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        riddles >> general problem-solving / chatting / whatever >> Belgian Bias for the Euro
        
(Message started by: Sir Col on Oct 30^th, 2003, 2:03pm)

Title: Belgian Bias for the Euro
Post by Sir Col on Oct 30^th, 2003, 2:03pm

I don't know if anyone else on the forum caught the rather old news now, but it has been reported that Belgian's Euro is asymmetrical.
http://www.guardian.co.uk/international/story/0,3604,627478,00.html

There has been, and seems to continue to be, a lot of discussion about this on the internet. The following analysis was quite interesting:
http://www.isip.msstate.edu/publications/seminars/msstate_misc/2002/euro_coin/presentation_v0.pdf

So, what does the jury think: is it a biased coin? :o

Title: Re: Belgian Bias for the Euro
Post by Icarus on Oct 30^th, 2003, 5:27pm

I'm not sure. It seems to me the way to find out is to perform more experiments. While it is possible for a series such as 140 out of 250 to come from flipping an unbiased coin, more repetitions would almost certainly come out even.

While I am no expert in probability, that second link seemed to me to be a case of "I don't like this number, so lets add more layers of analysis until one comes up that I do like". I particularly like that he comes up with a result saying that the evidence (coming only from this 140/250 experiment) actually favors an unbiased coin. This seems to me to be a definite giveaway of a biased analysis.

Title: Re: Belgian Bias for the Euro
Post by SWF on Oct 30^th, 2003, 6:21pm

I had similar thoughts to Icarus. Why would somebody go to the trouble of stopping at only 250 flips and then publish inconclusive results. Flipping 250 times must have taken maybe 15 minutes.

Was that Icarus who said he once rolled the same number on a die some ridiculous number of times in a row? Should have published those results.

Title: Re: Belgian Bias for the Euro
Post by towr on Oct 30^th, 2003, 11:00pm

I think I'll have to go check my wallet to see if I have any Belgian coins (Belgium is pretty close, so some coins should have migrated over here by now.. Then again, it's mostly German coins that are flooding my country..)

Title: Re: Belgian Bias for the Euro
Post by towr on Nov 2^nd, 2003, 1:31pm

First off, I'm pretty sure there is a bias, since I've had a flipping fun time yesterday ;)
But it's not actually when you flip the coin, but like in the article spin it..

I only spun it 80 times, but only 17 in total where tails.. which is a quite significant difference I think..
The chance of that is about 1 in 12 million

Flipping however is pretty fair, and much faster to do so I have a longer sequence there, 59 out of 128 heads about a 1 in 20 chance.

Here's the sequences if you want to do a little analysis yourself (I kept the whole sequence, not just the scores, since there is a lot more information here, like how often head follows tail and how often tails follows heads)

first the flipping sequence:
THHTT HHTHH THTHH TTTTT TTTTH TTTTT THTTH HTHTT HHTHT TTHHT TTTHH HTTTT HTHTH HHHHH TTTHH THHTT HHTHT HHTTT THHHT HTHHT TTHHT TTHTH TTHHH THHHH HTTTH HTT

Spin cycle 1:
HTTTH THHHH HTHHT THHHH HHHHH HHHHT HHHHH THHTH

Spin cylce 2 (I also kept track of the starting position, since I realized it might play a role, so the first row of 40 is the starting position, the second row the spin result):
TTHTH HTHTH HHHTT TTHTH TTTTT THTTH HHTTH TTTTH
HHHHT THHTT THHHH THTHH HTHHH HTHHH HHHHT HHHHH

undoubtedly it'd be fairer to check the fairness of a coin by having a mechanical device flip/spin it rather than do it myself, since I'm pretty sure at least in the spinning case, I put in a lot of bias (it usually ends up opposite of the starting position, which correspond to my observation that I can tell the result a fraction of a second after I send it spinning)

Title: Re: Belgian Bias for the Euro
Post by Icarus on Nov 2^nd, 2003, 2:43pm

Another question of interest is whether the Belgian coin is unique in this preference. Euros are a little hard to come by over here, but I will have to try it out on some US coinage to see if I can find a bias.

It may have something to do with the shape of the coin edge, rather than a bias in the weight of the sides. In fact, a slight angle to the edge, sloping inwards towards the tail side, would explain the favoritism for heads when spun. The slope need not be very big, and could even be the result of uneven cooling of the strike plates when they were created.

Title: Re: Belgian Bias for the Euro
Post by Sir Col on Nov 2^nd, 2003, 4:28pm

In case you were unaware, the 1 Euro is a bi-metal coin. Here's a picture of the Belgian Euro, featuring King Albert II of Belgium.

I think the fact that the 'common' side can feature one of three designs is significant too. You may find the following link interesting:
http://www.euro.ecb.int/en/section/euro0.html