Very early on, upon joining this board, iggy introduced a concept which he references in shorthand as 'N0'. It's a reference to a 'long
term' concept that doesn't have ER/EV as it's primary focus, but instead examines the length of play required before you have strong
confidence of positive (profitable) results.
This is a rather liberating perspective on play for, speaking for
myself at least, I can deal with a certain degree of uncertainty with
respect to closely achieving some given ER in my play -- but I have a
critical concern when it comes to the risk of loss. In other words,
if I play with a 1% positive return expectation, I'll deal just fine
if I only manage an actual return of 0.5%. But, where I really look
for some comfort is that I'm not exposed to undue loss risk.
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'NO' is the number of hands for a game after which you have a strong
expectation of positive results - namely where a shortfall from ER in
results of no more than one 'standard deviation' (SD) represents no
worse than a break-even result.
Without dwelling on the calculation of SD, the significance is that
for a given ER, the range of possible outcomes that are +/- 1 SD
represent 68% of all likely results. For example, if a game has an ER
of 100.5% and, after x hands played, the standard deviation is 1%,
then 68% of likely outcomes will fall between 99.5% and 101.5%. As
you play more hands, results are expected to more closely approximate
the ER, and the standard deviation decreases.
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Ok, cutting to the chase, the significance of all this is that for a
game such as FPDW, there is a given number of hands played for which
the value of 1 SD equals the positive return of the game -- in other
words, after that number of hands, the range of outcomes that lie
within 1 SD of the game ER all lie in positive territory, i.e. you
have a strong probability of coming away a winner. For FPDW, this
would represent the point in play where 1 SD = .76% and 68% of results
will fall between 100.76% +/- .76%.
With 68% of expected results falling within 1 SD of the ER, 32% of
results outside of that range. Half of that 32% will represent
results that are even stronger than that range -- at 1 SD, when you
reach 'N0' hands of play, you only have a 16% expectation of suffering
a loss in your play (and a considerably smaller expectation of a
'signfiicant' loss).
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What's really revealing here comes when you listen to the naysayers
who speak of the millions and millions of hands before which you
achieve long term results (i.e. expect to closely approach game ER).
If you set your sights on being satisfied, at minimum, with positive
results, the scope of that 'long term' shrinks tremendously --
particularly if you're talking about a game with a strong return and
yet modest variance.
The most notable example for LV denizens is FPDW -- and it's why there
are numerous locals who've enjoyed steady profitable play with only a
moderate downside, provided that they're sufficiently bankrolled to
survive the short-term swings.
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The last equation provided by iggy in the quote above defines how to
determine just how many hands it takes to reach this point in play.
What you'll find is that the number of hands for FPDW is quite
tangible for most reasonably active players. Apply the equation to a
thinly positive and more volatile game such as 10/7 DB, with modest
cb, and the number of hands required is greater by magnitudes. It
highlights the importance of game selection on 'survivability'.
Hope I didn't overly belabor this -- I find that iggy's introduced one
of the most valuable concepts expressed here to date but figure that
others, like myself, could use a little assist in filling in some details.
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