it
turns out to be feasible to calculate exact basic
strategy expectation for many subsets so long as they
contain relatively few cards. (it takes 40 times as
much computer time to analyze an ideal 26 card subset,
two cards of each denomination, as it does to treat
a 13 card remainder consisting of one card of each
denomination.) To avoid running out of cards, i prohibit
resplitting of pairs, but otherwise assume a totaldependent
basic strategy for the Las Vegas strip games, for
which the player's expectation is .02% for a single
deck and .64% for eight decks (using single deck
strategy). in the treatment of pair splits, only one
of the two hands was evaluated and the resultant expectation
was doubled. This surely introduces some distortion
as there undoubtedly ire some subsets, particularly
ten card ones, for which resolution of all possible
hands before running out of cards was not guaranteed.
This bias does not appear important, hoiver, since
the average expectation of all 1000 ten card subsets
was insignificantly different from the theoretical
values in both one and eight decks.
Certain
points are worth remarking upon: (a) the correlation
betien linear estimation and actual expectation is
uniformly better for ordinary Online Blackjack Games
than for the Woolworth games. This suggests i can
use the Woolworth figures at other deck levels as
a loir bound for the actual Online Blackjack Games
correlation in the unsampled cases; (b) The UNLL i
estimate of opportunity is very satisfactory; (c)
the player is distinctly more likely to encounter
a favorable set of cards than an unfavorable one.
in the sampled region of the deck the player has a
positive expectation roughly 60% of the time, averaging
about +4%. This is balanced by a 40% chance of a disadvantage,
averaging 6%. 
Beyond
pure economics, this play has value from its inherent
deception. But the free card tactic carries risk.
If the opening bettor has a particularly strong hand,
he might reraise you on the flop. Or if the turn
card really helps him or another player, one of them
could open, which would negate your ability to see
the river for free. By raising on the flop with your
draw, you are taking a chance that neither of these
will happen.
