Poker -- from Wolfram MathWorld Poker is a card game played with a normal deck of 52 cards. Sometimes, additional cards called "jokers" are also used. In straight or draw poker, each player is normally dealt a hand of five cards. Depending on the variant, players then discard and redraw cards, trying to improve their hands. where is a binomial coefficient. There are special names for specific types of hands. The probabilities of being dealt five-card poker hands of a given type (before discarding and with no jokers) on the initial deal are given below (Packel 1981). denotes a binomial coefficient. are Gadbois (1996) gives probabilities for hands if two jokers are included, and points out that it is impossible to rank hands in any single way which is consistent with the relative frequency of the hands.
Methods for Studying Coincidences One of my favorite mathematics papers of all time is called “Methods for Studying Coincidences.” By Persi Diaconis and Frederick Mosteller, it aims to provide a rigorous mathematical framework for the study of coincidences. Using probabilistic analysis, the paper explores everything from why we see newly learned words almost immediately after first learning them, to why double lottery winners exist, to even the frequency of meeting people with the same birthday. They even explore whether or not we can statistically state that Shakespeare used alliteration, or if the frequency of words with similar-sounding beginnings could simply be explained by chance alone. For example, when it comes to newly learned words, we are often astonished that as soon as we learn a new word, we begin to see it quite frequently, or at least soon after we learn it. With a large enough sample, any outrageous thing is likely to happen. The whole paper is well worth a read.
New Mayan calendar discovered: world won't end in 2012 Earth has a new reason to celebrate. It's looking like we will make it past Dec. 21, 2012. According to LiveScience, researchers have unearthed the oldest-known version of the ancient Maya calendar in the Guatemalan rainforest. Archaeologist David Stuart of the University of Texas, who worked to decipher the glyphs, told LiveScience the calendar does not mark the end of the world. In fact, quite the opposite. Stuart said, "The Mayan calendar is going to keep going for billions, trillions, octillions of years into the future. According to SFGate the calendar, which is said to be exquisitely preserved, was found in a 1,000-year-old house in Guatemala. More from GlobalPost: Mexico uses Mayan doomsday prediction to lure tourists The newly discovered astronomical tables are at least 500 years older than those preserved in the Maya codices, said Science magazine. The ninth-century structure was first found in 2010, according to SFGate, by Max Chamberlain, a student of Saturno.
Prime Time - Mathematicians have tried in vain to this day to discoversome oreder inthe sequence of prime numbers... An Overview of Cryptography As an aside, the AES selection process managed by NIST was very public. A similar project, the New European Schemes for Signatures, Integrity and Encryption (NESSIE), was designed as an independent project meant to augment the work of NIST by putting out an open call for new cryptographic primitives. NESSIE ran from about 2000-2003. CAST-128/256: CAST-128, described in Request for Comments (RFC) 2144, is a DES-like substitution-permutation crypto algorithm, employing a 128-bit key operating on a 64-bit block. A digression: Who invented PKC? 3.3. Let me reiterate that hashes are one-way encryption. Hash algorithms that are in common use today include: Message Digest (MD) algorithms: A series of byte-oriented algorithms that produce a 128-bit hash value from an arbitrary-length message. A digression on hash collisions. Without meaning to editorialize too much in this tutorial, a bit of historical context might be helpful.
- StumbleUpon Perpetual Futility A short history of the search for perpetual motion. by Donald E. Simanek Popular histories too often present perpetual motion machines as "freaks and curiosities" of engineering without telling us just how they were understood at the time. They also fail to inform us that even in the earliest history of science and engineering, many persons were able to see the futility and folly of attempts to achieve perpetual motion. Sometimes a particular device comes to us with a label, such as "Bishop Wilkins' magnetic perpetual motion machine." Bhaskara's Wheels. Villard de Honnecourt was born in the late 12th century and probably lived and worked in the north of France from 1225 to 1250. The most celebrated of his machine designs was for a perpetual motion wheel. Many a time have skilful workmen tried to contrive a wheel that should turn of itself; here is a way to make such a one, by means of an uneven number of mallets, or by quicksilver (mercury). Mark Anthony Zimara (1460?
A new formula for avoiding supermarket queues Supermarket queues are dreaded by many. In the TV series ‘Supernatural’, people standing in an endless queue are used as an example of what hell really looks like. (Photo: Colourbox) In researcher Kebin Zeng’s office hangs a big whiteboard filled with mathematical formulas and functions. ”You could say that I convert everyday life into mathematical models. His research, which is supported by MT-LAB, aims to improve on the existing mathematical models that calculate the probability of queues in places such as supermarkets or post offices. “It will for instance be possible to use our models to create an iPhone app that tells you the ideal time to go shopping if you want to avoid long queues,” he says. For an example of how to calculate supermarket queues, see the box below this article. Sorting out phone queues Zeng is far from being the first mathematician to create models for waiting times in queues. Kebin Zeng A handy scheduling tool It’s all about probability Software free for all
An App That Encrypts, Shreds, Hashes and Salts The Wickr app. When it comes to mobile apps and social networks, the devil, increasingly, is in the default settings. Companies have little, if any, incentive to let users opt out of services that siphon their personal data back to the advertisers who pay their bills. Nor do companies have any legal mandate to secure users’ personal information with hacker-proof encryption. The responsibility is very much on the user to opt out of services and read through the fine print in privacy policies to understand how their personal data is used, secured and sold. A group of computer security experts want to turn that model on its head with Wickr, a new mobile app that they hope will set a new standard for how personal data is disseminated. Wickr’s motto: The Internet is forever. Text messages, photos and videos sent via Wickr are secured using military-grade encryption and never stored. The co-founders snubbed advertising in favor of a “freemium” business model. Ms. Wickr is not without loopholes.