Consider the following two theoretical systems. System 1: There is a 60% chance that you win your bet ; there is a 40% chance that you lose your bet. System 2: There is a 3% chance that you win 100 times your bet ; there is a 57% chance that you win your bet ; there is a 38% chance that you lose your bet ; there is a 2% chance that you lose 100 times your bet. These two systems have identical winrates and identical win/loss ratios, but it's hard for me to believe that they are "equivalent". What say you? Is there some objective measure of whether one system is better than the other?

Unless I messed up the math, system 2 has higher expectancy. System 1: expectancy = (0.6*1 - 0.4*1) = 0.2 System 2: expectancy = (0.03*100 + 0.57*1 - 0.38*1 - 0.02*100) = 1.19

Excellent point. How much you can expect to win per unit risked may be the best way to go. But here's the fly in the ointment. System 3: There is a 60% chance that you win 100 times your bet ; there is a 40% chance that you lose 100 times your bet. The expectancy of system 3 is 20 (i.e., 100 times the expectancy of system 1) BUT the Kelly fraction of system 3 is .002 (i.e., .01 times the Kelly fraction of system 1). So an optimal bet is identical for both systems. For a $1000 betting account: System 1 says to bet $200 for an expected return of $40. System 3 says to bet $2 for an expected return of $40. So are system 1 and system 3 equivalent or does expectancy trump optimal bet size?

It might be a matter of semantics, but in any game I can think of at this time the amount bet is the amount you are willing to lose ... as a result, system 3 is identical to system 1. I would suggest you normalize all these scenarios so that the maximum loss is the amount bet.

Semantically speaking, I would say that system 1 and system 3 are not identical but they are equivalent in performance. Thanks to stevegee58, I figured out how to improve my performance measure. Rather than the Kelly fraction times the average win, much better is the Kelly fraction times expectancy. With that in mind, k[ 1 ] = .6/1 - .4/1 = .2 k[ 2 ] = 0.00235 k*E[ 1 ] = 0.2*0.2 = 0.04 k*E[ 2 ] = 0.00235*1.19 = 0.0028 System 1 is better than system 2.

There is always a slight chance your system will hit 5 times of the 2% - lose 100 times bet in a row. After that you get strike out ?

Good systems are not proved on paper with algebra but based on balance account. Institutions would seed both and then after 6 months drop one or both (most probably ).

Do you think large institutions with money and time to burn are the only entities interested in evaluating trading systems? Seriously?

No, but that are the only entities that can do it on a large scale with real money and that is one reason they have an edge over retail. I hope you see the difference.