Do you believe in luck? Gamblers do. They believe in lucky numbers, lucky breaks, lucky colours and even a lucky rabbit’s foot (It wasn’t so lucky for the rabbit.) But more than anything else gamblers believe in patterns.
The Coin Flip
If we flip a coin an infinite number of times Heads:Tails ratio will be 50:50. But if you think of infinity as a long, long ribbon with a HTTHTHHTTT pattern then random flips means any pattern is possible. 10 H in a row is possible… or 20 H. It’s just that we suddenly see meaning in this pattern. This is the Gambler’s Fallacy. We see 10 H in a row and we say ‘Aha! The next flip has to be Tails.’ But it doesn’t have to be Tails. The next flip – as with all flips – has an equal 50:50 chance of being Heads or Tails. That’s all. But we are surprised when we see an extended streak of, say, Heads. What has happened in the past does not effect THE NEXT FLIP!!!!!
The Rouette Wheel
Roulette Wheel has 36 numbers and an equal number of Red and Black slots. ‘The most famous example of such a phenomenon occurred in a Monte Carlo Casino in the summer of 1913 when a roulette wheel landed on black 26 times in a row.’ The Decisive Moment How the Brain Makes Up Its own Mind Jonah Lehrer (Text Publishing 2009)
What do you think the gamblers did that night???
After a few Blacks in a row they started to think it was Reds turn and kept backing Red.
The Casino kept raking in the francs. It was a very good night for the house.
With the World Fuel Crisis in play, this post from 2014 seems more relevant than ever.
Note: All ‘imaginary’ human fat will be sourced from Liposuction facilities.
Of course, in heavy traffic you are burning up the bio-fuel/fat getting nowhere.
Fuel Consumption (F) can plummet, even for the Mini, from 3.4 kg/ 100 km to 6.8 kg/100 km to 8.8 kg/100km. You may as well get out of the car and walk!!
This April Fool’s Math Test has been soooo popular, it deserves a reboot.
Tell your year 8 or 9 students that this test is designed to test their ability to concentrate and use logic while doing a challenging test under pressure.
Tell students to circle or note the ‘correct’ answer. Then wait to see how long it takes them to think you have totally lost the plot! You can make copies of the test using the PDF links below or project it onto a Smartboard, then put the answers up later.
This April Fool’s Maths Test has been soooo popular, it deserves a reboot.
Tell your year 8 or 9 students this test is designed to test their ability to concentrate and use logic while doing a challenging test under pressure.
Tell students to circle or note the ‘correct’ answer. Then wait to see how long it takes them to think you have totally lost the plot! You can make copies of the test using the PDF links below or project it onto a Smartboard. You can put the answers up later.
Consider the example of the coin rolling around a coin of the same size. Intuitively we think …’OK. Same circumference, so the coin will rotate once as it rolls around a same-size coin. But this doesn’t happen. It rotates twice.
TWICE!
This observation is SOOOOOOOO counterintuitive we have to know why?…
Why?
The answer is interesting. The relevant point in the ROLLING COIN PARADOX is the centre of the rolling coin. The rolling coin rotates about that point. And that centre (the red dot in the gif below) moves through a circle twice the circumference of the stationary coin. It is much easier to understand when you see it. (Below)
Air resistance is a significant factor used by ski jumpers to increase their jump distance.
Ski jumpers crouch going down the ramp to reduce their X-section area and therefore their air resistence. Once they leave the ramp, ski jumpers try to increase their X-section area to increase their air resistence like Ski Divers to slow their vertical fall. But they have to land safely, so they keep their skis at a minimum angle.
Austrian Stefan Kraft in the Men’s Olympic Ski Jump at Milano Cortina 2026
Abby Hughes, USA, practicing in a wind tunnel.
Abby Hughes, USA, in the air
Here are the X-section areas for Abby Hughes:
Mathspig calculated the X-section area by the old-fashioned method of counting squares and rounding off the final count. Mathspig sized the two pics of Abby Hughes so that her head was the same size in both pictures.
Here is the formula for Air Resistance of Drag:
D = ½CApv2
Where C is the drag coefficient or constant, which depends on the shape and spin of an object. It is found by testing the object in a wind tunnel.
With Valentine’s Day approaching Mathspig has reposted this warning.
Chocolate contains a chemical called Theobromine. This alkaloid ( other alkaloids include cocaine, nicotine, caffeine, and strychnine) can kill humans. More infoWired Magazine.
How much chocolate is too much?
Firstly, the darker the chocolate the more Theobromine it contains.
According toAbout Chemistrybased on the highest possible toxicity:
* Vetmedicine: Cooking chocolate contains 8-10 times the Theobromine in Milk Chocolate.
According toWiredlarge doses of theobromine may cause “nausea and anorexia ….. sweating, trembling and severe headache.”
The Royal Society of Chemistrynotes that chocolate does not contain caffeine, but theobromine induces similar symptoms.
LD50 for the lethal dose for 50% of the population for Theobromine is:
If we flip a coin an infinite number of times Heads:Tails ratio will be 50:50. But if you think of infinity as a long, long ribbon with a HTTHTHHTTT pattern then random flips means any pattern is possible. 10 H in a row is possible… or 20 H. It’s just that we suddenly see meaning in this pattern. This is the Gambler’s Fallacy. We see 10 H in a row and we say ‘Aha! The next flip has to be Tails.’ But it doesn’t have to be Tails. The next flip – as with all flips – has an equal 50:50 chance of being Heads or Tails. That’s all. But we are surprised when we see an extended streak of, say, Heads. What has happened in the past does not effect THE NEXT FLIP!!!!!
Mathspig Blog 
