50%
2.47%
2.44%
2.41%
2.38%
2.35%
2.32%
2.30%
2.27%
2.24%
2.22%
2.20%
2.17%
2.15%
2.13%
2.10%
2.08%
2.06%
2.04%
2.02%
2.00%
1.98%
1.96%
1.94%
1.92%

Y3
100.00%
73.33%
35.56%
22.50%
15.06%
10.68%
7.94%
6.13%
4.86%
3.95%
3.27%
2.76%
2.35%
2.03%
1.77%
1.56%
1.38%
1.23%
1.10%
1.00%
0.90%
0.82%
0.75%
0.69%
0.64%
0.59%
0.55%
0.51%
0.48%
0.44%
0.42%
0.39%
0.37%
0.35%
0.33%
0.31%
0.29%
0.28%
0.26%
0.25%
0.24%
0.23%
0.22%
0.21%
0.20%
0.19%
0.18%
0.17%
0.17%
0.16%
0.15%
0.15%
0.14%
0.14%
0.13%
0.13%
0.12%
0.12%
0.11%
0.11%
0.11%
0.10%
0.10%
0.10%
0.09%
0.09%
0.09%
0.09%
0.08%
0.08%
0.08%
0.08%
0.08%
0.07%
0.07%
0.07%
0.07%
0.07%
0.06%
0.06%
0.06%
0.06%
0.06%
0.06%
0.06%
0.05%
0.05%
0.05%
0.05%
0.05%
0.05%
0.05%
0.05%
0.05%
0.04%
0.04%
0.04%
0.04%
0.04%
0.04%
0.04%

As we have said before, a good lesson for auctioneers is that there is a point that the advantages of one more bidder is outweighed by the expense of securing such bidder.

Mike Brandly, Auctioneer, CAI, CAS, AARE has been an auctioneer and certified appraiser for over 30 years. His company’s auctions are located at: Mike Brandly, Auctioneer, RES Auction Services and Goodwill Columbus Car Auction. He serves as Distinguished Faculty at Hondros College, Executive Director of The Ohio Auction School, an Instructor at the National Auctioneers Association’s Designation Academy and America’s Auction Academy. He is faculty at the Certified Auctioneers Institute held at Indiana University and is approved by the The Supreme Court of Ohio for attorney education.