Comparing 50% Kelly with full Kelly in the last post really
didn’t lead to significant conclusions. So, I elected to try again with a wider
range of multipliers. I started with 0.1 multiplier of the Kelly recommendation,
adding 0.1 until I reached 2.0 times the recommended Kelly. Following is a
table of the results. (Note that the numbers generated for 0.5 and 1.0 don’t
quite match those in the last post. That’s because looping through varying
multipliers changed the sequence of the random numbers.)
|
Kelly Mult
|
Ave Kelly Pct
|
Ave Kelly Bet
|
Ave Kelly Net
|
Ave Final Net
|
Max Last Balance
|
Min Last Balance
|
Positive Seasons
|
Ave Wins
|
Ret/$
|
|
0.1
|
0.56%
|
$5.61
|
$0.38
|
$37.98
|
$237
|
-$154
|
73.1%
|
55.1
|
1.068
|
|
0.2
|
1.10%
|
$11.45
|
$0.77
|
$77.29
|
$526
|
-$287
|
72.0%
|
55.1
|
1.068
|
|
0.3
|
1.66%
|
$17.52
|
$1.18
|
$117.95
|
$875
|
-$401
|
71.6%
|
55.1
|
1.067
|
|
0.4
|
2.20%
|
$23.84
|
$1.60
|
$159.96
|
$1,297
|
-$499
|
70.5%
|
55.1
|
1.067
|
|
0.5
|
2.74%
|
$30.42
|
$2.03
|
$203.34
|
$1,804
|
-$583
|
69.4%
|
55.1
|
1.067
|
|
0.6
|
3.30%
|
$37.26
|
$2.48
|
$248.09
|
$2,412
|
-$654
|
68.3%
|
55.1
|
1.067
|
|
0.7
|
3.86%
|
$44.38
|
$2.94
|
$294.21
|
$3,138
|
-$713
|
66.8%
|
55.1
|
1.066
|
|
0.8
|
4.40%
|
$51.78
|
$3.42
|
$341.71
|
$4,003
|
-$764
|
66.2%
|
55.1
|
1.066
|
|
0.9
|
4.96%
|
$59.47
|
$3.91
|
$390.59
|
$5,028
|
-$806
|
65.6%
|
55.1
|
1.066
|
|
1.0
|
5.50%
|
$67.47
|
$4.41
|
$440.84
|
$6,240
|
-$842
|
64.5%
|
55.1
|
1.065
|
|
1.1
|
6.06%
|
$75.79
|
$4.92
|
$492.46
|
$7,669
|
-$871
|
62.7%
|
55.1
|
1.065
|
|
1.2
|
6.60%
|
$84.43
|
$5.45
|
$545.44
|
$9,345
|
-$895
|
61.6%
|
55.1
|
1.065
|
|
1.3
|
7.16%
|
$93.42
|
$6.00
|
$599.78
|
$11,307
|
-$916
|
60.1%
|
55.1
|
1.064
|
|
1.4
|
7.70%
|
$102.75
|
$6.55
|
$655.46
|
$13,593
|
-$932
|
57.9%
|
55.1
|
1.064
|
|
1.5
|
8.24%
|
$112.44
|
$7.12
|
$712.47
|
$16,250
|
-$946
|
57.0%
|
55.1
|
1.063
|
|
1.6
|
8.80%
|
$122.50
|
$7.71
|
$770.80
|
$19,325
|
-$957
|
56.3%
|
55.1
|
1.063
|
|
1.7
|
9.36%
|
$132.94
|
$8.30
|
$830.42
|
$22,874
|
-$966
|
55.4%
|
55.1
|
1.062
|
|
1.8
|
9.90%
|
$143.77
|
$8.91
|
$891.31
|
$26,953
|
-$973
|
54.1%
|
55.1
|
1.062
|
|
1.9
|
10.46%
|
$155.01
|
$9.53
|
$953.44
|
$31,625
|
-$979
|
52.9%
|
55.1
|
1.062
|
|
2.0
|
11.00%
|
$166.67
|
$10.17
|
$1,016.80
|
$36,958
|
-$983
|
51.0%
|
55.1
|
1.061
|
Not unexpectedly, the higher the multiplier the higher the
Kelly percentage. This results in larger bets, net profits, final net, higher maximum
year, and higher maximum losses. The “Ret/$” falls at higher multipliers. An
interesting number is the percent of positive seasons. These decline from 73.1%
at 0.1 to 51.0% at 2.0. I could not see any significant change at 1.0 from
those around it.
I posted this table on sportsbookreview.com in the Handicapper
Think Tank forum. User “HeeeHAWWWW” responded with a formula that indicates the
1.0 is the mathematically proven optimum multiplier. Further, using a 2.0
multiplier will ultimately results in $0 expected gain. I believe that is
likely true if instead of using 1,000 seasons of 100 bets, one just looked at 1
season of unlimited bets.
