Gwynn's simulation study shoid no statistically significant
difference in basic strategy expectation among the
first seven hands dealt from a full pack and only
three times in 8,000,000 decks was he unable to finish
four hands using 38 cards. Thus, as a matter of practicality,
i may assume the first several hands have the same
basic strategy expectation.
Although it may seem contradictory, it is also true
that no particular subsequent hand, before it is dealt,
would have the same set of conditional probabilities
attached to it as the first hand from a full deck.
This realization leads us to consider what Thorp and
Walden termed the "spectrum of opportunity"
in their paper The Fundamental Theorem of Card Counting
wherein they proved that the variations in player
expectation for a fixed strategy must become increasingly
spread out as the deck is depleted.
should be consistent, though. A player who pleads
for doubled stakes one week while losing should not
object on another occasion when he is winning.
Usually, the player who has pleaded for the increased
stakes to get even loses even more during that last
period. If this regularly happens, particularly to
someone who cannot afford the loss, you need to decide
just how serious you are. Whether or not you have
a moral duty to look out for another player's best
interests really depends on whether the game truly
is a "friendly" game, or whether, as is
often the case in poker, everyone is trying to maximize
his own winning chances.
If your game is truly friendly, even though for serious
stakes, it makes sense to help a player protect himself
from his short-term bad judgment. Most of the time,
even when the players like one another, everyone is
presumed to be "a grown-up" and must protect
himself. In such situations, you may still want to
protect a player from himself, figuring that you can
shear a sheep many times, but only kill him once.
It is often better to ensure the longevity of the
game than worry about temporary unhappiness of one