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 02-19-2014, 03:11 PM #1 metaschima Senior Member   Registered: Dec 2013 Distribution: Slackware Posts: 1,536 Rep: Is a coin toss fair ? You may find the answer to be rather surprising ... no. http://www.stat.berkeley.edu/~aldous...in_tosses.html The mathematical proof is found: http://comptop.stanford.edu/u/preprints/heads.pdf A coin is more likely to land as it started (not accounting for you flipping it at the end, in which case it would be the opposite). I think this is important because coin tosses are a popular and sometimes official method (sports) of "fairness".
 02-19-2014, 03:15 PM #2 TobiSGD Moderator   Registered: Dec 2009 Location: Hanover, Germany Distribution: Main: Gentoo Others: What fits the task Posts: 15,653 Blog Entries: 2 Rep: But wouldn't the fairness be restored if no party knows the starting conditions? AFAIK, you decide for one side before the coin is tossed, before knowing the starting conditions.
 02-19-2014, 03:25 PM #3 mostlyharmless Senior Member   Registered: Jan 2008 Distribution: Slackware -current (multilib) with kernel 3.16.2 Posts: 1,571 Blog Entries: 13 Rep: I used to practice flipping coins so that I had a very good chance of getting heads or tails depending on the starting position. I'm sure a professional (ie magician) could do it nearly 100%. Just be careful who you flip with and how
02-19-2014, 05:00 PM   #4
metaschima
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 Originally Posted by TobiSGD But wouldn't the fairness be restored if no party knows the starting conditions? AFAIK, you decide for one side before the coin is tossed, before knowing the starting conditions.
Yes, but can it be done ? Maybe decide the end state, put the coin in a box, shake it around, then without looking, pick it up and toss it.

 02-19-2014, 06:31 PM #5 Habitual Senior Member   Registered: Jan 2011 Distribution: Undecided Posts: 3,624 Blog Entries: 1 Rep: Does the coin land on the ground or does one catch it and "flip it over" as some do?
 02-19-2014, 06:34 PM #6 metaschima Senior Member   Registered: Dec 2013 Distribution: Slackware Posts: 1,536 Original Poster Rep: Catching it may be the best thing to do. If it falls on the floor and bounces this is ok, but if it rolls or spins then that adds a huge amount of bias due to the uneven weight distribution of the coin.
02-19-2014, 06:41 PM   #7
TobiSGD
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 Originally Posted by metaschima Yes, but can it be done ? Maybe decide the end state, put the coin in a box, shake it around, then without looking, pick it up and toss it.
At least in sports it is usually a referee that tosses the coin, not one of the players, so I would gues that comes pretty close to not knowing the starting conditions.

02-19-2014, 07:58 PM   #8
metaschima
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 Originally Posted by TobiSGD At least in sports it is usually a referee that tosses the coin, not one of the players, so I would gues that comes pretty close to not knowing the starting conditions.
As long as the ref doesn't meet with the choosing team before the game, it should be ok.

 02-19-2014, 08:47 PM #9 metaschima Senior Member   Registered: Dec 2013 Distribution: Slackware Posts: 1,536 Original Poster Rep: As a side note, dice may also show bias if they have even small imperfections in manufacturing: http://www.awesomedice.com/blog/353/...s-gamescience/ I would say that casino dice are better to use if you are actually gambling (like in a casino) http://dicephysics.info/0107.htm
 02-19-2014, 11:56 PM #10 AnanthaP Member   Registered: Jul 2004 Location: Chennai, India Distribution: UBUNTU 5.10 since Jul-18,2006 on Intel 820 DC Posts: 659 Rep: I particularly liked linked page since it gives lots of approaches to what data to gather. Also the main article tells what further analysis can be done with the data. http://www.stat.berkeley.edu/~aldous...ugrad_res.html OK
 02-20-2014, 03:14 PM #11 metaschima Senior Member   Registered: Dec 2013 Distribution: Slackware Posts: 1,536 Original Poster Rep: How many shuffles do you think it takes to randomize a new deck of cards ? http://www.ams.org/samplings/feature.../fcarc-shuffle
02-20-2014, 04:41 PM   #12
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 Originally Posted by mostlyharmless I used to practice flipping coins so that I had a very good chance of getting heads or tails depending on the starting position. I'm sure a professional (ie magician) could do it nearly 100%. Just be careful who you flip with and how
I used to do that too and got pretty good at it.
I must try to teach myself again.

 02-20-2014, 06:05 PM #13 jefro Guru   Registered: Mar 2008 Posts: 12,087 Rep: Half the time it is fair I'd guess.
 02-21-2014, 05:43 AM #14 Pastychomper Member   Registered: Sep 2011 Location: Scotland Distribution: Debian Posts: 53 Rep: The article notes that it hasn't been proven empirically, and mentions the time needed to do a useful number of flips. That sounds like a job for distributed experimentation to me - anyone for Flipping@Home?
 02-21-2014, 10:29 AM #15 sundialsvcs Guru   Registered: Feb 2004 Location: SE Tennessee, USA Distribution: Gentoo, LFS Posts: 5,455 Rep: A coin-toss is theoretically "fair," but no coin is fair, and coin tossers can certainly train themselves to cheat you. Just as can any dealer in a casino, no matter what precautions "the house" might take to prevent it. (As if "the house" actually would . . . ) Yes, they can cheat you, and no, you will not see it being done.