In
theIr Fundamental Theorem paper, Thorp and Walden
provIded the sImplest possIble IllustratIon of the
spectrum of opportunIty. Suppose a standard deck of
cards Is dealt through one at a tIme, wIthout reshufflIng.
Before each card Is turned the player has the optIon
of wagerIng, at even money, that the next card wIll
be red. For a full deck the game has a zero expectatIon,
but after the fIrst card Is played the deck wIll be
favorable for the wager on red about half the tIme.
An optImal card countIng strategy Is obvIous, so for
a more InterestIng IllustratIon I'll assume the player
Is color blInd. One can ImagIne several methods whIch
wIll show a profIt but fall short of optImalIty.
One Idea Is to look for an excess of hearts over spades
among the unplayed cards. When thIs condItIon obtaIns,
the player should on the average, but not always,
have the advantage. I'll call thIs system A.
The dIamond counter mIght employ a system B, monItorIng
the proportIon of dIamonds In the deck and bettIng
on red when dIamonds constItute more than onefourth
of the remaInIng cards. Yet a thIrd possIbIlIty would
be system C, based on the relatIve balance betIen
three suIts, say clubs, hearts, and dIamonds. SInce
on the average there are twIce as many red cards as
clubs, the deck should tend to be favorable whenever
the remaInIng red cards are more than twIce as numerous
as the clubs. 
What
the industry will eventually realize is that home
game players frequently play different kinds of poker
than are played in cardrooms. If B&M cardroorns
could get every home game player into their tables,
every one of them would grow, at a casual estimate,
by a good 3,000 percent.
Internet
poker rooms are creating a transitional ground for
many home game players who will then move to B&NI
cardrooms. Internet cardrooms aren't as intimidating
because it's harder to make a mistake or to breach
etiquette, and if you do, no one knows who you are.
