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.”
Attachments:
Python programs: Roulette Programs
Additionally, 54 % of men and women say they’d love to see extra video from
brands. So in the event you’re not presently employing video as portion of your respective
internet marketing system, now’s some
time to get started on.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Stock videos can be utilized as aspects of a video to help you preserve costs on creation. Most inventory
videos are made use of as aspect of a bigger manufacturing for this function. You can find stock videos on an array of concepts and themes to fit your task.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Our purpose in digitizing these movies and Placing them online is to offer easy accessibility to your wealthy and
interesting core assortment of archival movies.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
The location provides a uniform Value per video across the
full web-site, with increased resolution data files costing additional
free porn | doega 2021 – Watch Mobile HD Sex,
Porno Videos
porn
What You will be CreatingColor correction is definitely
the A part of the video article-production approach where you harmony your
clips to neutralize hues and get a uniform…
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Only make use of the intuitive interface to refine your quest and locate the right inventory
video. There’s footage, backgrounds, and after outcomes.
Furthermore, you will discover a lot of inventory videos
in HD and 4K.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
This video is about apple cider vinegar for hair loss
information but also try to cover the following subject:
-how to use honest opinion apple cider vinegar for hair loss
-apple cider vinegar for hair loss treatment
-apple cider vinegar for hair loss and growth
Blender is made as a 3D animation suite but includes a purposeful video editor that needs to be more
than enough for many people’ requirements.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
https://buypropeciaon.com/ – Propecia
Cialis
Gay porn or male guy porn videos are not available on our site.
Fake Taxi 2021, Hotel, house.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Cialis E Psicofarmaci
FlixPress is a spot to build Qualified video templates. FlixPress also offers some video templates for free.
Just sign-up for an account and select the free
templates from their template library.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
I am a very long time, big fan of Vecteezy. They’ve a superb and simple to navigate Site with an abundance of written content, free or membership centered –
there is a large vary for the two possibilities.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Video Blender is a sizable selection of 201x-era media, comprising the styles of memes, videos
and performs on video sharing websites of some time.
They range in high-quality and exposition.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
http://buypropeciaon.com/ – finasteride prescription floroda
Useful resource window redesigned with choices to pick several documents at the same time,
export files in teams and delete data files.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Scene notion modified: now all visual objects can include things like
some other Visible objects, which was once accessible just for the sprite
ahead of.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Every one of these inventory video websites have their positives
and negatives, but something’s for specified: You can find heaps of wonderful free stock video footage around.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
When you are hungry for beautiful stock images rather than video,
We have got that included as well. Want copyright-free vectors?
You’ve got free stock illustration web sites for the people.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Merhaba Arkadaşlar Bu Site Dolandırıcıdır itibar etmeyin Bunlar Profesyonel Nitelikli Bir Dolandırıcı Firmasıdır itibar etmeyiniz.. porn movie
You are able to do this by incorporating text to the video,
or simply by writing the author’s particulars underneath the video.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
The application crashes on splitting a file into video and audio although the item
is locked; previewing Reverse audio effect; employing Shift, a change impact.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Becoming a member of a video conference need to be uncomplicated.
With Webex, you have a single button to drive Using the big inexperienced button and you also’re in.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Videvo is a source of hundreds of stock videos and movement graphics, which can be found read
more for down load without any cost. Video clips are organized in different types for simple searching.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
A superb video intro not only draws interest but will also provides the ideal impact
to possible customers. Videos may superior have interaction new
viewers. While developing great videos will consider time, hard work and ability, why not simply use inventory videos.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
All parameters of audio results may be edited in a visible editor, which enables people to create variations less
complicated and faster.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
http://buypropeciaon.com/ – propecia 1 mg
Merhaba Arkadaşlar Bu Site Dolandırıcıdır itibar etmeyin Bunlar Profesyonel Nitelikli Bir Dolandırıcı Firmasıdır itibar etmeyiniz.. porn movie
The quality of cost-free inventory video clips on Videvo varies: Some are extremely Specialist
and Many others have Evidently been shot and not using a
tripod. Some clips are shipped as MP4s and others in QuickTime format.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
The speed with the algorithms for rendering translucent objects is doubled
because of assistance for SSE2 technological know-how;
free porn | doega 2021 – Watch Mobile HD Sex, Porno
Videos
porn
The choice of supported formats continues to be expanded Together with the
MXF format – a video container structure for professional
video and audio written content that serves another of precise videotape in a very digital format.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
stream of pink blood cells in glowing plasma close up footage stream of red blood cells in glowing
plasma closeup footage
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Tienda Nº 1 en Camiseta Atletico de Madrid
Encontrarás cada camiseta atletico de madrid 2022 y ropa de entrenamiento
de los clubs y selecciones nacionales para adultos y niños.
Cialis No Me Hace Efecto
Kamagra Flavoured Oral Jelly
If you need stock shots, Pexels also offers a terrific collection of quality-top quality stills beneath the similar license.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Vidsplay Site presents the number of totally cost-free inventory
footage. The web site is up-to-date on a regular basis each individual
7 days with footage that’s certain to make your video job jump out.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Mixkit is actually a no cost website for video creators that features a gallery of awesome
free video clips, new music tracks and Premiere Professional
Templates.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
This means that you’ve possibility to at the same time develop lots of objects in random areas
and place in time.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
These videos are available totally free and are Prepared for use as b-roll footage to improve your video output expertise, or to elevate
the success of the future social media write-up.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
As video gets more common online, the need to down load totally free HD videos boosts.
It’s possible you’ll need material to help your brand name.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
The Lens flare impact, imitating a solid source of light-weight, included for
the “Open up GL” class of the video outcomes menu.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
The “Edit the defeat” Instrument added allowing buyers to synchronize any video outcomes to your qualifications audio.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Beachfront is usually a blogspot compilation more info
in which you can obtain exclusive HD stock footage and animated backgrounds for any production purpose.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
To find out more about restolin hair growth reviews,
This video is about restolin hair growth reviews but also try to cover the following subject:
-restolin supplement review
-restolin ingredients
-restolin hair loss
Something I saw when I was researching info on restolin hair growth reviews
was the lack of pertinent details.
Restolin hair growth reviews however is an subject that I know something about.
This video for that reason should be relevant and of interest to you.
Have I addressed all of your questions about restolin hair growth
reviews?
People who looked for restolin supplement review also searched for restolin ingredients.
For Experienced and industrial do the job, It truly is hard to defeat the quality and sheer a number of stock video out there on Shutterstock.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Their interface is incredibly effectively designed, which
makes it uncomplicated to search out what exactly you’re trying
to find. You can also lookup by resolution and frames for
every 2nd.
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn
Merhaba Arkadaşlar Bu Site Dolandırıcıdır itibar etmeyin Bunlar Profesyonel Nitelikli Bir Dolandırıcı Firmasıdır itibar etmeyiniz.. porn movie
Zeyno çok iyi yaptı bence Ozan artık öğrenmeliydi
zaten.Esra’nın da dediği gibi iş işten geçti artık bu seferde Esra affetmesin Ozan korfalıyı…
free porn | doega 2021 – Watch Mobile HD Sex, Porno Videos
porn