Dear Caruso, I'm sorry but I did not understood very well your post. Anyway I would like to make some comments,
Variance is nothing to do with anything other than in the clueless worlds of the majority of casino operators and, it seems, one or two webmasters. It is a short-termism.
As long as I know variance and reward are closely connected as is an x-axis with an y-axis. variance is as important as an average. If you say to me that you have 3 brothers, on average 30 years old, it does not mean much to me. You may have 3 brothers each 30 years old, or one with 15, other with 30, and the last one with 45. So, variance plays an important role.
In the long run, with infinite trials a player is expected to lose when playing any casino game. It does not matter if he plays on red/black at the same time or only on one single number. The house edge is always the same. It's easy to use math and statistics to prove that.
The best chance a player has to win some money at a casino is on the short term, I mean, if he plays only a few hands. Why?
The expected payoff of the games is still the same, but what gives him a possibility of winning is
the uncertainty of this result. The degree of uncertainty is the variance, and it plays a very important role on the short run. When you play 2 hands on red and win both, you end up beating the house, and what makes that possible is exactly the variance. Wizard of Odds have very good explanations on the role of variance (he not always refers to that as variance, sometimes he uses terms like risk and others).
When the casino gives you a bonus you're playing with money that is not yours. There is a very good reason to impose wager requirements and game restrictions. I can show you using math that a player with a bonus of 200% can
systematically beat casinos, if casinos don't impose correct wager requirements and game restrictions. When I say systematically, I mean, every time. He receives the bonus, plays on a very low variance game to fulfil the requirements, and then withdraw a profit. Then, he repeats the same strategy at every casino.
I can assure you that variance plays a very important role. When you are in good position , the best bet is to play low variance games, when you are in a bad position, the best bet is on high variance games. This can be easily understood. When things are good you want no uncertainty, when things are bad, uncertainty plays on your side. When I refer to the story of the man and the river I was trying to explain that but I think it was not very well explained.