Two Plus Two Newer Archives I flipped 100 coins
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#1
11-18-2007, 05:47 AM
 Nielsio Senior Member Join Date: Aug 2005 Posts: 10,570
I flipped 100 coins

I flipped a 20 eurocent coin a hundred times, to see what happened to the variance.

=0= 0:0
0
1
1
1
1
1
0
1
0
1
=10= 3:7
1
1
1
1
0
1
1
0
1
1
=20= 5:15
1
1
1
0
0
0
0
0
0
1
=30= 11:19
0
0
0
0
1
0
0
1
1
1
=40= 17:23
0
1
1
0
1
0
0
1
0
1
=50= 22:28
0
0
1
0
1
0
1
0
0
0
=60= 29:31
1
0
0
0
1
0
1
1
1
1
=70= 33:37
1
1
0
0
0
1
0
1
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0
=80= 39:41
0
0
0
0
0
1
0
1
1
0
=90= 46:44
0
0
0
0
1
0
1
0
0
0
=100= 54:46

Results:

Biggest difference is after flip #23 where the score is 5:18, a 13 point difference.

Longest string of the same side is 7 times 0 (flip 78 through 85).

If these numbers represent full stacked 60/40 through 40/60 flips then we should expect a lot of short-term variance. And that's only one aspect of the variance of the game.

It does seem to even out though. So keep trying to make good decisions and try to forget the results.
#2
11-18-2007, 05:54 AM
 holdme Senior Member Join Date: Jul 2006 Location: 100k in 20 days Posts: 6,277
Re: I flipped 100 coins

k
#3
11-18-2007, 05:56 AM
 Dire Senior Member Join Date: Nov 2005 Posts: 2,511
Re: I flipped 100 coins

I'm not sure if it's what you're implying or not, but you seem to be stating the gambler's fallacy. It doesn't even out, on average. At flip 23 where you're down 6.5 points off expectation, you should expect to be 6.5 points off expectation, on average, for the rest of eternity of flipping.

You approach your expected equity relative to your sample size, not in absolute terms. So say you're 5 flips off after 20 flips. That's a 25% difference! You should now expect to always be 5 flips off, but the percent will decrease as the sample size increases. So if you run at expectation for the next 80 flips, you'll still be down 5 flips but it will only be a 5% difference. As you increase your sample size you obviously get closer and closer to 0% difference (in other words running at expectation) but you'll always be down 5 flips.
#4
11-18-2007, 05:59 AM
 Irishman07 Senior Member Join Date: Jan 2007 Posts: 232
Re: I flipped 100 coins

true... but it also depends on the value of the coin. everyone knows that a 50 eurocent coin tends to come up heads more often than the 20 eurocent coin. then theres the whole exchange rate thing when you start flipping american coins. it can get complicated pretty fast.
#5
11-18-2007, 06:00 AM
 LearnedfromTV Senior Member Join Date: Jun 2005 Location: Coaching Posts: 5,914
Re: I flipped 100 coins

#6
11-18-2007, 06:01 AM
 Trikkur Senior Member Join Date: Mar 2007 Posts: 202
Re: I flipped 100 coins

So if I lose my first ever coinflip, I'm bound to be below expectation forever????
#7
11-18-2007, 06:02 AM
 74o_Clownsuit Senior Member Join Date: May 2006 Location: I FIGHT VAMPIRES Posts: 1,557
Re: I flipped 100 coins

Thanks?
#8
11-18-2007, 06:15 AM
 pdoran10 Senior Member Join Date: Oct 2006 Location: Minneapolis, MN, U.S. Posts: 2,681
Re: I flipped 100 coins

I always thought my second grade math teacher was lying to me. Its a good thing you posted this and the results support her claims.
#9
11-18-2007, 06:17 AM
 Dire Senior Member Join Date: Nov 2005 Posts: 2,511
Re: I flipped 100 coins

[ QUOTE ]
So if I lose my first ever coinflip, I'm bound to be below expectation forever????

[/ QUOTE ]

Past events have no bearing on future events. If you lose \$10 on your first flip, then you will always be down \$10 if you run at expectation for the rest of your flips.
#10
11-18-2007, 06:18 AM
 sputnik3000 Senior Member Join Date: Jul 2006 Posts: 288
Re: I flipped 100 coins

0_o

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