A Calculation of Odds in the Dice Game Langur Burja

A Calculation of Odds in the Dice Game Langur Burja

Gale Richard Walker
September 2017

Kids playing langur-burja

Kids playing langur-burja at Malekhu in Dhading district. (Bijay Gajmer/Republica)

Langur Burja, a dice game popular in Nepal and in the British navy (where it is known as Crown and Anchor), uses six identical dice, each with six different symbols on it. After bets are placed, the banker tosses all six dice at once. The betting rules and payouts to the players may be found on the Internet. Variations of the game are played in France, Vietnam, China, Belgium, and Bermuda. They are not described here.

Overall, the Langur Burja banker (commonly know as “The House”) who tosses the dice has a big edge — eight percent — over the players, but that is not the focus here. The purpose here is to show how to calculate the probability of each possible outcome of one toss of six dice. Any six symbols, pictures, colors, or numbers will do. In England, for example, the six symbols are a heart, a spade, a diamond, a club, a crown, and an anchor. Herein they are simply called colors, as any six colors on each die will do.

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enabling CORS on Apache

Many people struggle to get CORS (Cross-Origin Resource Sharing) enabled on their site to allow transmission of JSON, XML, or some other sort of data from one script to another, running on different domains. Simply adding Header always set Access-Control-Allow-Origin “*”  to .htaccess doesn’t do the trick for me.

Here’s what worked for me on Apache version 2.4.33… Continue reading “enabling CORS on Apache” »

gradually coming to grips with reality

Arthur Schopenhauer

Arthur Schopenhauer

All truth passes through three stages:

  1. The truth is ridiculed.
  2. The truth is violently opposed.
  3. The truth is accepted as being self-evident.

up and running with UserSpice 4.2.4

UserSpice v.4.2.4 was released yesterday, but I had a few issues with its installation. I got the following errors:

Parse error: syntax error, unexpected ',' in /users/init.php on line 49

Fix: change users/init.php line 45 from:

 'host' => 'localhost'


‘mysql’ => array('host' => 'localhost',
Parse error: syntax error, unexpected 'else' (T_ELSE) in /users/user_settings.php on line 217

Fix: change users/user_settings.php line to 217 from:





the battle of donetsk airport over time

In the following series of images I explore the 2014-2015 Battle of Donetsk Airport from Google Earth flyovers.

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for the people copy + spread!

You must unlearn all you know!

accelerating WordPress

Once a WordPress site is built out with themes, plug-ins, and what-not, the overall number of files necessary to transfer to the client increases. Each requests takes some time. Compiling code into fewer, smaller files can help speed the loading time for your visitors. One WordPress plug-in that enables this is Autoptimize.

Before using this plugin, this page requires 41 separate downloads:

After enabling Autoptimize, there are only 27 requests:

street/strip blown Civic build


Some photos of my car I supercharged in the summer of 2015.

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