numbers are derived by multiplying the effect of removing
a single card from the full 52 card pack (on the player's
basic strategy expectation) by -51. To assert that
these are "best" estimates under the criterion
of least squares means that, although another choice
might work better in occasional situations, this selection
is guaranteed to minimize the overall average squared
discrepancy betien the true expectation and our estimate
How do i use them? Suppose i're considering the residue
[2,4,6,7,9,T] mentioned earlier and we want to estimate
the basic strategy expectation (which we already know
to be -6.67%). i add the six payoffs corresponding
to these cards -19.4-28.0-23.4-14.3+9.2+26.0=-49.9andthen
divide by six, to average: - 49.9/6 = -8.32 (in %).
it is the ensemble of squared differences betien numbers
like -6.67%, the true expectation, and -8.32%, our
estimate of it, which least squares minimizes.
The estimate is not astoundingly good in this small
subset case, but accuracy is much better for larger
subsets, necessarily becoming perfect for 51 card
decks. A subsequent simulation study mentioned in
page Four indicates the technique is quite satisfactory
in the first 2/3 of the deck, where it is of most
practical interest, considering casino shuffling practices.
of the time, the ante in a $5-10 game will fall somewhere
between those extremes and as you gain experience,
you'll get a feel for what hands are playable at what
ratio of antes-to-bets.
Finally, you should remain aware of your opponents'
styles. Some players routinely play any ace or king
doorcard as if they have a pair when the odds are
certainly against that being the case on any given
occasion. Against such aggressive players you can
continue playing when you have a smaller pair, even
though every once in a while you will get trapped
when the aggressor really has the goods.