Harry,
You have given me a brilliant idea to carry this thread back to the
TDB original problem, by bringing up the whole Royal Family.
Let us leave the Queen of Comps alone, and let us go back on a time
machine to Paris in that horrible year of 1791, carrying with us some
TDB video poker machines. The people of France, sick of playing Faro
all the time, become fascinated with video poker and soon the `jeu
automatique du TDB' is all the rage in Paris, and is even played at
the National Assembly. One machine, of course, finds its way to the
Tuileries where the Royal Family, not by choice, has taken up
residence. Soon, everyone at the National Assembly is addicted to
video poker and a typically cruel motion is approved there resolving
what follows. The Queen -who is so fond of gambling that she spent
almost 48 hours non-stop from October 30th to November 1st 1776
gambling at Versailles- will be granted to play a freedom hand of
TDB. If she wins anything, then Mesdames Tantes, Adélaïde and
Victoire, will be let go to Rome. If she wins a Full House or better,
then la soeur du Roi, Elisabeth; the daugher Madame Royale, Marie
Thérèse; and the son, the Dauphin, Louis Charles, will be let go to
Vienna with the Emperor. If the Queen hits four aces or better, then
she can also leave for Vienna. If she hits the four aces with a
kicker, then the whole Royal Family can safely leave ghastly, gory
Paris for lovely Wien.
Assume the Queen agrees and she is dealt four aces with a kicker,
what does she hold? Keep in mind the National Assembly has not yet
decided to kill any of them, so this is not a question -as in the
example with the Queen of Comps- of an obvious decision dictated by
saving one's life. Keep in mind that the Queen, though no
mathematician, does have some knowledge of expected values and
probabilities in games, simply from playing often and from having
been told about the theories of Pascal and others. She is also a
mother and would like nothing better than to see her children safely
away in Vienna.
I believe the Queen drops the kicker.
Regards,
E
