What is a martingale?

C2
1

can you guys explain to me what martingale means? I was always under the impression (in math) that it’s about random time series’ expectation at future time being the same is the current time:

E[X | t+1] = E[X | t]

where X is the random variable… for example, a stock is expected to grow at the risk-free rate (so its future expectation is not the same as the current price)… a future price; however, is expected to be the same.

But I keep reading martingale here, and I’m not sure what you mean. Can someone help?

2

double your chip when you lose the on-hand game

1 Like
3

martingale is referred to casino-like strategies where you´re doubling down essentially or any variation from it. Also known as “adding to loosers”. I think that doubling approach at roulette was invented by a guy named Martingale.

1 Like
4

According to the Ralph Vince’s book: … martingale, has you double your bet after each loss until
ultimately, when a win does occur, you are ahead by one unit. However,
the martingale strategy can have you making enormous bets during a losing
streak. On the surface, this would appear to be the ultimate betting progression,
as you will always come out ahead by one unit if you can follow the
progression to termination. Of course, if you have a positive mathematical
expectation, there is no need to use a scheme such as this. Yet it seems this
should work for an even-money game as well as for a game where you have
a small negative expectancy. …

One way to prevent being sucked in such pos. size scheme is to ask at the developer how many MAX contracts that strategy or program can held at time. Because the Max contracts then are declared that will exclude martingale position size.

5

I think it was proven that you can only make money when expectation is positive (even with this scheme). But thank you all for the response.

6

Martingale, as used with trading systems, is a position sizing technique that increases position size after losing trades and decreases position size after winning trades.

Other posters have correctly stated that no position sizing technique can create a long-term profit unless the individual trades have a positive expectation.

Even with a positive expectation, Martingale position sizing guarantees bankruptcy. Here is an example using a casino game:

The table limits are $5 to $500. The minimum bet is $5, and the maximum bet is $500.

At the start of the session, and after every win, gather all winnings into your stack, then place a $5 bet.

If your play wins, start over at $5.
If your play loses, double your bet and continue to play. Eventually you will win, recovering all of your losses plus $5.

The sequence of bets for a losing series will be 5, 10, 20, 40, 80, 160, 320, 500. The eighth bet should be $640, but the table limit is $500. Win or lose on the eighth play, you are behind. And you will never catch up.

After some sequence of plays, even with a positive expectation, the Martingale technique requires using a position size that you cannot afford.

The alternative is “anti-Martingale” – “Bet the run of the table.”

When the system is working well – the model and the data are properly synchronized – increase position size after wins. When the system enters a losing streak, there is no way to tell when it is permanent or temporary, so reduce position size. Continued losses cause position size to drop to zero, at which time the system is retired and either returned to development or paper traded waiting for the possible return to profitability.

I have posted some videos on YouTube that will help understand:

Best regards,
Howard Bandy

1 Like
7

Martingale strategy will cause you bankrupt because there is a boundary.
In the statistic world, if your goal is a single subject in stead of population, the martingale is nonsense.

8

There is always a boundary.

In many applications, there are two boundaries – one on the success side, the other on the failure side. In trading, these are having gained enough to stop trading and going broke, respectively.

I do not understand “martingale is nonsense” in the previous post.

If that is to mean:
Martingale is not a useful position sizing technique? That is true.
The comments I made in the previous post are nonsense? Please explain.

Best, Howard

9

No to your post. What i am trying to say is if you have to chose one from 2 probabilities. and these 2 are random. the next trial will always be independent.

10

Hi Robert –

What is the relationship to Martingale bet sizing / position sizing?

Best, Howard

11

Roujee, In simple terms, suppose you bet on toss of coin (Head/Tail ).

  1. You bet $1 to win $1 but you guess wrong so you are down $1
  2. 2nd bet $2 to win $2 if you win you recover $1 from 1st bet plus win $1 - finish
  3. suppose you lost 2nd bet then you are down $3 so your 3rd bet is $4 ( double of last bet ). If you keep losing your losses become $7, then $15, $31, $63, $127, $255 etc…Eventually when/if you win you will recover all your losses plus $1. You need substantial amount of money if things don’t work out !!!