A caveat: never having read or studied Singer's system -- and really, has anyone? -- I make no claim that my understanding of it, from this forum, is in any way an accurate portrayal. But here's my attempt at making sense of it and, for the curious, comparing it to the "system" most of us here seem to use.
“Singer Smart” (SS) strategy claims making “special plays” when a machine is in one of its “preprogrammed hot cycles” will have a positive expectation over the short term, even if the “special plays” have a negative expectation over the long term, and will help a player achieve a specified “goal.” If a machine is in one of its “preprogrammed cold cycles,” SS recommends the player change machines. The probability of the player achieving a specified “goal” thus depends largely on the player’s ability to predict a machine’s “cycles” accurately.
But SS provides no definite answers to the questions of:
exactly how to determine when a machine is in one of its “preprogrammed hot cycles”
exactly how much more often a “special play” can be expected to succeed when a machine is in one of these cycles compared to other times
So, even granting the underlying assumptions of SS, if using “special plays” fails to achieve the player’s “goal,” the system cannot tell us whether the machine was actually not in one of its “preprogrammed hot cycles” and the player failed to predict this, or whether the failure is due merely to normal variance within such a cycle.
“Advantage Play” (AP) strategy claims VP is as perfectly random as possible, so it obeys probabilistic laws. Therefore, there is no way of predicting the exact outcome of any play before it is completed; any play’s short- and/or long-term expected return can be calculated to any degree of accuracy; and changing machines has no affect on the probability of achieving a specified “goal” as long as the paytable is the same.
SS claims playing a “progression” of machines with constantly increasing denomination and variance will help a player achieve a specified “goal.” AP claims that neither denomination nor variance affect the expected return, expressed as a percentage of coin-in, of any game positively or negatively provided only that the paytable is the same. Under AP the probability of achieving any specified “goal” while playing any machine or combination of machines can be calculated to any degree of accuracy.
Points of agreement between SS and AP include:
In many if not most cases, sacrificing a small, but certain, payoff for the chance of a larger one is negative over the long term. This applies both to the kinds of games played and the kinds of plays made in those games.
VP players should set both positive goals and negative limits for their play and exercise the discipline needed to stick to them.
In the long term, the actual return of any VP game will approach the expected return of the game under AP calculations.
With regard to the last point, granting the assumptions and using the strategies of AP, the expected return of any VP game over any period of time can be calculated to any degree of accuracy. However, granting the assumptions and using the strategies of SS, the expected return of any VP game over any period of time shorter than “infinity” depends on both a machine’s “preprogrammed hot and cold cycles” and a player’s ability to detect and predict those “cycles” and so cannot be calculated accurately.
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