This is an interesting thread and you've raised some good points.
I've been working on a program which attempts to answer some of the questions you've raised - its based on the ideas in Philip Koetsch's book "Conquer the Casinos". I agree with you in that I too believe that a solution (if one exists) will be based on mathematical analysis.
what is the most negative expectation we can encounter in 200 spins?
It is always possible to get the permanence of horror right from the start.
The program so far will answer the first question and also address the 2nd point in that it will tell you what % of sessions will start of with a loss and never get to a +ve balance throughout the session. The program simulates even money roulette (betting on red) and the le partage rule (1.35% edge) with 100,000 sessions of length 200 spins.
For flat betting:
number of sessions always in a net loss = 6553 (6.55%)
average peak gain within a round = 9.44
average peak loss within a round = -12.11
actual peak gain in 100,000 rounds = 58.00
actual peak loss in 100,000 rounds = -62.50
So 93.45% of the time you can expect to quit at some point within the session with a profit - even if it's only 1 unit.
The second figure (average peak gain within a round) would suggest that if you get a profit of 9 or 10 units in the session and continue to play on you are making a bad bet, statistically speaking.
The final figure (actual peak loss within a round) suggests that a bankroll of 60 - 70 units is sufficient.
The program is work in progress and I intend to add more analysis including the number of "reversals" within a session, a reversal being a swing from +ve to -ve balance or vice versa within a session. In theory by knowing the average number of reversal for a system you can then keep track of them and quit on a +ve balance if you have "used up" your reversals in a session.
I've experimented with various systems and the best so far in terms of being able to make a profit at some point (ie; the lowest % of sessions without making any profit at all throughout the session) is the Maxim principle. Note that according to the author this is only meant to be used for craps and also I haven't simulated any of the exit points.
Using a maximum stake of 50u:
number of sessions always in a net loss = 261 (0.26%)
average peak gain within a round = 63.98
average peak loss within a round = -156.53
actual peak gain in 100,000 rounds = 122.00
actual peak loss in 100,000 rounds = -1692.50
A 99.74% chance of quitting with a profit, but of course this is offset by the hugely increased bankroll necessary and attendant risk involved.
For a maximum stake of 10u (ie; the progression is 1,2,4,5,6,7,8,9,10) and start over when you get to the end.
the results are:
number of sessions always in a net loss = 1131 (1.13%)
average peak gain within a round = 43.46
average peak loss within a round = -64.63
actual peak gain in 100,000 rounds = 121.50
actual peak loss in 100,000 rounds = -412.00
From my testing so far it seems that most volatile systems (those that offer more "reversals") are those that incorporate both -ve and +ve progressions (like the Maxim principle).