TITLE: A basic question on Martingale and betting games
QUESTION [0 upvotes]: I am new to Martingales. Why the betting strategy where if I loose then I double the amount (so, with the first win I get whatever I lost plus the amount of initial bet) is called the "martingale strategy" ? How does this match with the definition that the conditional expectation at time $n+1$ is same as the the observation at time $n$. 
BTW, what is a good book for self-studying the theory of martingales ?

REPLY [1 votes]: Martingale betting system dates from the 18th century, originating in France and is very simple to put into practice.
Here's how:
Place a first bet of a minimum odd of 2.00.
If you win you double your money. If you lose, double your initial bet.
You stop doubling when you win, in which case you make a profit equal to the initial bet. Thus, a series of six bets, you lose the first five and manage to make a profit on the initial bet if you catch the sixth.
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