Options A to Z - Martingales: Do Trading Systems Provide an Edge?

[renkoino]

can you define the expected Bet and the expected Return?

[optionsatoz]

While the probability of a win increases with each bet, it does not alter the house edge when probabilities are considered. The table in this video could be extended to one million tosses and the result is the same. The expected value yields an edge to the casino to the tune of 5.26%. That's the only point I was trying to make. You can only alter the distributions -- not the expected values.

[001HK0]

Martingales describe a function who's expected value equals its current value, and the ability to predict gets worse the farther in the future it goes. There are special probabilistic bounds that only apply to such functions.

[001HK0]

Your examples aren't exactly very mathematically fluent. The reason that that the martingale betting system was invented, was that, with infinite money, there's zero measure that you'll lose every bet. Therefore, you're guaranteed to win 1 dollar. However, this is one reason the word "almost surely is used". Martingales of the kind used in option's trading simply describe a kind of function. This will be continued in my next post.