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
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As you know that printable calendars are available in the market and online, where you will find various categories
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Bahçelievler Halı Yıkama
20 yıllık tecrübesi ile Mis Oruç Halı ve Koltuk Yıkama İstanbul genelindeki müşterilerine, gelişen ve
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olarak gelen bir uygulamadır. Bu çevrimiçi yayın platformunda, birçok Disney + Free Accounts prodüksiyonuna bir ücret
karşılığında erişebilirsiniz. Geçtiğimiz yıl ABD, Kanada ve Hollanda’da piyasaya sürülen uygulama daha sonra
Avustralya ve Yeni Zelanda’da lanse edildi. Kullanıcılar başta çok fazla sorun olduğundan şikayet
etseler de, üreticiler bu kusurları kısa sürede giderebildiler ve şimdi kesintisiz bir akış sürdürdüklerine dair olumlu yorumlar görüyoruz.
Bedava Disney Hesap
Discord Free Accounts 2021 | Discord Account And Password ,
discord bir ortam, etkileşim. In fact, discord can be
thought of as a lot of places because it is. Discord is an environment that is
generally used for communication and chat, hosting game servers.
So if you are looking for a chat environment, discord may be just for you.
You ask why; no ads, privacy, quality, speed.
So what more could a person want after finding these in a chat.
So please install discord and continue if you think like me.
After installing Discord, you need to login. So if you do not have
a discord account, you may be asked to log in.
So to log in, create a discord account and
log in with that account information. If you
do not have an account and are having trouble creating an account, we can create an account for you.
Discord Free Accounts
Clash Royale Account Free 2021 | Gems, Accounts & Password ,
Nobody knows the game of clash royale. This game has been appealing to many players since years ago.
It is a deep-rooted game with a huge player base. People didn’t know this game at first, and as time went by, it became known. The game is
entirely for action, tactics and adventure lovers.
If you like strategy, this game is for you.
While playing the game, you may have difficulties at
first, this is very normal. As time passed, you would begin to understand the game and play it fully.
And that’s when you might think you are a very strong
player. You ask why; Because you understand and fully comprehend
the game, you will act in a very knowledgeable way.
Clash Royale Account Free
Bedava Brawl Stars Hesap (Gems) 2021 | Supercell tarafından geliştirilen ve yayınlanan Brawl Stars Passwords, Brawl
Stars, dünya çapında popülerlik kazanan nadir mobil oyunlardan biridir.
Hatta mobil oyun dalında BAFTA oyun ödülüne aday gösterildi.
Bu nedenle, 2006 yılında beta sürümü
ile piyasaya sürüldü. In, 12 Aralık 2009’da dünya
çapında piyasaya sürüldü. En son 9 Haziran 2014’te Çin’de sunuldu.
Beta sürümünün sona ermesinden sonra, gerçek çıkış tarihi dünya çapında 12 Aralıktı 2018,
9 Haziran 2020’de Çin’de iken. 2017’de lanse edildi ve 2018
ve 2019’da geniş kitlelere ulaştı. Üretim,
bir günde 5 milyon ön kayıt almayı başardı. Başlatıldığı zaman. Küresel lansman öncesinde cebine 6 milyon dolarlık bir gelir bile koydu.
Bedava Brawl Stars Hesap
Shutterstock Free images | Free Account and Passwords 2021 , I
will give you free photo accounts. So these accounts belong to us and have been specially prepared for you.
So if you really want help from us, you are in the right place and on the right page.
We have purchased accounts for you on the shutterstock site and
presented them to you. So if you want, you can also have one or more of these accounts.
Shutterstock was once the most popular company and is now among the
most popular companies. If you need a professional photo, shutterstock is for you.
Shutterstock Free images
Darkorbit Free Accounts 2021 | New Free Account And Password.
DarkOrbit is a web-based space game that has been in service for many years.
It is one of the rare web-based games that has managed to maintain its popularity until today.
It has a theme that deals with war and space.
So it has a large player base in the world. It has also increased from time to time in our
country and has managed to gather large masses.
The game has been very popular in the past, as it is completely in Turkish.
In 2006, Bigpoint Games company released the game. Although there has been a decline in the number of players from
time to time since its release, it still
hosts a considerably large audience.
Darkorbit Free Accounts
Bedava Yahoo Hesap 2021 | Yeni E-posta Hesabı ve Parola.
Yahoo nedir? Yahoo bir ana arama motoru olmasına rağmen bu güne gelen en büyük
özelliği mail servisidir. Yahoo Mail uzun yıllardır birçok kişi tarafından tercih edildi.
Maalesef bu durum bugün pek hareketli değil. Çünkü
yerini Google ve Yandex aldı. Arama motoru sektöründe Google tüm dünyayı ele geçirirken Yandex, Rusya gibi büyük bir ülkeyi ele geçirmeyi
başardı. Yahoo’nun arama motorunun sektörde fazla bir şeyi
kalmadı. Bazı insanlar ve bazı ülkeler hala kullanıyor
ama maalesef eski değeri eksik. Mail durumunda, Google Mail genel olarak bu durumu devralmıştır.
Gmail, günümüzde en çok kullanılan posta hizmetidir.
Ücretsizdir, kullanımı kolaydır ve Gmail, Google’ın arkasındaki dev markalardan biridir.
Bedava Yahoo Hesap
Bedava Amazon Hesap Prime 2021 | Hepimizin bir yerden duyduğu Account And
Password, Amazon, e-ticaret, bulut bilişim, dijital
akış ve yapay zeka ile uğraşan Washington merkezli bir şirkettir.
Ücretsiz amazon hesapları 5 Temmuz 1994’te kitap pazarı olarak kuruldu.
Daha sonra şirket büyüdükçe elektronik, oyun, mobilya,
yemek, giyim ve oyuncak gibi diğer pazarlara da açıldı.
2015 yılında piyasa değeri ile Amerika’nın en değerli perakendecisi olmayı başardı.
Bugün birçok sektörde yer alan Bedava Amazon Hesapları adını duyuyoruz.
Bedava Amazon Hesap
Bedava Fortnite Hesap 2021 | Ücretsiz Hesap, Geçiş Ve Cilt.
Yani PUBG’nin popülerleşmesinden sonra ortaya çıkan yeni bir modla duyulan fortnite, Epic Games tarafından hazırlanan bir
oyun. Özgür olması kısa sürede meşhur olmuş ve geniş bir oyuncu kitlesine ulaşmayı başarmıştır.
Bu yüzden Fortnite ücretsiz hesapları güncellemeler almaya devam
ediyor ve birçok yenilik yapıldı. Aslında oyunda canlı konserler yapılıyordu ve başka tür etkinlikler de vardı.
Böylece 2018’de Teen Choice En İyi Video
Oyunu Ödülü’nü aldı. Ve aynı yıl, En İyi Çok Oyunculu Oyun ve En İyi Devam Eden Oyun için Oyun Ödülü’nü aldı.
Bedava Fortnite Hesap
Bedava Dota 2 Hesap 2021 | Yeni Hesap ve Parola.
Dota 2 nedir? Dota 2, Valve Corparation tarafından geliştirilen ücretsiz bir MOBA oyunudur ve güncellenmeye devam etmektedir.
Dota 2 Free Accounts aslında önceki oyunlardan esinlenen bir oyun olarak biliniyor ancak türünün en büyük oyunu olmayı başardı.
Bedava Dota 2 Hesap
Free Boom Beach Accounts (Diamonds) 2021 | Account & Password .
One of the leading names in the mobile gaming industry, Supercell’s recently famous game Boom Beach is a strategy game.
It attracts great attention in our country and has managed to cause a boom in the mobile game industry.
You have an island in this game that looks like a side game of Clash of Clans and you develop your island
against attacks by improving it. You can also
capture spoils by attacking other islands. By developing your strategy well, you need
to protect your island and develop further by organizing attacks.
You have an economy in the game and you are responsible for keeping it balanced.
Free Boom Beach Accounts
Bedava World Of Warcraft Hesap 2021 | Yeni Ücretsiz Wow Hesabı.
World of Warcraft nedir? World Of Warcraft Ücretsiz Hesapları
, Blizzard Entertainment tarafından geliştirilmiş ve oyunculara
sunulmuştur. Bu bir MMORPG oyunudur. Diğer kısaltılmış adı WoW’dur.
WoW, çevrimiçi ve çok oyunculu olarak oynayabileceğiniz bir rol yapma oyunudur.
İlk olarak 1994 yılında Warcraft: Orcs & Humans oyunuyla tanıtıldı ve piyasaya sürüldü.
Warcraft, serinin 4. oyunu olarak biliniyor. WoW’dan önce çıkış yapan oyunlar, bir strateji türü olan RTS kategorisi altında.
Diğer oyunlar gibi WoW da Azeroth adlı sanal bir gezegende gerçekleşir.
World Of Warcraft Ücretsiz Hesapları ilk olarak 2 Eylül 2001’de açıklandı ve 23 Kasım 2004’te
satışa çıktı.
Bedava World Of Warcraft Hesap