By type of game, we consider additional information usually available
to a player before selecting squares. We have already found that to
maximize the probability for winning two or more squares, the optimal
strategy is to pick squares in a single column corresponding to the
underdog team. If the column happens to correspond to the favored team,
turn the 10 x 10 grid by 90 degrees. The underdog and favorite teams are
determined by the pregame point spread or line (points by which the
favorite team is expected to win).

In addition, before a
game, the over/under (O/U, how many points are expected to be scored
totaled for both teams) is also something that is usually known. The
player can use this information and may choose to alter selections
depending on the type of game that is involved. We study by selecting
sub-samples of the 4953 games from 1994-2012. We divide the total number
of games into five sub-samples. We consider 957, 1080, 929, 1102, and
985 games with the O/U<=37.0, 37<O/U<=40,
40<O/U<42.5,42.5<=O/U<45.5, and O/U>=45.5. In terms of
expected scoring, these five sub-samples represent expected extreme low
scoring, low scoring, average scoring, high scoring, and extreme high
scoring games. Simulations of each of these five sub-samples have been
run - each with 100 million trials.

The first
observation from looking at the results of the trials is that the
patterns that represent the possible player selection choices are
exactly in the same order as previously discussed under "Configuration
Strategy" no matter which sub-sample is considered. A second observation
is that the five sub-samples could be described by three: O/U<=37,
37<O/U<42.5, and O/U>=42.5 as there is not much difference
between low and average scoring. Nor is there much difference between
high and extreme high scoring games. The figure below shows, as a
function of the different configuration patterns when selecting four
squares, the probability of winning two or more squares. Note how the
five sub-samples form essentially three bands.

Consider
the configurations A and H which represent selecting four squares each
on a unique row and column (A) and selecting four squares in the column
of the underdog team (H). When it is expected to be an extreme low
scoring game, configuration A has a 2.47% likely chance of winning two
or more squares and configuration H has a 3.19% chance. When the game is
expected to be high scoring, it is less likely that teams will score
"0" in a quarter and less likely that scores will be correlated and thus
less likely that winners will win two or more squares. For
configuration A, only 2.08% of the time would winning two or more
squares occur and for configuration H, only 2.80%.

The
basic strategy to be more likely to win two or more squares always
holds. Pick them in a column corresponding to the underdog team. If you
choose to select squares only if it is also expected to be an extreme
low scoring games, you will enhance the likelihood of winning two or
more squares. If your goal is to have the largest chance for winning at
least one square (most often a single square), then picking squares in
unique rows and columns always holds. For a low scoring game, you would
have 13.09% chance if you pick four squares. For a high scoring game,
your likelihood increases to a probability of winning 13.74% (but from
the figure above, you'd only have a 2.08% chance of winning two or more
squares).

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