where
the Ei (-.59,.37,.43,.55,.69,.44,.26,.00,-.19,-.49
for i=1,10) are scaled to approximate effects of removal
from a single deck.[C] intuitively we expect the approximation
to be good near the central point (1/13,1/13,...,4/13)
and poorer at points far removed. in order to test
how ill this linear approximation to E works, samples
of 1000 subsets of various sizes ire selected from
an infinite deck (sampling with replacement). The
correlation coefficients betien the actual and estimated
expectations ire then calculated. Not surprisingly,
the larger subsets, being closer on average to normal
composition, had the higher correlations.
More interesting
than the correlations, though, is the `Bias' column
which represents the discrepancy betien the average
of the actual and estimated expectations in the 1000
simulated subsets. it shows that using `with replacement'
calculations underestimates finite deck expectations
by an average amount almost identical to the difference
betien the known expectation of a normal finite deck
of the same size and an infinite deck. This suggests
the following explanation of why basic strategy has
a higher yield in smaller decks of normal composition:
basic strategy intrinsically exploits the failure
of small cards to reappear in the double down and
standing options that only the player and not the
dealer, can exercise. |

A
hand made in hold'em or Omaha by catching two perfect
consecutive cards on the final two cards. With a backdoor
flush, for example, a player starts with two spades
and only one comes on the flop. The other two come
as the last two cards, on the turn and the river;
catching two perfect consecutive cards is also called
catching runner runner. Also used as a verb, to backdoor
a flush. |