Kelly comparison to a another approach

It’s impossible to prove that Kelly provides the ultimate bet sizing versus all other systems using simulations. That’s because there’s an infinite number of alternative systems. I decided to compare Kelly with a similar system. Kelly uses the expected result to determine a percentage that is multiplied by your remaing bankroll to get a bet size. Thus, in a good season, your bets and returns grow somewhat exponentially. So, I ran simulations using bets based on a percent times bankroll, where the percent isn’t based on expected results but a constant. Following is a table of the results.

Ave Pct	Ave Bet	Ave Net	Ave Final Net	Max Last Balance	Min Last Balance	Positive Seasons	Ave Wins	Ret/$
0.50%	$5.07	$0.26	$25.96	$182	-$129	70.6%	55.1	1.051
1.00%	$10.28	$0.53	$52.54	$394	-$244	70.6%	55.1	1.051
1.50%	$15.64	$0.80	$79.73	$640	-$345	70.6%	55.1	1.051
2.00%	$21.14	$1.08	$107.52	$926	-$433	70.6%	55.1	1.051
2.50%	$26.80	$1.36	$135.92	$1,256	-$511	70.6%	55.1	1.051
3.00%	$32.62	$1.65	$164.93	$1,637	-$579	63.6%	55.1	1.051
3.50%	$38.60	$1.95	$194.54	$2,076	-$639	63.6%	55.1	1.05
4.00%	$44.75	$2.25	$224.74	$2,581	-$691	63.6%	55.1	1.05
4.50%	$51.07	$2.56	$255.53	$3,159	-$736	63.6%	55.1	1.05
5.00%	$57.57	$2.87	$286.90	$3,820	-$775	63.6%	55.1	1.05
5.50%	$64.24	$3.19	$318.85	$4,574	-$809	63.6%	55.1	1.05
6.00%	$71.11	$3.51	$351.37	$5,433	-$838	63.6%	55.1	1.049
6.50%	$78.16	$3.84	$384.45	$6,408	-$863	63.6%	55.1	1.049
7.00%	$85.42	$4.18	$418.08	$7,512	-$884	56.4%	55.1	1.049
7.50%	$92.87	$4.52	$452.25	$8,759	-$902	56.4%	55.1	1.049
8.00%	$100.54	$4.87	$486.96	$10,166	-$918	56.4%	55.1	1.048
8.50%	$108.41	$5.22	$522.18	$11,748	-$931	56.4%	55.1	1.048
9.00%	$116.51	$5.58	$557.91	$13,522	-$943	56.4%	55.1	1.048
9.50%	$124.83	$5.94	$594.13	$15,509	-$952	56.4%	55.1	1.048
10.00%	$133.38	$6.31	$630.83	$17,727	-$960	56.4%	55.1	1.047

The results show the same as trends as the Kelly results in the previous chart. Bigger bets and better results as the percent increases. But the number of positive seasons and “Ret/S” get worse with higher percentages.

If you compare the corresponding lines in this table with the Kelly table in the previous post, you will note that these wagers are about 10% higher. But the results are significantly higher across the board. The net result is a demonstration that Kelly (with whatever multiplier) is significantly better than this approach.

It’s time to wind up this project and draw some conclusions. That will be the next post. I’ll tweet on twitter, @ole44bill, when this is done.