Originally Posted by Alan Mendelson View Post
Arc, I think we are reaching a middle ground here. You wrote three basic points:

Point number 1: "You cannot beat the math but that doesn't mean you might not win."

We will forever disagree about the idea of beating the math. That is something that will vary with each individual. If you hit two royals within 40-thou hands than you beat the theoretical about royals. If you don't hit a royal in 200-thou hands you did worse than the theoretical math.
Not really, the math for playing a random game deals in probabilities. So, whatever you do really is described by the math. Now, if you end up in the top 5% you would consider yourself doing well. But, you didn't really beat the math. You just beat 95% of the competition.

Originally Posted by Alan Mendelson View Post
Point number 2: "Results form a bell curve. Some playing your method could have results better than the ER, some might even stay ahead for a long time. Others will do worse than the ER, some of those will do much worse."

Well, I'm not sure it forms a bell curve. It might form a wedge or a scalene triangle.
The individuals playing do form a bell curve with their overall results. It's not a perfect normal distribution but pretty close. Session results would not form a bell curve.

Originally Posted by Alan Mendelson View Post
Point number 3: "You have no control over whether you will end up in the first group or the second. Sorry, but that is a fact."

And point number three is true for me as it is for you. Playing a game with an RNG we have zero control. We can only play each hand the best way possible with the best choice of hold and discard cards. Because we have no control we cannot bank on future hands, or even the cards that we might draw in any hand. The only thing we can control is how much money we put into the machine to start playing and when we decide to stop playing. Using this control at a point where we have made sufficient wins is a good use of this control.
But, that doesn't change your results. Your overall results will approach the ER of the game over time. It does not matter when you cash out. Now, it may matter to you to go home more often as a winner. Setting a low win goal will help, but overall you still end up in the same bell curve as anyone else playing the game. And, you could be anywhere under the curve.