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The question is whether "negative expectation" is a valid concept for anything other than, say, a million rolls. It's not, of course, it's only valid of the rolls generate a normal distrubution, and on a craps table, it's unlikely to happen for anything under, say, 100 rolls.


Tell me you're kidding. Expected outcomes do not derive validity from the number of trials. Trials impact the distribution of results around the expected outcome, but the expected outcome remains the same, with or without normal distributions or the central limit theorem. If I gave you a jar of 51 green marbles and 49 red marbles, green I win and red you win, and asked you to pick once at even odds, how would you decide whether to play? Is the distribution of marbles (expected outcome) irrelevant for a single trial? Mind if I add a few more green then?

That's been my whole point all the way through this discussion, and I'm not sure if I am not making my point clearly, or people are too stuck to the idea of looking at things from the casino perspective, where tables run 24/7. With 100X odds, I will always get even (minus my 1% if I lose it), but since I can walk after I go up, it does not fit the definition of negative expectation. A wrench is thrown into this plan if I can't use a large bankroll to support my waiting to get even, but assuming I have this bankroll, or assuming I will have the occasional loss, this isn't a scenario where the definition of negative expectation fits.

Neither the perspective nor the ability to walk away is relevant. If you walk into MGM an play one roll of craps you are more likely to lose than win. On that roll. Just because the variance is enormous, doesn't mean the odds shift. Your option to walk away from the table is equally unhelpful, except that walking away from a negative expectation game is always economically beneficial. The only exception would be if we lived in the land of ininity - inifinite bank rols, bets and time - and then Martingale like progression would allow the ability to walk away to matter. Since we don't, Martingale is bogus, and so is the idea that the option to cease trials impacts expected ex ante outcome.

And, Raken, you cannot beat baccarat (a negative expectation game) by counting sequences. I don't know anything about what this Lyle Stuart thinks, but I'm certain it's mathematically inaccurate if it relies on sequences of bank, player or tie. The only way to get a positive expectation in baccarat is to perfectly count cards, to perform combinatorial analysis with the capacity of a department of defense computer, all while finding the one game in the country that charges only 4% on bank wins.
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