Stritar's chronolog

The Risk board game dice roll probability calculator and battle simulator

Sun, 17 Mar 2013 16:32:12 GMT

I know there are plenty of you out there who love to play the board game Risk. We're hooked on the Lord Of The Rings edition, and I still need to check out the very rare expansion pack one of my friends recently got. As you will see, I'm getting ready for it with all I've got, developing myself a weapon that will help me dominate the game. Something that will turn the odds in my favor without actually cheating. Say hi to my Risk battle simulator, which is able to calculate the chance of winning for specific Risk situations.

Launch

Risk is an interesting game, powered by simple mathematics. In the battle, the attacker throws three dice, the defender throws two. The attacker's advantage is the one extra die. The defender's advantage is that he/she wins when the dice are tied. Which, in the general situation of 3 dice vs. 2 dice roll, translates into the following odds: the attacker has 37.17% chance of winning, the defender has 33.58% chance of winning, and there's a 29.26 % chance of tie - they will both lose one army. But what about specific situations? How can I know if my 10 armies are enough against my opponent's 5+4?

Since I'm a developer and not a mathematician, I decided I will rather build a simple brute force JavaScript simulator than try to derive the formula behind the battles. An application that simulates 10.000 Risk fights (around 50.000 dice rolls) and calculates the result odds. That should be enough to make an approximation, right?

Risk's rules specify that the attacker always has to leave one army behind (can't use it to attack), and can attack any number of territories in a single turn. Which the calculator also takes into account. Every territory the attacker wins, his/her number of armies is subtracted by 1 (one army is left behind), and the last army is not able to attack. I think I got it right, but if you find and error, please let me know.

Risk dice roll battle simulation.

Besides, the simulator also knows how to calculate probabilities for specific single battle situations for different numbers of dice the attacker and defender throw, by going through all the possibilities of dice throw results (which means 7.776 (6⁵) different dice throws in 3 vs. 2 battle).

Risk dice roll possibilities and odds.

I made this to help myself and others understand and appreciate the statistics behind the dice. So, the next time you play Risk, don't forget to bring your phone and use the simulator to your unfair advantage. And if you're a developer, feel free to upgrade the algorithm (available on Github). Game on.

http://diceroll.stritar.net/risk.html
https://github.com/gstritar/DiceRoll

Trends of 2010, according to Facebook, Google and Twitter

Tue, 21 Dec 2010 07:42:29 GMT

The year is coming to an end, and our favorite big brothers all published reports about trends inside their ecosystems (Facebook, Google, Twitter). Even though the services are not perfectly comparable (information gets pulled and pushed: while you search, you pull data; on social networks the data gets pushed to you), I think they can provide a clear picture about the general state of the Web in 2010. Three obvious winners emerged, coming strong in all the charts. Apple made the iPad the most wanted gadget around, FIFA World Cup mania took over the whole planet, and Justin Bieber topped the celebrity world. I was curious about the comparison, so I've joined all three lists, gave all topics a score, and put the results into pictures. Sadly, I'm not a designer to make a really cool infographic about it, so this will have to do.

#	Google (points)	Facebook (points)	Twitter (points)	Total (points)
1	HMU (10)	Chatroulette (10)	Gulf Oil Spill (10)	iPad (21)
2	World Cup (9)	iPad (9)	FIFA World Cup (9)	World Cup (18)
3	Movies (8)	Justin Bieber (8)	Inception (8)	Justin Bieber (16)
4	iPad and iPhone 4 (7)	Nicki Minaj (7)	Haiti Earthquake (7)	Haiti (13)
5	Haiti (6)	Friv (6)	Vuvuzela (6)	Oil Spill (10)
6	Justin Bieber (5)	Myxer (5)	Apple iPad (5)	Chatroulette (10)
7	Games on Facebook (4)	Katy Perry (4)	Google Android (4)	Inception (8)
8	Mineros / Miners (3)	Twitter (3)	Justin Bieber (3)	Nicki Minaj (7)
9	Airplanes (2)	GameZer (2)	Harry Potter (2)	Friv (6)
10	2011 (1)	Facebook (1)	Pulpo Paul (1)	Vuvuzela (6)

I've only left out "HMU" (Hit me up) and "Movies", because the first is an expression, and the second is a generic term. Hope you like it, see you around in 2011.

Apple has enough money to buy Slovenia's entire yearly production

Fri, 12 Nov 2010 22:00:34 GMT

Apple is currently hot like a chili pepper. Its products are well accepted, their sales and revenues are growing, and their stocks are going sky-high. A few months ago Apple even managed to dethrone Microsoft as the largest technology company in the world and ~~second~~ third largest according to market capitalization (behind Exxon and PetroChina). Their yearly revenues are currently around $65 billion, which is a lot, and that figure is even more interesting if put into perspective.

Slovenia is a small country in Europe. It has around 2 million inhabitants who almost manage to live in peace. Its GDP in 2009 was around $24k per capita or $49b in total. We are so small that our neighbors are making jokes about it, but we are still a proud nation of capable people, who try hard to make it. Speaking of small - nowadays it's not that unusual for large corporations to have bigger revenues than a small country's GDP, but if a company has more money than a country's GDP, well, that's simply ridiculous. But Apple now sits on more than $50 billion (11 billion in cash + 14 billion in short-term marketable securities + 25 billion in long-term marketable securities), which means that it's actually capable of buying the whole yearly gross domestic product of Slovenia.

Apple obviously won't do that, but eventually it will have to do something. There are speculations about them wanting to buy Facebook (estimated value 33 billion), focusing on mobile payments, and many others. It will be interesting to see what happens, but I'm almost sure Steve will do the right thing. The company is very healthy, the demand is high, so it should be a piece of cake. Just take a look at these interesting facts or the figures below, which display the case of Apple vs. Slovenia. I guess we truly are small.

	Apple	Slovenia
Full name	Apple Inc.	Republic of Slovenia
Established	1976	1991
Capital	Cuppertino	Ljubljana
Government	~~Monarchy~~ Empire	Parliamentary republic
Leader	Steve Jobs	Danilo Türk
Population	49,400 (2010)	2,054,199 (2009)
GDP	$65.225 billion (2010)	$49.217 billion (2009)
GDP per capita	$1.320 million (2010)	$24,417 (2009)

Source: Wikipedia, Apple

Twitfluence prototype calculation for measuring Twitter influence

Sun, 01 Aug 2010 11:54:40 GMT

The prototype calculation of Twitfluence uses the data available form Twitter API to measure your Twitter influence and coolness. The basic technical specifications of the application is available, but I will also be supplying the basic information about how the algorithm works. The actual calculation is already online for beta users, and generally speaking, there are three major components that add up to the score: your followers, your mentions and retweets, and your lists, all accounted as ratios between you and others.

Followers

The strongest component of the calculation is the number of followers you have. In my opinion, your presence on Twitter and getting followers can be influenced by at least the following three major factors concerning you and your Twitter account:

Persona – how known you are. Measured by the number of followers you have, compared to your time on Twitter.
Engagement – how engaged you are. Measured by the number of followers you have, compared the number of people you follow; Measured by the number of followers you have, compared to the number of mentions and retweets you’ve made.
Wits – how smart and creative your tweets are. Measured by the number of followers you have compared to the total number of tweets you've made.

For this part, I gave the followers/following ratio the weight of 3, the followers/tweets a weight of 2 and the followers/time a weight of 1. The followers/(mentions + retweets) has a weight of 0.5 and works in the negative way, so people who bother other people get a bit of a minus to their followers result. Besides, those who are able to get the same number of followers without mentioning people, must have a small advantage.

(Needs to be upgraded with taking into account only your mentions and retweets of people who don’t follow you.)

Interaction (mentions, replies, retweets)

The second most important part of the calculation is the ratio between mentions and being mentioned, together with the number of retweets you get with the absolute "reach" of those retweets (measured in the number of people who follow people that retweeted you). A similar reach is also accounted in the mentions and replies. This component of the calculation uses only the data from the last month, also to make Twitfluence a bit dynamic for multiple calculations for a single user over time. To finalize this part, the total number of tweets in the last month also contributes a small score.

(Needs to be upgraded with unique reaches of your retweets and mentions. For now, it just adds them together.)

Lists

Twitter lists are getting used more and more, so they are also considered in the calculation. The number of lists you appear on, the number of people who follow those lists and the number of people, who follow lists you've created are the basic parameters for the calculation. This component adds only a small bit to the final score.

(Needs to be upgraded with unique reaches)

The basic ratio calculation

All ratios in the calculation are based on the same elementary formula, which looks like this:

Generic result = Sqrt(others / you) * Log10(modifier + 10)
Followers = Sqrt(followers / following) * Log10(followers + 10)
Mentioned = Sqrt(mentioned / mentions) * Log10(mentioned + 10)

I've decided to go for this architecture because of a number of reasons. F.i., the followers / following and other ratios are used to get an objective value for all Twitter users. This ratio gets square rooted so the differences between people are not so huge. The multiplication is there for adjustment, so people who have the same ratio and the absolute number are bigger, get more points. The logarithm is used to make this modifier of absolute number smaller, while + 10 is used so this number is always bigger than 1 (and the logarithmic function becomes more stable after the result 1: Log10(10) = 1). This means that the modifier for those who follow 10 people is around 1, 100 people around 2, 1000 around 3 etc.

Putting it together

The three major components currently have the following weight in the final score:

Followers: around 60%
Mentions and retweets: around 30%
Lists: around 10%

That's about it for now. I've tested the behavior with some real accounts (thanks for help @TejaSmeja and @jakasibicekaka), together with some projections, and it seems to be working quite OK. But the real test will happen after it analyzes results of actual people, which will allow real insight into the performance and objectivity. The Twitfluence will be online soon, and I will be asking you to help with testing the prototype. You also more than welcome to leave any kind of feedback about the calculation as I've described it.

Let's play.

The Web is going rogue. The Web is going mainstream.

Fri, 23 Jul 2010 17:16:40 GMT

Times are changing, and the World Wide Web isn't any different. You've probably already noticed your mother on Facebook and it's not too hard to understand that interests of specific generations can be a bit different. The same goes for young people, who are obviously growing up in a world of their own, a confusing world overwhelmed with infinite amounts of information.

In the USA, already 93% of people under 18 are online. A massive group, which is probably the main driving force behind changing how the Web looks, and they are actually doing quite a good job in making it mainstream and pop. The Web used to be a part of the geeky subculture, but lately it's becoming just one of the mass media, another television on steroids.

YouTube

A great example of this pop transformation are top videos on YouTube. Star Wars Kid, David After Dentist and other classic home-made videos are starting to look unimpressive compared to Lady Gaga's and Justin Bieber's music videos. If you check the current list of most viewed videos, you can see that YouTube is really becoming more of a PopTube, where record labels are dominating the chart with high budget music videos. Lady Gaga managed to be the first pop artist with the most viewed YouTube video, but was quickly dethroned by Bieber. A sad fate for the biggest online video sharing tool.

Twitter

When people who actually have something smart to say are getting less followers on Twitter than pop princesses, you know something's gone wrong. Ashton Kutcher, the king of Twitter and the guy who beat CNN to one million followers, was overtaken by Britney Spears in the number of followers just a few moths ago. This is just the beginning - the following list provides information about top Twitter users, where you can see more and more pop stars whose accounts are emerging and taking the lead. Perhaps I'm not the correct target group, but Britney's Twitter account with her 423 tweets pretty much sucks!

Google

Google is kind enough to allow us insight into it's most popular searches of every year, which offers great overview of the culture of a specific era (Google Zeitgeist: 2007, 2008, 2009). This is The spirit of the times, as seen by world's biggest search engine:

In 2007, there were no people or other pop brands on the top 10 list of searches.
In 2008, Sarah Palin became 1st and Obama took 6th place, but that was mostly because of the US presidential elections, which can't really be considered pop. Pop star searches included Heath Ledger on 5th (because of his death) and the band Jonas Brothers on 10th place.
In 2009, the trend of pop searches continued. Michael Jackson became 1st (due to this death), New Moon (Twilight movie) finished 6th and Lady Gaga 7th. Creepy enough, but wait until Justin gets on the list in 2010.

These are some of the cases showing the evolution of the World Wide Web, currently ruled by it's undisputed queen, Lady Gaga. The scary part is that all of this is probably just a virtual portrait of the real world of today, where Pop Stars and Supermodel reality shows are helping to create new values and a wannabe society. And the Web is not just a victim of this trend anymore, it became an active player helping to promote this new and strange culture.

All of this saddens me a bit, and this is my puny effort to change this trend. Or maybe I'm just getting old.

The impact of hyperlinks, toolbars and URL shorteners on Google Analytics

Tue, 09 Mar 2010 18:51:45 GMT

In the past few weeks I've done an extended analysis of visits on my blog, which made me wonder how the super fancy new web gadgets and features influence Google Analytics and traffic reports. By these new gadgets I mean the nowadays very popular URL shorteners, such as tinyurl or bit.ly, and the annoying inside-browser toolbars, used by Digg, Stumbleupon, Google images and other services. These inventions made me wonder, as well as probably many other bloggers, web developers and marketers do - are these things messing up the traffic statistics? To be sure, I had to try it out by myself and found out the following: No, they do not. Or better put, Google is smart enough to know what's happening.

The methodology

Google Analytics and other statistical software is based on combining the user agent (operating system, browser), IP and browser cookies to calculate visits on a site. While others are captured for different information, cookies are still the base of elementary web metrics, so it's crucial to understand them and have them under control. I did just that each time I did a test – clean Google's cookies, close the browser, open the browser, check it out. I made a hidden post for testing, one which definitely wouldn't get any other referrers other than me, besides using some old and already forgotten posts I made on Digg months ago and some indexed by Google images. Then I started testing different cases, which would help me understand the behavior of all the above mentioned things.

Referring vs. navigating

The first interesting thing I found out was that Google Analytics knows the difference between clicking on a link and manually navigating to a page by entering the URL in the browser. In the first case it recognizes the referrer, and in other one it doesn't (it is displayed as google / organic in the statistics). This is caused by the referrer information captured in the HTML header of every web page. So, if somebody manually enters your web page's address after seeing a link on Facebook, Facebook won't be counted as a referrer, but if they click on the link, it will be.

Url shorteners

I tested a few url shorteners, tinyurl, is.gd, skrci.me and the one Twitter automatically uses (bit.ly). I found out that the ones I manually created and clicked on them inside the URL shortening site showed this site as the referrer. But in the case of Twitter, on which I made a tweet, clicked on the link and deleted it within seconds, Twitter was correctly shown as the referrer, even though the click first went to bit.ly and than to my blog. I went further, created a new shortened URL, put it in a hyperlink on a server, clicked on it, and again, this server was shown as the referrer. Because url shorteners only make the redirect, the click is keeping the original referrer, which enables the referrers to be fully captured, even if they go through the shortened URL.

Toolbars

I use a few Web 2.0 services to promote my blog, and it's been a trend for them to provide toolbars, which display the target site inside the parent site. The main reason for them doing this is to keep users inside their site, and in my opinion, it's annoying and it sucks. But at least it doesn't influence the statistics. I tested this behavior on Digg toolbar and on Google images (without removing or closing the toolbar) and in both cases it worked perfectly – the referrer was correctly recognized. After all, upon technically examining both cases, it's only an iframe opening the designated page below the toolbar, so the target page actually does fully open anyways.

Proof

The screenshots of Google Analytics below support my theory. In the case of the hidden post, I managed to create the following situations which prove my discussed behaviour of hyperlinks and URL shorteners:

I clicked on a link from neolab.si (one referrer from neolab.si),
I manually navigated to the post from neolab.si twice (by entering the url in the browser while being on neolab.si), shown as google / organic,
I clicked on a shortened link on the is.gd site, later I pasted another is.gd short url directly to my browser (two referrers from is.gd),
I clicked on a shortened link on the tinyurl site (a referrer from tinyurl),
I clicked on the automatically bit.ly generated url in a tweet (a referrer from Twitter),
I generated the skrci.me short url, put it in a hyperlink on localhost and clicked on it (a referrer from localhost).

The second report displays the referrers from Digg and Google images, both services using toolbars. On the first occasion, I opened two different posts inside the Digg toolbar, and on the second, two posts inside Google images toolbar, all of them without closing the toolbar (I went for one post twice, to check out if a session is also created and found out it is). As you can see, the referrers are all there and the toolbars don't corrupt the data in any way.

Conclusion

Look like we don't need to worry about these things anymore. I'm actually quite surprised about finding out the mentioned things work like a charm, not influencing the analysis and statistics in any case. From now on, there can be no more blaming these new features and gadgets on low traffic and weird referrers. The World Wide Web has been well planned and Google Analytics is able to know everything, so if your statistics seem weird, there is probably more chance that you are the one who's wrong.

An approach to statistics and data analysis

Mon, 30 Nov 2009 20:32:06 GMT

When information systems evolve, they become greedier for both operational and advanced strategic statistics and data analysis. This need is a part of a natural evolution. The more data you have, the higher potential for extracting information you have. Looking at business environments using IT platforms, that's what analytics are actually all about - getting useful information from usually bad data. It turns out the task of analytical reporting is not so complex as it seems, but you definitely need a set of different skills / people to make it work.

There are tons of different statistical approaches, methods and theories, but it turns out that for average business needs you only need basic mathematics, where the most complex operations are sometimes logarithms. So, if it's so simple, where does the problem lay? Why do information systems often lack analytical support, which can be used for decision making?

In my opinion there are three main steps to consider when trying to make useful statistics and data analysis, and ignoring or underestimating any one of them will make your reports suck.

Data

Data is the king. If you don't have the data, you might as well give it up. If your data is bad or weak, you might consider rebuilding it. But you should know one thing - the better the structure of your data is, the better your analysis will be. Using a flat database such as a text file or an Excel spreadsheet gives you few analytical opportunities. Relational databases, such as Access, MySQL or SQL offer cross-data querying and advanced reporting, but huge and complex calculations can take a lot of time. For those, a multidimensional OLAP database designed strictly for analysis becomes the only option.

Challenges in this step: Technical

Information

The data discussed above defines the scope of potential information you can deliver. In this step, the main goal is simple - you need to know what you want to know. Business needs, process flow, strategic goals or just plain simple amusement are the main factors that need to be addressed. Having someone who is able to recognize these opportunities is crucial, because data is just numbers, but aggregated data - information - is knowledge. It's quite clear you won't be able to get something if you don't know what you want to get.

Challenges in this step: Analytical

Visualization

A picture can tell a thousand words and this goes a long way for data visualization. Even if you can't use charts, you can color information and use measures such as font size to represent another dimension of information or trends. Besides, always keep in mind that less is more, so you should put irrelevant information in the background and punchlines in the spotlight. Check out different chart types, they're useful for different representations and experimenting with them can display things that don't seem there at first sight. Observe patterns. Try to imagine a playground, where information can satisfy your curiosity and while doing it, it also brings useful and valuable results.

Challenges in this step: Creative

If you have the will, you can do all sorts of crazy stuff with statistics and data analysis, but you should know they sometimes take a lot of time. I'm proud my chronolog already has two nice looking children of these activities. The first one is a simple recommendation engine used for content ranking and the other one a set of reports which offer insight into activity and interactions of the chronolog. What can I say, I like to play around, and it may as well be any information system I can get my hands on. Give me the data and I'll give you information.

Hot on the chronolog - and how it works

Sat, 10 Oct 2009 19:49:41 GMT

When I first published my chronolog, a few people were making remarks about how it resembles FriendFeed, Twitter or Tumblr. I can't deny that. The influences of Web 2.0 are huge both on my personal and business life, so why should the chronolog be any different? It is a mashup of different web services and it displays information from different sources, so it's a kind of a Web 2.0 stream. But besides that, it's also my own personal playground for testing and developing high level services and functionalities, which will hopefully be cool and fun and make the chronolog interesting for all of us. Demonstration of concept and technology, if you like.

I already have a few of those smart features planned, and I can give you a little teaser already. I really look forward to developing the custom view of the chronolog, where advanced users will be able to do a bit of configuration. The prototype is already half developed, but sadly far from production. A different thing I'm working on is a complex set of statistics and analytics, which should give us deeper insight into the chronolog, it's data and our interactions with it. This one will probably go out next and it actually inspired the one already complete. From this day forward, the chronolog supports Hot on the chronolog, accessible from the views menu top right, which shows the most interesting posts in the desired time period.

A few Web 2.0 portals (specially those oriented in social news or social bookmarking) have recommendation engines, which give users access to information based on their interaction with the system. I would like to try that one out too once, but because I don't have registered users, the chronolog probably won't be the environment. What I can give you now, is the Hot view, which displays the most important posts based on the interaction (views, likes, comments) of all users of the chronolog. A global recommendation engine of some sort. I'm quite pleased with the algorithm I've developed, it looks like it's working, so you can give it a try.

Some of you will be interested in how it works. The core is a really super mega awesomely complex algorithm that gives ponders to different interactions in the selected time span. Well, it's not that complex from the mathematical point of view, but it still pretty smart. Combining these ponders and number of interactions, using a few square roots and logarithms, plus a small modifier for insert date (if two posts are tied, the older one appears "stronger"), it calculates which posts are more interesting and relevant and gives them a score accordingly. Simple as that. Besides, is also able to make that calculation for any time period. You can even hack it by changing the ?d=# in the url to any number of days you like.

When viewing longer periods (months, years), blog posts will probably take most of the top spots, because they are supported with social networking sites and have the most interactions. In the shorter periods (days, weeks), other types of posts will also take higher ranks. We will see if the algorithm works in the longer term too, when more users will be clicking around, but if needed, the calculation will be changed or modified. Oh, I almost forgot about the design touch I added - the importance of a post is portrayed using transparency, which looks quite cool and is a great exaple of using design for function.

The chronolog becomes smart. Hope you like it.