I've only had time for a quick look at this Bluff. (http://www.cut-the-knot.org/ctk/Parrondo.shtml)
It seems to me (particularly from the "visual" example of the staircase and the ball) that the argument rests on a reasonable distribution of results. In other words, just as the Martingale will winn at roulette if you always get ABABABABAB, so the losing strategies can win here. However, I haven't had more than two minutes (literally) to look at it, so I may be missing something.
Obviously the Merrill line follows the same false bankroll management concept of stopping when you are ahead by a certain amount. Mathematically you are (very) likely to end up in front over a single year, but that does not mean you have maximised your expectations over 20 years.
To take the visual example of the escalator in the link above, what if the movements were less predicably periodic? In that case, every so often the ball would disappear off the bottom of the screen (very quickly), rather than slowly rising to the top of the screen. This is the visual equivalent of the Martingale gone wrong or Target-Driven-Investing when the markets go belly-up.
Re: Parrondo's Paradox
(http://www.cut-the-knot.org/ctk/Parrondo.shtml)
It seems to me (particularly from the "visual" example of the staircase and the ball) that the argument rests on a reasonable distribution of results. In other words, just as the Martingale will winn at roulette if you always get ABABABABAB, so the losing strategies can win here. However, I haven't had more than two minutes (literally) to look at it, so I may be missing something.
Obviously the Merrill line follows the same false bankroll management concept of stopping when you are ahead by a certain amount. Mathematically you are (very) likely to end up in front over a single year, but that does not mean you have maximised your expectations over 20 years.
To take the visual example of the escalator in the link above, what if the movements were less predicably periodic? In that case, every so often the ball would disappear off the bottom of the screen (very quickly), rather than slowly rising to the top of the screen. This is the visual equivalent of the Martingale gone wrong or Target-Driven-Investing when the markets go belly-up.
PJ