> "The Player may choose to play exactly the same rules
> as the Dealer is REQUIRED to play; or the Player may choose some of the
> other
> options. Since the Player has more choices or options in play than does
the
> Dealer, why does the Dealer have the statistical advantage? It seems to
me
> the
> Player would have the advantage."
> ------------------------------------
>
>
> Doesn't the law of large numbers figure in here somewhere too:
>
> 1. The probability of winning with the house strategy is known a priori
and
> it is optimal (as someone else pointed out).
> 2. An individual playing with this same strategy may win or lose more or
> less in the short run.
> 3. With the volume of games the house plays, the empirical probability
will
> approach the a priori probability in the long run--to the house's
advantage.
>
> Simplistic and poorly articulated I am sure, but I think it captures the
> essence of the mechanism at work here.
No. *If*, as originally suggested, the game were symmetric except for
certain possibly useful choices that player could make and the dealer could
not, the expected winnings of the player would be positive, and the expected
winnings of the house negative, on each individual game [assuming
intelligent play]. Now, E(sum(X_i)) = sum(E(X_i)) regardless of
distribution or even joint distribution. So the house would lose in the long
run *because* it lost in the short run, not despite that.
What is going on is that the rules of the game are not as was supposed.
Ties in which both hands are under 22 are [with some exceptions? help me!]
no-win-no-lose, but if both player and dealer bust, the house wins.
-Robert
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