Math and science

It seems that some scratch tickets might be able to be cracked. Why?

There was a time when scratch games all but sold themselves. But in the past two decades the competition for the gambling dollar has dramatically increased. As a result, many state lotteries have redesigned their tickets. One important strategy involves the use of what lottery designers call extended play. Although extended-play games—sometimes referred to as baited hooks—tend to look like miniature spreadsheets, they’ve proven extremely popular with consumers. Instead of just scratching off the latex and immediately discovering a loser, players have to spend time matching up the revealed numbers with the boards. Ticket designers fill the cards with near-misses (two-in-a-row matchups instead of the necessary three) and players spend tantalizing seconds looking for their win. No wonder players get hooked.

The two pieces here mean that cards are not random and clues to the algorithm used to make the tickets are on the ticket. In this case it turned out the clues were pretty obvious:

Srivastava was looking for singletons, numbers that appear only a single time on the visible tic-tac-toe boards. He realized that the singletons were almost always repeated under the latex coating. If three singletons appeared in a row on one of the eight boards, that ticket was probably a winner.

The statistical problem is that it’s difficult to get really random numbers and even more difficult to get somewhat random numbers with a certain property. This is hard statistics and it involves billions of dollars.

In other news, it seems that electrical stimulation strategically placed in the brain can make people better at solving problems:

Once we have learned to solve problems by one method, we often have difficulties in generating solutions involving a different kind of insight. Yet there is evidence that people with brain lesions are sometimes more resistant to this so-called mental set effect. This inspired us to investigate whether the mental set effect can be reduced by non-invasive brain stimulation. 60 healthy right-handed participants were asked to take an insight problem solving task while receiving transcranial direct current stimulation (tDCS) to the anterior temporal lobes (ATL). Only 20% of participants solved an insight problem with sham stimulation (control), whereas 3 times as many participants did so (p = 0.011) with cathodal stimulation (decreased excitability) of the left ATL together with anodal stimulation (increased excitability) of the right ATL.

I find this type of stuff to be fascinating, trying to understand how things work and trying to understand what makes us ourselves. It seems that other people are different:

By now the entire planet has heard O’Reilly’s bizarre litany about tides, and how he claims they prove the existence of God. As he has said on many an occasion, “tide goes in, tide goes out, never a miscommunication.” By this he means that the harmony of nature, the amazing interconnection between things, clearly argues for God.

I understand (or at least I hope this is what he meant) that O’Reilly wasn’t saying that no one knows why there are tides or where the moon, planets , or sun was formed. I think he was looking at the philosophical why more than a how (as in: why was the universe made so that tides would work they way they do?). Still, this shows an attitude of not caring about how things work, since the ultimate answer is always: God. And I really don’t understand this.

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