The table on the following page exhibits the 20 possible
threecard subsets, their expectations, as ill as
the predictions and errors of both the interactive
model and simple linear approximation as ill.
As an example of the ingredients necessary for these
approximations, one can easily compute the overall
mean M=516, M, = 768, M2 = 636, M3 = 540, M,2 = 1080,
M,3 = 885, M23 = 690. From these i get P,Z = 180,
P,3 = 30, and P_3 = 120, whose average value is 90,
the interactive estimate for subset 1 1,2,3 }, while
P, =744, P, =84, and P3 = 396, the average of which
is 144, the simple linear estimate for the same subset.
The multiple correlation coefficient for interactive
prediction is .99 and that for simple linear prediction
is .91, but a comparison of these two figures does
not really do justice to the improvement in approximation
afforded by the interactive model. More to the point
is the fact that the proportion of squared error for
the simple linear model is .1675, whereas this is
reduced to .0218 for the interactive estimates. 
Expect
to lose on your bluffs so you can make money the rest
of the time." This is one of the most widely
misunderstood concepts in poker and has cost more
players more money than almost any other "conventional
poker wisdom," because actually it is not wise
at all.
The reality
is that in the course of making bluffs that you hope
will succeed (win the pot), you will get caught/called
often enough to do all the "advertising"
you need. People will remember these unsuccessful
bluffs, and because they are looking for excuses to
play, and hate the idea of getting bluffed out of
a pot, will later call you when you actually have
a real hand. This means you certainly don't need to
make bluffs you know will fail.
