I realize now what the problem is here.
First, you misread my original question which was: if there are 1700 plays, and he makes special plays perhaps only 5% of the time, how many thousands of hands of video poker would he have to see before each "special play" was made?
What I was looking for was how many hands it would take for each and every one of his "special plays" to be played? Can you still answer the question? Because whether or not you can answer this question gets to the heart of the debate over Singer's strategy.
You can't answer the question because you cannot determine when Singer will utilize a special play in the first place. The truth is none of us know this except for Rob himself.
Singer has only told us about the special plays but he hasn't told us when he makes them. Oh, he says he makes his special plays to reach a win goal or when he needs a big win, but these are not specific answers that can be tested or examined. This is, quite frankly, why we can't (at this point) make an accurate analysis of his special plays and his entire system. There are too many blanks for us to try to figure it out.
What we do know is this:
He says he follows conventional strategy 95% of the time. We do not know how much of his overall wins come from that conventional play. We also do not know how much of his overall wins come from the special plays.
Arc, you can analyze his special plays up the gazoo for the next hundred years and your analysis will tell you the same thing that Rob Singer has been telling us: his special plays always have a lower expected value than the conventional or "optimal" play. What you can't tell us is Singer's return (actual wins) on conventional versus special plays, and what you can't tell us is what triggers the use of special plays.
His figure of using special plays 5% is akin to saying a royal will appear one in 40,000 hands. In fact, he might use his special plays 30% of the time in one year or only 1% in another year. And that is the same as hitting three royals in 40,000 hands or hitting zero royals in 200,000 hands.
Frankly, Arc, instead of arguing what you supposedly found about the return of Singer's special plays, you should be asking Singer for more specifics of his use of his strategy. Honestly, there isn't enough information available yet to analyze Rob's system. And that really is the bottom line here.
And the more I find out about Rob's system and his success the more questions I have. He might surprise us and we might find out that his special plays are not the big factor in his success, but rather his conventional strategy, money management, progressions, and loss limit disciplines are what drove his success. On the other hand, we might find out that he has made notations on his W2Gs that indicate what the special play was that landed the big win.
There is no need to call anyone a liar or confused or misguided. Instead, you should be asking for more information. On the other hand, if your mind is already made up there's nothing left to discuss.