10,000 Nights at a Casino – Using Python to test my Roulette Strategy

A few years ago, friends and I took a pit stop in Macau during a trip through Asia after our graduation.  While there, I came up with a fairly simple roulette strategy that I thought could work for someone with enough of a bankroll.  Since then, my friend Steve and I have argued about 15x about the validity of this strategy.  In fact, Steve even wrote a VBA program to prove that I was wrong.  Well, Steve, I wrote my own program this past rainy Sunday (to highlight my gambling prowess, this Sunday I also doubled up in Texas Hold ‘EM poker after flopping a full house with 7, 2 off suite – but that’s a story for another day).

The strategy is as follows: put $1 on black.  If you win, take your winnings off the table and put a new $1 bet down.  If you lose, then put $2 down, if you lose again, double it to $4, if you lose again, double it to $8, and keep doubling down until you win, then take all of your money off the table (your winnings will offest your previous string of losses and leave you with a $1 profit), and start again with a $1 bet.  Of course, the problem becomes, what happens when you lose 10 times in a row.  Well, I’m glad you asked.

First off, let’s analyze the probability of you losing that many times in a row.  There are 38 possibilities in a roulette wheel – numbers 1-36, 0, and 00.  So, your chances of not hitting your color are ((38-18)/38, or about 53%.  So, you don’t have a great chance of winning if you just play once.  But, what are the chances of you losing several times in a row?  The below table illustrates how low these odds become (‘Necessary Bet’ is the bet needed to recover losses and make $1.  The ‘Probability’ is the cumulative probability of losing n many times in a row.  See R1:T17 of the first tab of the excel I link to at the bottom of the post for the calculations):

Below is a graph of what your pay offs may look like.  Note that you are winning only $1 at a time until you eventually get really unlucky, somewhere around your 13,000th spin in this case, and lose money beyond your bankroll which forces you to quit and walk out of Macau penniless (but hopefully not indebted to some Asian Gangsters).  Notice how the blue bar suddenly drops to -$9,000…

This type of payoff structure is analogous to “picking up nickles in front of a steam roller.”  If you haven’t already, you should read When Genius Failed, the story of the demise of Long Term Capital Management.  LTCM was a hedge fund run by Nobel laureates who made thousands of tiny bets using computer programs in a strategy called statistical arbitrage, among others.  The hedge fund blew up as they thought the scenarios that would cause their fund to collapse would only occur once every few centuries (it only took a few years for the fund to meet its very spectacular end in one of the first “too big to fail” situations.  Fun fact: all Wall Street banks pitched in to help unwind the fund’s assets, and thus divert a systemic break in the economy, except for Bear Stearns who refused to help…).

Below is a zip file with three Python programs whose outputs are captured in the excel.  The programs assume that you start with $100, and can borrow up to $5,000 from your friend (except for the last one that assumes you can borrow $15,000).  So, just as LTCM relied on leverage to try to double down on their bets and save their fund, this strategy also relies on loans to stay afloat in bad times when the odds go against you.

The first program is what would happen if you sat down and played until you went bust.  I ran this program once, and you make about $6,000 before hitting some bad luck and going bust (this is shown in the line graph above).  The second program basically runs the first program 10,000 times in order to get an average payout.  However, this one assumes you are only willing to play 100 games in a row as even 100 games would probably take a very long time in reality.  The last program is the same as the second, except that the player can lose up to $15,000 before quitting, and, if they have played 100 games and are at a negative value at the 100th game, they will play until they either recoup their losses, or go bust and lose $15,000.  This last scenario actually yields a positive expected value of about $4 (see the third table of the excel file I link to at the end of the post.  Expected value is what you would expect to win, on average, if you played this strategy many times).  Here is the distribution of returns from spending 10,000 nights in the casino with your friend that has $15,000 he can loan you if need be.  Pay no attention to the long tails where you lose $8,000 – that’s like a 10 sigma event and would NEVER happen 🙂

Conclusion: is this an effective strategy?  Not really.  Even if you found a table that let you start with $1 bets, and you had the patience to sit down and do this, and you had the bankroll, it’s just not going to yield all that much cash over time.

Please feel free to look over my code and let me know if you come up with any other conclusions by modifying it!  Also – I’m not a programmer – these scripts were very easy to do and took me only a few hours to write all three and conduct all analysis because Python is super easy!  If you want to learn more, MIT has FREE courses on Python that you should check out.  Enjoy!

To quote a really great “anti-recruiter” LinkedIn profile describing time spent at a large quant hedge fund: “I earn above-market returns 95% of years by collecting theta, selling volatility in the form of financial derivatives, naked short put options, and in summary, collect nickels and dimes in front of steam rollers, hoping the black swans never appear during my lifetime.


The Excel: Roulette Output

Python programs: Roulette Programs

NYU 0260 Entrepreneurship Conference

Last week I had the pleasure of attending a few of the morning sessions at the NYU 0260 (as in take your business from 0 to 60) Entrepreneurship Conference.  The event was organized by Solidea Capital, and the brand new NYU Berkeley center for entrepreneurship.  I’ve made a few jokes about the “illustrious” Stern undergraduate program at NYU.  And, while we may have really high SAT scores versus other programs, there is a large problem in that the majority of students coming out of both the undergraduate and graduate programs seem to have blinders on with their focus being Wall Street banks.  I’ve met dozens of people from Baruch, Fordham, and Columbia starting companies and close to zero from NYU.  That upsets me because I’m very competitive and don’t want to lose out to other schools, and also because I know there is a very deep talent pool at NYU that simply isn’t pursuing startups.

That’s why I was excited when it was announced that the NY Tech meetup will now be held at NYU each month, and that there are programs like this week’s entrepreneurship conference being held at the school – and attracting large audiences.  While the school has a long way to go, Firstmark Capital founder and NYU professor Larry Lenihan stated that he wants NYU to be the Stanford of the 21st century.  That is a lofty goal.  But, with the rapid expansion of the NY Tech scene, who knows?

NYU also recently merged with Poly, a technical school which broadens the University’s offerings and now enables undergrads to study engineering for the first time.  Poly also started the first incubator in New York, and is taking applications for their Manhattan program now!

Overall, the conference itself was tremendous and featured many great speakers.  In my opinion, it was a bit light on networking.  But, I did get to meet a new friend, Rohit, who was also a Stern undergrad and now spends his time helping startups who want to raise money.  Sounds like a lot of fun.

My hope is that the technical expertise of Poly and Courant are more and more matched with the increasingly creative and entrepreneurial Sternies (along with Tisch, Gallatin and the rest) to support a growing community within NYU that will no doubt spill into New York and the rest of the world.  I also hope I can contribute to this success in one way or another.  Very exciting.

This Week in Venture Capital (TWiVC)

TWiVC is a new podcast from the folks that brought us This Week in Startups, along with a few other noteworthy programs (these are also available through the iTunes Podcast directory).  They are on their third week, and have already grown to 25,000 listeners.  But, I thought I’d write a short post to help them “get the SEO juices flowing.”

First off, I’d just like to say that my new obsession is podcasts.  They are a great way to discover new music (I’m still a huge Pandora fan – but PodRunner helps me survive my now weekly runs along the Hudson), and there are many easily downloadable and free programs that cover almost any interest.  And yes, most are FREE, including the aforementioned.  My walks to work are now much more efficient so thank you Apple for access to the great content (Apple really takes it to heart when I give them a shout out on my blog).

TWiVC is an hour program that covers the past week’s transactions and happenings within VC.  The hosts are Jason Calacanis and Mark Suster who have a wealth of knowledge and great first hand vignettes that make the program very enjoyable (I’ll let it slide that neither of them knew who FirstMark Capital was).  Jason’s ADD approach to the show makes it quite entertaining as he is constantly voicing whatever opinions are on his mind and dishing out random facts.  His no-apologies style of commentary, and Mark’s insight make this my new favorite podcast!

If memory serves, the first week or so was very Twitter heavy, but overall the content has been great and sheds a lot of light on the trends within investments which are very closely tied to the trends within startups generally.  This is also a great tool for learning about how some of these companies have evolved, as well as how a VC like Mark would think about certain companies and how the VC process works generally.

My one “value add” – it would be great to have a deal sheet of sorts that accompanies the broadcast (basically the cheat sheet that Mark reads off which I assume includes a listing of recent deals, post money valuations, investors, previous investors, what the companies do, etc).  It’s tough to try to go back into the podcast and dig up this information if you do forget the name of a company, investor, etc.

Overall TWiVC is a great program and what I would consider necessary listening for anyone interested in learning about trends within VC/Startups.  The content is a solid channel for learning about ventured backed companies you may not have heard of.  And, I think that Jason’s energy and personal stories can be quite inspiring.  Please let me know what you think!

The economics of BK Kickball Sponsorships

Friends and I recently tried to get into what is apparently an exclusive kickball league in Brooklyn.  There are 32 teams in the league, 31 of them being occupied by returning teams, and 1 slot that 5-6 other teams will fight it out for.  Like any good Sternies (and a few Tischies along for the ride), we decided to circumvent the playoff by offering the league a sponsorship from Pepsi in exchange for the coveted 32nd spot.

How we would have procured this sponsorship is somewhat irrelevant – basically one of our friends works at a senior role within Pepsi where he thinks about marketing strategy all day long and could have made it happen

So – the very irrational league manager and our friend went into negotiation mode.  Apparently, Pepsi was supposed to foot the bill for the entire league, and also offer free snacks and drinks for all those involved.  When at first offered free drinks for participants in the weekly league, the league owner (who signs his email in the format: firstname F***ing lastname) responded that it wasn’t even worth him writing a reply email at the prospect of free drinks.  This got me thinking.

Let’s run through a few numbers.  Let’s assume that Pepsi drinks are sold for $1.00 in retail stores, and that 30 cents of this goes to distributors and retail stores (I’m assuming that Pepsi makes the product, it gets sent to a distributor, then on to a retailer.  Distributor margins are notoriously low at around 5-7% net and retailers are worse still at 3-5% net.  Some of this math may get skewed by the recent acquisition of Pepsi’s bottlers, or my lack of understanding of the Pepsi supply chain.  But, the point is to get to an estimate, and hopefully I can get an expert’s opinion to follow up on this post).  So, Pepsi sells their drink to distributors for 70 cents (don’t worry the overall analysis actually isn’t that sensitive to this number, I checked).  Their gross margins are around 54%, Cokes’ are 64% for reference.  Therefore it costs Pepsi about $0.70 * (1-.54) = $0.32 per drink.

There are 32 teams, each of which have 15 players, and play 10 games in the season.  Assuming each player drinks 1.5 drinks per week, on average, that’s 32 * 15 * 10 * 1.5 = 7,200 drinks!  That’s $2,318 out of Pepsi’s pocket.  Now, add in 2-3 Pepsi representatives at each of the game, the fact that people outside of the league will no doubt grab a few drinks, and other associated costs.  All of a sudden we are talking about ~$4,000.  And, from the perspective of our wonderful league owner, this is really more like 7,200 * $1.00 = $7,200 (aka what it would cost him to procure these drinks himself).

I personally thought that our narcissistic league owner would jump at the chance to brag about sourcing a Pepsi sponsorship and wouldn’t care to what extent the material benefits were.  I was sadly mistaken and the negotiations fell apart when it became apparent that we’d have to pull some major strings just to play an hour of kickball in McCaren Park a few times this summer.

At the end of the day, we went with Zog Sports.  They don’t accept bribes (maybe that’s a good thing), but they also seem to be a much more rationally run business and I’m sure wouldn’t balk at a few thousand dollars.  Somehow that just sits well with me.

My goal is to have my Pepsi friend write a follow up to this post debunking any faulty assumptions and also explaining how a consumer packaged goods company like Pepsi thinks about this type of sponsorship and the potential benefits to their brand.  So, please be on the lookout for part 2.

Some Thoughts on Pricing Models for Lead Gen. Busineses PT. 2

Last time I wrote about lead generation and some thoughts on how to price leads.  Now, I’d like to walk through an example of how to get to a starting price.  I’ll lay out some of the basic math, some of the finer points that have to be considered on a case by case basis, and what I consider to be the best way to get the data necessary for this type of analysis in a nascent and undefined market where secondary sources are lacking.

Example: Company A is the buyer of leads, Company X is the seller of leads (aka the lead gen company).

Company A makes 1,000 outbound calls to get 100 leads, which converts to 30 appointments, which converts to 5 sales with an average selling point of $10,000.  So, for those 1,000 outbound calls, Company A grosses $50,000 (these numbers are totally fictitious by the way).

Company X’s leads are “more qualified” because people opt-into them only when looking to make a purchase decision.  Therefore, 90% turn into appointments.  Every 100 qualified leads => 90 appointments => 15 sales = >$150,000 in new revenue.

This is where things get tricky.  We know how much revenue our leads are potentially worth.  But what does this translate to in terms of what they are worth to Company A (taking into account the extra FTEs freed up that don’t have to spend their time prospecting)?  Let’s assume that the internal sales person makes 20 prospecting calls in an hour and their time is worth $25/hr.  Our 100 leads convert to 90 appointments which would be the result of 3,000 outbound calls (3,000 calls=>300 leads => 90 appointments).  These calls cost Company A (3,000/20)*25=$3,750, or $37.50 per qualified lead.  Of course, this number doesn’t include a whole lot of other factors that could get in the way, but you get the idea (we could also factor in the lower cost of converting Company X leads in appointments even from the “lead” part of the funnel since they require fewer conversations given the higher lead => appointment conversion rate, and thus less time.  But, let’s keep this simple).

These numbers are good starting points in getting a picture of how much to charge per lead.  Basically, we want to get a sense for where our leads fit into the customer’s pipeline, and how much it would cost Company A to get the same quality of lead without us.  That’s what it’s all about!

These are just preliminary thoughts.  But how to get this data?  My advice would be to join the relevant LinkedIn groups for salespeople in your industry, and cold email them.  Why are sales people in this industry giving you accurate information (or even talking to you in the first place)?  Because you are an entrepreneur, they are intrigued enough at the prospect of talking to a potential employer, and are therefore willing to ingratiate themselves through providing (hopefully) insightful and accurate data around their sales efforts.  Plus, salespeople just like to talk.

Here are some questions I’d ask the people you get a chance to speak to: the all in costs of each sales person (base + bonus + benefits.  If you’re going to be replacing FTEs with your leads, then you need to know the ROI you’re providing Company A); what the sales cycle is (how long does it take, what is the overall process), and where your leads will fit into this equation; whether you’d have the same appointment to sale conversion rate on qualified leads as on prospected ones (qualified leads are actively searching and therefore will be evaluating your competitors whereas cold sourced leads may not be, but cold sourced leads may not really be in the market for the product); the organizational challenges of managing a large sales force; the ability your leads may offer for Company A to specialize its sales force (i.e make some people dedicated closers, and others focused on prospecting, or get rid of prospecting all together which may raise morale and increase efficacy).  There are, of course, many more relevant questions.  But, hopefully this list would provide a solid starting ground.  Remember, the bottom line is figuring out where your leads fit in and why, how much value they are offering your client, and starting from there.

Each industry has their own idiosyncrasies, and you have to keep in mind why your pricing makes sense versus your “competition” (internal sales teams in our example, but quite easily other lead gen companies or outsourced sales resources).  Are you going to under price and offer an ROI analysis for potential buyers of your leads?  Are you going to replace an existing lead service that offers unqualified leads at a discounted price?  Will these be exclusive leads?  All very interesting questions!

If you have any feedback on any of my posts or just want to say hello, please email me: phil (at) philstrazzulla (dot) com.

Some Thoughts on Pricing Models for Lead Gen. Busineses PT. 1

The other day I had a very interesting conversation with an entrepreneur who is about to launch what is essentially a lead generation business in a nascent but well defined vertical (which will remain unnamed for now).  We were talking about his revenue model, which is still very much in the works, and also some initial thoughts on how to price his leads which I thought would be interesting to share.

For the uninitiated, lead generation businesses develop potential sources of new business and sell these sources to companies interested in reaching these sources of business.  An easily understood example is that of financial planning lead generation.  There are many websites that capture data on people looking for advice on Annuities, ETFs, etc.  The companies that capture this data then sell it to financial planners as qualified leads.  The process looks a little something like this:

These leads then find their way into the sales funnel of the buyer of the leads. Below is an example of what a typical sales funnel for a financial planner may look like (the leads that we would collect as a third party lead generator would fit in somewhere between leads and appointments, more on that later):

If you’re providing leads into this funnel as a third party, it’s important to track the efficacy of your specific leads throughout this funnel.  In fact, many lead generation companies do not get paid per lead, but rather based on the number of appointments their leads can generate which is a proxy for how well qualified the leads are.

Now, about the actual pricing of the solution.  I’d like to shift away from financial services for the time being as that market is fairly well defined.  The competition you’d face within financial services is other lead generation companies (as this is a mature market as far as lead gen goes) and therefore the price is set at the market rate unless you can offer a differentiated product.

Shifting towards my entrepreneur friend’s nascent market – there are no other lead gen businesses, nor is there any outsourced sales organizations servicing this vertical.  Therefore, the focus is on competing with internal sales forces.  Understanding the compensation structure was the most important take away that I could offer.  Most internal sales reps, especially those selling big ticket items, are paid a minimal base salary and large performance based bonuses.  The key is to figure out where your leads fit into their sales pipeline, and then figure out the expected value of that lead to the company, as well as the expected cost associated with that lead if it were brought in through the internal sales team through telesales, direct mail, etc.  As this post is getting a bit long and Lost is on tonight, I’ll leave walking through an example with some numbers until part 2.

PHP MySQL Workshop at Hive 55

This evening I attended the PHP MySQL workshop at Hive 55, which is one of the growing number of shared workspaces in New York City.  For the unfamiliar, shared workspaces are locations where people from many different walks of life choose to work for anywhere from 1 to 30 days per month.  It’s a great way to network, meet people with complimentary skill sets, and avoid the temptations inherent in working from home.  These types of initiatives will no doubt catalyze the growth in Silicon Alley that everyone keeps talking about.

Plus, they host cool events like tonight’s PHP/MySQL workshop which covered some of the tools used to build basic dynamic web pages.  Tonight’s lecture was given by Hans from http://www.bootup.io/.  I think we were all a bit shy at first, but the discussion got very interactive and there was some great networking afterwards.  I was lucky enough to meet Ryan Clarke and Dave Tomback who shared some of the challenges they are currently facing in building their respective startups.  The underlying theme was that business people like us need a technologist co-founder, especially if you’re thinking of outsourcing development.  Easier said than done in NYC, but good advice nonetheless.

As far as PHP tutorials, I’d also like to recommend the PHP Academy page on Youtube.  These videos are short, sweet and very useful.  Alex is one of the very best developers that I’ve come across when it comes to being able to explain concepts in an easily understandable manner.  I was even more impressed to find out how young he is.

Also, if you’re wondering how I found out about tonight’s event – I receive the NYC Edition of the weekly Startup Digest.  If you live in NYC and have any interest in attending tech related meetups, job fairs, etc, I highly recommend signing up for this newsletter.  They have editions for about 25 other cities, so check them out.  Enjoy!

Hello World

There is always a bit of awkwardness in a first interaction, so I will break the ice with an introduction.  My name is Phil.  I am 24, live in New York City, and work in finance which I was trained to do at the illustrious Stern school of business at NYU.  Beyond any formal training, finance, business, and the confluence of the two are subjects I’ve been interested in for quite some time now.

I recently built a site: www.wrestlingontv.com.  I was (and still am) a huge fan of amateur wrestling, but find it very hard to track when the world’s oldest (as in first sport in almost every culture known to man) and greatest sport will be on TV, or even streaming on the internet.  I’m guessing the same problem goes for a lot of fans of non revenue, tertiary sports.  So, I am trying to develop a scalable model to track all of the wonderful coverage that my sport deserves and make it easy for others to know when they can enjoy this coverage.

I started with close zero technical ability (unless you count building really long formulas in excel, or that one week in 8th grade I spent learning BASIC in the hills of Western Massachusetts).  Therefore, I thought it would be helpful to document some of the resources I used to learn a bit of PHP, Drupal, MySQL, etc.  Also, I have a much more ambitious and involved project which will hopefully develop over the next several weeks and months which will be a lot of fun to write about.

While I’m keeping the newer project a bit of a secret for now (something most VCs would probably frown upon and call me paranoid for), I think that a lot of what I’m learning about SEO, databases, etc will be worthwhile to post.

I also am excited to write about my thoughts on the economics behind everything from Night Life to Brooklyn Kickball.  Please stay tuned, and send me an email if you are so inclined.