Solitaire: Chance for Starting Duplicates

In Klondike Solitaire, what's the chance for starting with two face-up cards of the same rank & color (what we might call "shadows", cards which don't help us very much)?

There are 7 face-up cards in starting Solitaire, so we consider the ways to choose 7 cards randomly without any duplicates. Every time we select such a card, the number available for the next draw (avoiding "shadows") goes down by 2, while the cards in the total deck goes down by 1. Therefore the chance for no-shadows is:
$${52 \over 52} \times {50 \over 51} \times {48 \over 50} \times {46 \over 49} \times {44 \over 48} \times {42 \over 47} \times {40 \over 46} \approx 0.63$$
This in turn means that the complement event, i.e., getting any shadows at all (at least two cards with duplicate rank & color), has a probability of:
$$1 - 0.63 = 0.37 = 37 \%$$
That is: About one chance in three.

More about Solitaire. 


Facebook Learning Debacle

Yesterday, the New York times published an expose on how schools in certain (poor, rural) places are being used as guinea pigs and getting "Zucked" by the Facebook founder's "Summit Learning" initiative, yet another plan to replace teachers with computer time. The highlights are sad and predictable:
  •  A program that promises "personalized learning" at each student's individual pace. Software free of cost, but school district must buy everyone a laptop.
  • Also, Facebook/Summit collects reams of information on the students involved, and expects to keep tracking students through college and beyond. 
  • The program was built by a grand total of 5 Facebook engineers (no information on whether they have any training in education or pedagogy issues). 
  • A spokesperson says it is based on, "building a curriculum from the open internet", that is, mostly links to outside web sites. Examples given include links to the Daily Mail tabloid and Christian conversion therapy sites.
  • The program "asks schools to commit to having students meet weekly in person with teachers for at least 10 minutes", but reports say not even this is happening.
Students are reporting high levels of anxiety, eye strain, hand cramps, and even seizures. Said one parent who visited a classroom, “We’re allowing the computers to teach and the kids all looked like zombies”. Some places are seeing pushback like student protests, walkouts, and parent removing their children from schools.

One reminder from yours truly: the promise of "personalized learning" is not new. It's been around at least since multimedia in the 90's, or the PLATO computer system in the 60's, or correspondence courses in the 40's, or the Gutenberg printing press, depending on how you count such things. None of them have come close to denting the need for real human teachers.


Honeybee Addition and Subtraction

Researchers in Australia and France claim to show honeybees learning to do symbolic addition and subtraction (really just incrementing and decrementing) based on 1-5 colored shapes at a time. Interesting ramifications if that's true.


Many animals understand numbers at a basic level for use in essential tasks such as foraging, shoaling, and resource management. However, complex arithmetic operations, such as addition and subtraction, using symbols and/or labeling have only been demonstrated in a limited number of nonhuman vertebrates. We show that honeybees, with a miniature brain, can learn to use blue and yellow as symbolic representations for addition or subtraction. In a free-flying environment, individual bees used this information to solve unfamiliar problems involving adding or subtracting one element from a group of elements. This display of numerosity requires bees to acquire long-term rules and use short-term working memory. Given that honeybees and humans are separated by over 400 million years of evolution, our findings suggest that advanced numerical cognition may be more accessible to nonhuman animals than previously suspected.


Computer-Based Naval Training Failures

A fascinating article by a PhD candidate in military history: On the U.S. Navy's switch from face-to-face classrooms for training officers in surface warfare combat to independent computer-based training (CBT) aboard one's ship from 2003 - 2012 -- which turned out to be both a training disaster and also wildly inequitable, and was replaced with renewed face-to-face training after that time.

For me, this seems to echo the recurrent drumbeat of hopes for distance/computerized classwork saving time and money, turning out to be generally complete failures, but administrators for various reasons eternally refusing to face up to the facts and evidence (out of an abundance of vain hopes). At least here we have a case study of an institution that has some higher motivation for responding to the failure, in that people's lives and billions of dollars in equipment are immediately at risk from obviously poor training. A key quote, I think, and more widely applicable:
Finally, changes undertaken with the principal goal of saving money or hurrying a process are fraught with danger. The overriding pressure to achieve financial or time savings threatens to overtake innovative ideas and turn them into quick-fix vehicles for the achievement of specific goals. 

(Coincidentally, my gaming blog today has a link to some excellent documentation on the history of wargaming used to train officers in the U.S. Navy: see here.)