I flipped 100 coins

[Nielsio]

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
0
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.

[holdme]

k

[Dire]

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.

[Irishman07]

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.

[LearnedfromTV]

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[Trikkur]

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

[74o_Clownsuit]

Thanks?

[pdoran10]

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.

[Dire]

[ 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.

[sputnik3000]

0_o