Martingale strategy_ Head and tail winning

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What is the Martingale Strategy?

 

Popularized in the 18th century, the martingale was introduced by a French mathematician by the name of Paul Pierre Levy. The martingale was originally a type of betting style that was based on the premise of "doubling down." Interestingly enough, a lot of the work done on the martingale was done by an American mathematician named Joseph Leo Doob, who sought to disprove the possibility of a 100% profitable betting strategy.

The mechanics of the system naturally involve an initial bet, however, each time the bet becomes a loser, the wager is doubled such that, given enough time, one winning trade will make up all of the previous losses. The introduction of the 0 and 00 on the roulette wheel was used to break the mechanics of the martingale, by giving the game more than two possible outcomes other than the odd versus even, or red versus black. This made the long-run profit expectancy of using the martingale in roulette negative, and thus destroyed any incentive for using it.

To understand the basics behind the martingale strategy, let's take a look at a simple example. Suppose that we had a coin and engaged in a betting game of either head or tails with a starting wager of $1. There is an equal probability that the coin will land on head or tails and each flip is independent, meaning that the previous flip does not impact the outcome of the next flip. As long as you stick with the same directional view each time, you would eventually, given an infinite amount of money, see the coin land on heads and regain all of your losses, plus $1. The strategy is based on the premise that only one trade is needed to turn your account around.

 

 

 

Examples

 

 

 

Assume that you have a total of $10 to wager, starting with a first wager of $1. You bet on heads, the coin flips that way and you win $1, bringing your equity up to $11. Each time you are successful, you keep on betting the same $1 until you lose. The next flip is a loser and you bring your account equity back to $10. On the next bet, you wager $2 in the hope that if the coin lands on heads, you will recoup your previous losses and bring your net profit and loss to zero. Unfortunately, it lands on tails again and you lose another $2, bringing your total equity down to $8. So, according to martingale strategy, on the next bet you wager double the prior amount to $4. Thankfully, you hit a winner and gain $4, bringing your total equity back up to $12. As you can see, all you needed was one winner to get back all of your previous losses.

 

However, let's consider what happens when you hit a losing streak:

Once again, you have $10 to wager, with a starting bet of $1. In this scenario, you immediately lose on the first bet and bring your balance down $9. You double your bet on the next wager, lose again and end up with $7. On the third bet, your wager is up to $4 and your losing streak continues, bringing you down to $3. You do not have enough money to double down and the best you can do is bet it all. If you lose, you are down to zero and even if you win, you are still far from your initial $10 starting capital.