little thought will convince you that in this case,
with a starting count of zero, we always have an expectation
of 0 when the running count is +4 (indicating that
the number of white and black balls remaining is equal).
Hence, the pivot point for this game is +4. Further
reflection will reveal that we now need the running
count to be equal to or greater than +5 to have the
advantage. The key count for this game is therefore
+5. As you can see, both the key count and the pivot
point changed in response to altered starting conditions.
Since this can all become a bit unwieldy, we can,
if we choose, make an adjustment in the point at which
we begin our count. That is, we adjust the "initial
running count" (IRC) in order to provide more
convenient key-count and pivot-point numbers. For
example, we could start the IRC at, say, +2, and then
we'd have the advantage when the running count was
equal to or greater than +7. Or we could use an IRC
of -4, in which case we'd have the advantage when
the count was equal to or greater than +1.
The point of all this is that the pivot point and
key count are a function of what we choose as the
IRC. We'll see later how this can be used to simplify
To get an advantage in our gumball game, we can assign
an integer value to each colored gumball and keep
a running count of those we've seen come out of the
Two special count values are the key count, at or
above which we have the advantage, and the pivot point,
at which we have reliable information about our expectation.
The key count and pivot point will depend on our initial
Counting cards is not dissimilar to counting gumballs.
First, just as there were good gumballs, bad gumballs,
and neutral gumballs, in Online Blackjack Games there
are good cards, bad cards, and neutral cards. And
just as we assigned a value to the different gumballs,
we can also assign a value to each type of card. We
then start with an initial running count and count
through the deck as the cards are played. Once the
running count reaches the key count. we know we generally
have the advantage. When the running count is equal
to the pivot point, we have a reliable estimate of
you will be playing with your own money. This makes
sense. For almost everyone, poker is a hobby, even
though it can be a profitable hobby. You don't borrow
money to go to the movies or collect coins, so why
should you borrow money to play poker, There are many
good reasons why both borrowing and lending money
for poker are usually bad ideas. Let's examine them.