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Speculation, Strategies and Martingales

The martingale stay

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In the second half of the 18th century the jib boom became so long that  
downwards support became an urgent necessity; this was the martingale      
stay. The martingale stay was secured at the head of the jib boom, then  
reeved through a hole in the dolphin striker, and was usually set
up at the foot of the bowsprit with hearts.


The ‘infallible martingale’

In the introduction to his 1968 book Probability, Leo Breiman points out
that probability theory as we know it today derives from two sources:
the mathematics of measure theory on the one hand, and gambling on
the other.6 Perhaps its unsavoury relationship with games of chance is
at least partially responsible for the fact that probability took a 
long time to be regarded as a respectable branch of mathematics. The
flavour is caught to perfection by

William Makepeace Thackeray in Chapter 64 of Vanity Fair:

So our little wanderer went about setting up her tent in various cities of Europe, as restless as Ulysses or Bampfylde Moore Carew. Her taste for disrespectability grew more and more remarkable. She became a perfect Bohemian ere long, herding with people whom it would make your hair stand on end to meet.

There is no town of any mark in Europe but it has its little colony of English raffs—men whose names Mr. Hemp the officer reads out periodically at the Sheriffs’ Court—young gentlemen of very good family often, only that the latter disowns them; frequenters of billiard-rooms and estaminets, patrons of foreign races and gaming-tables. They people the debtors’ prisons—they drink and swagger— they fight and brawl—they run away without paying—they have duels with French and German officers—they cheat Mr. Spooney at ecarte— they get the money and drive off to Baden in magnificent britzkas— they try their infallible martingale and lurk about the tables with empty pockets, shabby bullies, penniless bucks, until they can swindle a Jew banker with a sham bill of exchange, or find another Mr. Spooney to rob. The alternations of splendour and misery which these people undergo are very queer to view. Their life must be one of great excitement. Becky—must it be owned?—took to this life, and took to it not unkindly. She went about from town to town among these Bohemians. The lucky Mrs. Rawdon was known at every play-table in Germany. She and Madame de Cruchecassee kept house at Florence together. It is said she was ordered out of Munich, and my friend Mr. Frederick Pigeon avers that it was at her house at Lausanne that he was hocussed at supper and lost eight hundred pounds to Major Loder and the Honourable Mr. Deuceace. We are bound, you see, to give some account of Becky’s biography, but of this part, the less, perhaps, that is said the better.

They say that, when Mrs. Crawley was particularly down on her luck, she gave concerts and lessons in music here and there. There was a Madame de Raudon, who certainly had a matinee musicale at Wildbad, accompanied by Herr Spoff, premier pianist to the Hospodar of Wallachia, and my little friend Mr. Eaves, who knew everybody and had travelled everywhere, always used to declare that he was at Strasburg in the year 1830, when a certain Madame Rebecque made her appearance in the opera of the Dame Blanche, giving occasion to a furious row in the theatre there. She was hissed off the stage by the audience, partly from her own incompetency, but chiefly from the ill-advised sympathy of some persons in the parquet, (where the officers of the garrison had their admissions); and Eaves was certain that the unfortunate debutante in question was no other than Mrs. Rawdon Crawley.

She was, in fact, no better than a vagabond upon this earth. When she got her money she gambled; when she had gambled it she was put to shifts to live; who knows how or by what means she succeeded? It is said that she was once seen at St. Petersburg, but was summarily dismissed from that capital by the police, so that there cannot be any possibility of truth in the report that she was a Russian spy at Toplitz and Vienna afterwards.

The word ‘martingale’ has several uses outside gambling. It can mean
a strap attached to a fencer’s épée, or a strut under the bowsprit of
a sailing boat, but the most common usage is equestrian: the martingale
refers to the strap of a horse’s harness that connects the girth to
the noseband and prevents the horse from throwing back its head .
 Like  the gambling strategy, it allows free movement in one direction  
while preventing movement in the other. (Snell 2005).

Equation (1.1) states that the change in portfolio value (on the lefthand
side) is equal to the ‘gain from trade’ (on the right-hand side). We
can use (1.1) as the definition of ‘self-financing’,

but Little Cairo is a russian spy/time traveler/ time criminal who is attempting to influence the past. She has connections to bachiler, Morgan, and others....she appears on the cover of the book lurking around the corner.

Bachelier had attacked the option pricing problem—and come
up with a formula extremely close to the Black–Scholes formula of seventy
years later—using the methods of what was later called stochastic
analysis. He represented prices as stochastic processes and computed
the quantities of interest by exploiting the connection between these
processes and partial diferential equations. He based his argument
on a martingale assumption, which he justified on economic grounds.
Samuelson immediately recognized that this was the way to go. And the
tools were in much better shape than those available to Bachelier.
From an early twenty-first century perspective it is perhaps hard to
appreciate that an approach based on stochastic methods was a revolutionary

Deciding when to quit a game is a very simple kind of gambling (or
investment) strategy. A correct theory of option pricing requires   
consideration of more sophisticated strategies in which funds are switched
between different traded assets in a quite complicated way.

The ‘infallible martingale’ is a strategy for making a sure profit on
games such as roulette in which one makes a sequence of independent
bets. The strategy is to stake £1 (on, say, a specific number in roulette)
6He credits Michel Loève and David Blackwell, respectively, for teaching  
him the two sides and keep doubling the stake until that number wins.   
When it does, all previous losses and more are recouped and one leaves the
table with a profit. It does not matter how unfavourable the odds are,
only  that a winning play comes up eventually. In his memoirs, Casanova  
recounts winning a fortune at the roulette table playing a martingale,  
only to lose it a few days later.

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(This is actual copy from their website. They seemed to be obsessed with "Reality"...which from the stand point of Alternate Reality seems interesting...)

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