bigplayer, thanks for helping me reason thru it. help me consider your last sentence which is 100% unassailable: " add up all of the results from either pattern of distributions the house wins exactly what it's supposed to win over the long haul." please analyze the following which starts out all too familiar but hang in there:

assume no advantage play but perfect basic strategy. assume that the "approach" taken is flat betting with losses till losing so much that the variance is unlikely enough to return you to even that you "declare you have lost" and go back to "even" (maybe somewhere around minus 30 units the "characteristics" or "math" of blackjack are such that the flat bet is ever-less likely to return you to even so it is here that you "accept the loss" and return to your "approach" to "even") (no "system" "works", we all know that) --as you said, it will happen as often as it should. so far, we are disciplined, take the loss when we must and start over, 100% accepting of the math--no hocus-pocus notions, just an "arbitrary" approach that "pretends" it is ok to re-define and re-set "even".

NOW, no "system" on the upside, just an "approach". the characteristics of the approach are as follows: flat bet till winning then bet up and the math guarantees that sometimes you are going to simply destroy a good win and return to even, with all its perils. other times variance will grant you further success and, unlike when losing, you throw caution to the wind and press to whatever you "guess" the traffic will bear. once again, the math rears its ugly head and, depending on where you stop, you either give back to even or diminish what was shaping up to a pretty nice run. HOWEVER, that same math will, NOT-ALL-THAT-RARELY, (not often, either) grant you one of those fabulous runs where, unlike on the losing side, you enjoy an absurd outlier of a win, quit somewhere prudently and return to "the rules" of your flat bet, as if you were at "even". NOTHING has violated your last sentence, the math will eventually do EXACTLY as you say BUT, because you used an approach that eventually gave you an OUTLIER WIN on the upside and NEVER allowed the house the same when the math gave them your downside, you "create" a disproportionate "win" to "offset" the ugly reality of playing at a disadvantage.

many players have war stories of their wild, outlier win, without advantage-play-----plug one of those in, with the downside discipline that did not offer the house the chance to "get it back" and for a season, this guy is looking pretty good. over time, the expectation, with the math being honored, is that this same guy will continue to add outlier wins (rinse and repeat)--your last sentence remains entirely intact but an approach that arbitrarily assigned the words "even" and "start over" on the downside and some kind of "artsy", "the moon" approach to when to quit on the upside and it was arrived at on a rocket of much higher bets than downside bets, thus creating NO asymmetry in mathematical expectation of events (your point) but every kind of asymmetry in dollars won or lost.

i believe bright folks fall for magic thinking or fallacy all the time and i may well be doing that but i appreciate any reasoning thru this any of you might do that would help me see it, as i absolutely do not---i think it is sound reasoning and is also very common in many other "real world" endeavors in which a superior "approach", rather than an "advantage" leads to lifetime, good outcomes.