The MARTINGALE… and how to bring ‘im down!

A gambler is playing an even money bet: for each dollar he wagers he can win a dollar. And he’s been on a lucky streak, building his stake up to $5000. He started with only $2500 so that’s a 100% win so far. He can’t lose. ūüėČ

So the gambler decides to bet 20% of his stake, or $1000.

Ouch. First loss in a while… but that’s okay. With $4,000¬†to burn he has plenty of opportunity to win back that thousand bucks. Hmmm… “Putting up $1,000”, he says. “If I win, that’s a grand back in my pocket and I’ll be where I was.”

Ouch again. Our gambler bet $1,000 of his $4,000, 25% of his stake on another losing play. He now has only $3,000 left.

“I’m not going for the whole $5,000 I got up to. I just want to return to what I had a SECOND ago, the $4,000. Then I’ll just quit.”

He bets $1,000, or about 33% of his remaining $3000. Yikes… one more loss takes him from a $3,000 stake down to $2,000.

“ARGGH!” the gambler is frustrated. Only moments ago he had $5,000. Hard to wrap his head around the idea of starting the day with $2500, working his way up to $5,000… and now he has less than he started with. “That’s IT! Just one more play with $1000. If I win I’ll be back up to $3,000 and I can quit the day with more than I started.”

He bets HALF… 50%… of the $2000 he has left on yet another losing play. The gambler looks at his remaining stake of $1,000. What is he likely to do next?

You’ve just seen an example of Gambler’s Ruin, or the Martingale effect. It takes many forms but the most common is what I’ve just described: the gambler uses equal amounts to try and win his stake back, but the percent of his stake that he gambles increases exponentially.

It’s an even WORSE situation if the gambler increases his bet size every time, trying to get back to where he was in better days. This effect is called The Martingale or Gambler’s ruin. The gaping maw of the Martingale has swallowed alive¬†many hopes and dreams… not only of starry-eyed Vegas victims, but of traders as well.

Losing 20% of one’s stake means having to win 25% based on the remaining stake. Losing 25% means you must win 33% to get back to square one… losing 33% demands a 50% win… and a 50% loss means¬†you¬†gotta DOUBLE your money, make a 100% gain… and still have no bragging rights. Because after all, what you did was get back to exactly where you started.

What if we failed to make that 33%, 50%, 100% gain when we really needed to? It’s a slippery slope indeed.

So what’s the solution?

Savvy traders know that they need to skew expectancy in their favor. Expectancy is a mathematical term that means how much you can expect to win or lose over time, given the¬†factors of risk, reward, and probability. A negative expectancy situation is what you almost always face in games of chance, i.e., ANYthing you can play in Vegas ūüėČ .

A positive expectancy situation can be set up in a number of ways. By skewing either the reward in your favor, mitigating risk, or simply increasing your chances of a good play, you might swing expectancy in your favor.

Here’s the formula for expectancy:

E = [P x W] – [(1-P) x L]

E: Expectancy or Expected Return per Play
P: Probability of winning, expressed as a fraction
W: Win amount
L: Loss amount

Let’s plug in the numbers: say you have a 50% chance of winning a coin toss. Expressed as a fraction, that’s .5 for the P value above. Then the win: if you get paid¬†two-for-one, then that’s $2 for every winning play in which $1 was wagered. The first part of the equation, [P X W] then is .5 X $2.00 = $1.

Then we have to account for losers. The probability of a loss is equal to 1 minus the probability of a win, expressed as a fraction. So, (1 – P) in this case is 1 – .5, or .5. Multiply that times that amount wagered, L, and you have [ .5 X $1 ] = .50 cents.

Now take let’s complete the equation. E = [P x W] – [(1-P) x L] in this case comes out to:
[.5 X $2] Р[(1 Р.5) X $1] or E = .50

In other words, for every dollar played you may “expect” to win .50 cents.

Play one dollar. You lose. Aww… Play again. You WIN this time, bringing it two dollars. You’ve won once, lost once, that’s $2 minus $1 equals $1 total for two plays… or .50 cents each. Yup, the formula is on track.

Would you play this game? So would I, but only on days that end in “y”.

ūüėČ

That’s because over a long enough time horizon, I can bet on the coin toss results tending toward 50/50. There will be strings of losses, to be sure, but then there will be strings of winners as well.

This is a positive expectancy situation. Is there a negative side to it? Of course… the unfortunate soul on the OTHER side of the table from you that has to keep paying you double when you are right, and only win even money when you are wrong.

How does this apply to a trading account? The saying is “Cut your losers short, let your winners run!” The way that RadioActive Trading works with this principle is by controlling the one thing that we CAN control… the dollar amount, percent of the trade itself¬†and percent of our total portfolio that’s AT RISK… while leaving the upside open.

That means that the E = [P x W] – [(1-P) x L] equation has a good chance of tipping in our favor over a period of time because there is no limit to how high the win side might go, but it’s tightly controlled on the losing side.

The married put in RadioActive Trading, coupled with our track record of winning picks,¬†tells us exactly¬†what’s going on in the “loss” portion [(1-P) x L] of this equation. Now all we have to do to set up positive expectancy is to close trades that win a greater amount than that in the [P x W] portion.

It’s both harder AND easier said than done. But it IS within the realm of control for a disciplined trader.

Hey, guess what? Though it’s fairly easy to adjust our trading rules to get to a positive expectancy…¬†we’re only halfway there. There’s another, all-important ingredient¬†that goes along with expectancy… and that is bet sizing. Without proper bet sizing (called position sizing or asset allocation when we’re trading as opposed to gambling), one might STILL lose in a positive expectancy game.

WHAT..? You mean it’s possible to set up an “edge” in the market and still lose? Yup. That problem… and more importantly, the solution… will¬†be the topic of the next post. See you out there!

Happy Trading,

Kurt

Comments? Lay ’em on me. Only room for 20 this time though, so make it quick!

 

About Kurt Frankenberg

Kurt Frankenberg is an author and speaker about entrepreneurship, martial arts, and trading the stock and options markets. One of several "Biznesses" he founded as a teen, The Freedom School of Martial Arts, has been in continuous operation since 1986. Kurt lives in Colorado Springs with his wife Sabrina, German Shepherd Jovi, and his ninja cat Tabi.