Take a look at Bill Benter’s chart at 30:00 dead in this 2004 presentation to the International Congress of Chinese Mathematicians:
http://wmedia.hkedcity.net/archive/05/0 … pt04Ex.wmv(the whole thing is around a 120Mb download)
he starts on horses at about 23:20.
Thanks for that Wit
The graph Benter displays may not look remotely sinusoidal but as he points out the y-axis (on-going profit) is logarithmic rather than arithmetic and therefore smooths the line by attenuating the discrete maxima and minima; which perhaps somewhat misleadingly presents the on-going profit as a rather curvaceous steady climb without ‘hiccups’. Also the x-axis (number of races or bets) is a sample of 6000 (arithmetic) data points crammed into a narrow confine, which therefore compresses the discrete maxima and minima
I suspect that had the graph been arithmetic on both axes and the sample been say 500 data points taken over the same x-axis confine then it would have more closely resembled the over-simplistic "skewed sine wave" I proposed
In wave-form terms his graph both decreases the amplitude (logarithmic attenuation on the y-axis) and increases the frequency (arithmetic compression on the x-axis)
I think