Games of chance are influenced by probability.  If you flip a coin 49 times and it comes up heads, there is a 50-50 chance that the coin will come up heads on the 50th flip.  That is the essence of probability theory.  Past history does not influence future results.  Everything seems to fall neatly on a bell-shape curve (also known as a Gaussian, or normal distribution).

I am not a mathematician, but I do know that there is a 68% probability that prices will end within one standard deviation from the mean over a given period of time.   There is a 95% chance that it will end within two standard deviations.  All pretty basic stuff — assuming you know what a standard deviation is.

A number of brokers offer clients a tool called a Probability Calculator.   The tool is very fun to play with, in my opinion.  And it is REALLY useful if you are evaluating the probability of success on a spread option trade.  With a credit spread, for instance, you are collecting premium up front.  Usually you have at least one break-even point.  If you are trading an iron condor or a butterfly strategy you may have two break-even points.  Based upon an option pricing model, the probability calculator can tell you the calculated probability of your trade being successful.  Success is defined as making one penny, or more, on the trade.

To use the calculator, simply enter the underlying symbol, and establish your target prices and your time frame.  If you have that iron condor trade on your mind, enter the break-even points on the strategy as your price targets.  The calculator will then instantly give you the probability of touching your target prices within your defined time frame a well as the probability of your strategy finishing above, or below, your target prices — assuming you take it to expiration.  Everything is a risk-return trade-off, but if you are doing a credit trade, you want a better than 50% chance of having the trade become successful.

I use a probability calculator to check just about any spread trade I want to put on.  First, I establish my strategy in the more powerful, and more graphic, Profit and Loss Calculator.  Here’s the rub, though.  (Very important.)  You have to believe that probability theory is the best theory to explain price results in stock markets.  That’s been questioned lately as we are seeing more and more black swan events that are supposed to happen only once every 500 hundred years.

You can find a Probability Calculator at TradeKing  Zecco or OptionsHouse.  But before you dive in, read this review of a book by Benoit Mandelbrot’s called “The Misbehavior of Markets” along with the comments on the review.  The basic idea is that probability theory is flawed with it comes to predicting stock prices.

It may get you thinking that perhaps probability theory is not all it is cracked up to be.

OptionsHouse offers a big-boy Web-based trading platform that was built by experienced traders.  It is one big AJAX application just in case you are tech-savvy enough to know what that means.  From a functional standpoint, that means there is very little fluff.  Chains are streaming and so are the charts.

OptionsHouse is designed for ergonomic trading.  Its current advertising tag line, “Fast Matters”, resonates the first time you place on option order directly from an option chain in about two seconds.  If you know what you are doing you will appreciate this flavor of brokerage.  OptionsHouse clears through Penson Clearing.

Recently OptionsHouse introduced a new streaming charts and news tool.  Although this tool could be more snugly integrated into the trading platform  (you can’t place a trade directly from the chart tool) it is a welcome addition.  Other new additions include the Profit & Loss Calculator, Probability Calculator and number of volatility charts and screeners.  With one volatility chart view, you can look at the differences in implied volatility between the 25 delta call and the 25 delta put.  Most professional traders know that the price of calls and puts, at the same strike price, tend to be at parity.  But this strategic comparison of implied volatility is worth a closer look.

OptionsHouse offers a sleek platform and probably one of the best virtual trading tools out there.  It is all part of the same platform, so there is no need to jump to another part of the site.  Simply click on the “Change Account” button and the colors change from the OptionsHouse green to virtual-trading orange (pumpkin, actually).  You start with $3,000 in fake money but you can pump in as much virtual cash as you need.  It’s an excellent way to get all of those bad option trades out of your system before you start trading with the family nest egg.

Pricing at OptionsHouse is super-discount low — a flat $2.95 for stock (up to 4,000 shares) a flat $9.95 for a single-leg option and a flat $14.95 for spreads (up to four legs).  You can trade a 50-contract iron condor for $14.95.  Tough to beat that price.

On the negative side of the ledger, OptionsHouse comes across as being a little too expert, sometimes.  Intermediates need not apply.  The educational material provided on the site doesn’t make it any easier.  You get a strange brew of 888-options content and slick videos from a sister company called Financial Markets Education (FME).  The video material is almost impossible to absorb.  It’s basic material presented by a smart guy.  Must be worth knowing, but he lost me at “hello”.

Zecco has built itself into a powerhouse broker that appeals to the cost-driven, active trader.  It offers a full-range of trading capabilities including tools, education, community and, most recently, forex trading.

Over the years, Zecco has established a strong foothold in the market by featuring zero-dollar stock trades.   With value-based appeal, the firm now challenges the big boys on providing mainstream brokerage services to the masses.  Zecco’s clearing firm, Penson Clearing, is the same firm used by thinkorswim and OptionsHouse.

Zecco has strong European influence.  Jeroen Veth, the company’s CEO, is from the Netherlands — as are other members of the management team.  As you might expect, they add a certain European flare to the company along with a willingness to innovate.  Out of the gate, Zecco embraced new media and social networking as a fundamental part of its brokerage experience.  I guess you would expect that from a firm based in San Francisco.

What I like about Zecco is that the trading center is centralized.  You can easily switch from a view of your portfolio holdings to any number of stored watch lists — without jumping to a new page.  That is easy to get used to and it is surprising how few brokers offer that basic convenience.

For a monthly fee, Zecco offers QuoteStream Professional, a streaming portfolio, news and charting tool from QuoteMedia.  I have used it and I think it is one of the better packages out there.  Obviously, I wish it were free, but if you can accept that real-time quote data costs real money, it’s a great tool to have.

If you are into PIPs, Zecco recently rolled out Forex trading.  Forex trading requires a separate account from your Zecco Trading account (forex trading is governed by a different body).  Highlights include a virtual trading environment and round-the-clock trading.  The city never sleeps.

Every brokerage firm appeals to a different part of the market and I think Zecco’s sweet spot is the under-40 crowd with its abundance of cool and just the right amount of attitude.   Despite a liberal use of pink throughout the site, these guys are not Legally Blond wannabes.  They are well-financed, secure and always looking to add innovative product improvements.

One of the year’s most enjoyable corporate events was a Zecco Meet and Greet that was part of its Lunch 2.0 series.  It was nice to have my online broker invite me to a reception that was fully catered.  You would never see that from Scottrade.

On the “needs-improvement” side of the equation, I think Zecco has too much clutter on its site.  That starts with an abundance of banner advertising that simply overwhelms the senses (The Trading Center is ad free).  In the beginning, zero-dollar stock trades  required this revenue stream to keep the lights on, but now that free trades only apply to accounts with balances in excess of $25,000, I think the ads have to go.

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TradeKing is a full service online broker and winner of many accolades from Barrons and SmartMoney magazines.  Feature-rich with tons of research extras and tools, TradeKing provides a great platform for trading stocks, options, ETFs and fixed income securities.

TradeKing uses separate trade screens for each option strategy.  Some folks like this, others prefer a single-format trade screen.  I like separate screens for each strategy.  For one, it integrates well with separate option chains for each strategy which I find is great for drilling down and learning how a strategy works.  For another, it makes it easier to pre-populate the order ticket (especially multi-leg option trades) directly from a research tool.

We all know that real men don’t use option symbols, but it is nice how TradeKing shows the symbols throughout the site and even helps you look them up within the trade ticket.

TradeKing’s trader network is very cool.  You can choose to publish your trades and make your trade notes public.  A lot of traders do.  As a published trader, you can elect to show quantities of shares traded, or not.  Return on investment is calculated using Maxit — the best portfolio tracking tool for options.  I find it fascinating to sort through the community performance data.

Who can argue with TradeKing’s pricing?  $4.95 for stocks and ETFs and $4.95 per option trade, plus $0.65 per contract.  That may not be the absolute lowest commission in the marketplace, but it is the cheapest without requiring an oath of allegiance, a minimum deposit, or an advanced degree in option trading.  Broker-assisted trades are charged at the same price as Internet trades.

Another one of TradeKing’s many strengths is its clearing firm, Legent Clearing.  Legent used to clear for optionsXpress when it first opened its doors.  A few days back, I did a side-by-side comparison of how much time it took to clear a stock position I sold and then transfer the cash proceeds into my checking account via ACH transfer.  I sold shares from two different brokerage firms (one firm was TradeKing) at exactly the same time.  The result?  TradeKing beat the other firm by 24 hours.  That extra day comes in very handy when you need to pay the electric bill.

TradeKing is one of the few brokerage firms that allows investment club accounts to trade without forming a corporation, partnership or LLC.   It is really nice to have a clear process for opening an investment club account.  In fact, TradeKing is THE brokerage firm for investment clubs – period.   Plus, you can share a view of the account with club members on a read-only basis and create a dedicated private forum within TradeKing’s trader network.

What needs improvement?  I think TradeKing needs more streaming data.  When I am sitting in my bathrobe like “Vinnie the Chin”, making some trades, but mostly just watching the screen change, I want action.  TradeKing needs to make a streaming portfolio tool available — even if it is fueled by semi-delayed quotes.

Options involve risk and are not suitable for all investors.  Please read Characteristics and Risks of Standardized Options.

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The stock ended up jumping 23% — and trader took a loss on the short option position.  He had to buy back the puts which he sold for $0.65 for $2.40.   Ouch.  But maybe this guy was not so dumb after all.  His gain from the stock (married to this option strategy) far outweighed the loss from writing the put option.

With a married put strategy, you own shares of stock (in round-lot increments of 100 shares) matched with one put option for each 100 shares.  That gives you a degree of downside protection.  This is an example of using puts for insurance.  You can do this with shares you have owned for awhile, or shares you buy at the same time you make the option trade.

As usual, the moneyness of the option makes all the difference in the world.  To get the maximum insurance value at the lowest net cost, you should buy the put “at-the-money”.  Yes, the time-portion of the option’s premium is at it’s highest, but you get some nice upside potential if the stock breaks out and still get all that juicy downside protection.

The guy Steve talks about obviously was approved to sell naked options.  There is no such thing as a “covered put”.  So you have to wonder why he didn’t BUY the put instead of sell it.  My read is that this trader was pretty bullish on the stock and he was prepared to double up if the stock made a run for it (i.e. he was put additional shares).   By selling the option, he ended up giving away half the profit on the gain from the stock.  But if the stock had tanked, he would have netted the premium from selling the option and covered any loss on the stock position.  That’s cool.

When you think about using married puts as insurance, you should also think about the completely-hedged alternative — which is just to convert to cash and sit on the sidelines.