Money management and multiple entries

To give you an idea about what money management is and how it may affect strategy performance, let me tell you about probably the most famous – or infamous – kind of money management technique, known as martingale.

The origin of martingale is in gambling. Imagine the simplest gambling game of a coin toss. You toss the coin and if it comes up heads, you win; if it comes up tails, you lose. We can use 1 for wins and -1 for losses and the series of tosses can be represented by a sequence as follows:

S = {1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, ...}

If you put at stake an equal amount of money each time you toss the coin, we can multiply the sequence by that amount and write it like so:

S1 = {b, -b, -b, b, -b, b, b, b, -b, -b, b, -b, ...}

Here, b refers to the size of the bet. Obviously, your total win in the game is the sum of the entire series. In an idealistic model, the results of each toss are independent of each...