Your 2nd part, Martingale doesn't always have negative expectancy(I don't think). If you were to play up to 20 hands, and you had enough to cover 20 losses. The odds of you winning just 1 roll, you would have a positive expectancy...
If you're playing a game with a house edge then you always have a negative expected value. Anything else is silly. Consider a game where the site gave the player the edge. Could you think of any way of betting that would give you a negative expected value?
Yep, I could. If you went all in every time you bet to infinity, you are going to lose eventually. Thus, negative expected value.
Yes, even with a house edge you can have a positive expected value(math someone?) Like in my example. 20 losses, or if you had 200 losses to cover, and you only wanted to win 1 base bet. Your expected value should be darn close to the base bet no? Any math people out there, Doog you have been good at this, I could be wrong as well just figured
Looks like you have a misunderstanding on "expected value".
Take your 20-hand martingale as an example.
P(20 consecutive losses) = 0.505^20 ~= 0.000116366%
P(win 1 base unit) = 1-0.505^20 ~= 99.999883633%
EV = P(win 1 base bet) * 1 - P(20 consecutive losses) * 2^20 = -0.22019120361 < 0
So, you have a very high chance to win 1 base unit, but you are still having a negative EV.