Two Plus Two Newer Archives - I flipped 100 coins

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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
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.

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.

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.

Re: I flipped 100 coins

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

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.

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.

Re: I flipped 100 coins

did you really sit around and flip 100 times? im sure you can program a simulator or just search the internet for one.

Re: I flipped 100 coins

[ QUOTE ]
did you really sit around and flip 100 times? im sure you can program a simulator or just search the internet for one.

[/ QUOTE ]

It helps when you do the experiment yourself, to integrate it into your experience.

Re: I flipped 100 coins

my god you ran bad from flip 80-90.

Re: I flipped 100 coins

[ QUOTE ]
[ QUOTE ]
did you really sit around and flip 100 times? im sure you can program a simulator or just search the internet for one.

[/ QUOTE ]

It helps when you do the experiment yourself, to integrate it into your experience.

[/ QUOTE ]

You should probably integrate some basic statistics into the experience.

Re: I flipped 100 coins

[ QUOTE ]
adsdfasdfasdfgf

[/ QUOTE ]

Re: I flipped 100 coins

well done. i think the sample size is not quite big enough.

why don't you do it again, this time with 1000 flips and then do another report

Re: I flipped 100 coins

[ QUOTE ]
fold flip 83

[/ QUOTE ]

lol

Re: I flipped 100 coins

But seriously Nielso, thanks for doing this.

Before this experiment I thought that if you flipped a coin a hundred times the result would be
Heads-tails-heads-tails-heads-tails-heads-tails-heads-tails-heads-tails-heads-tails-heads-tails........

I'm actually quite shocked it turned out like this.

Re: I flipped 100 coins

Maybe you should submit this to a journal?

Re: I flipped 100 coins

this should have been post 10k

Re: I flipped 100 coins

[ QUOTE ]
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.

[/ QUOTE ]
lol

Re: I flipped 100 coins

I bet if FGators did the flips it would come out like 17/83, man that guy runs bad.

Re: I flipped 100 coins

did you try a rigged coin?

Re: I flipped 100 coins

You must have been so bored... there's programs to do this many times for you.

Re: I flipped 100 coins

[ QUOTE ]
did you try a rigged coin?

[/ QUOTE ]

Obviously this coin was rigged, didn't you see the results???

No way these flips come out random.

Re: I flipped 100 coins

tldr: there's variance in poker.

Yawn.

Re: I flipped 100 coins

[ QUOTE ]
But seriously Nielso, thanks for doing this.

Before this experiment I thought that if you flipped a coin a hundred times the result would be
Heads-tails-heads-tails-heads-tails-heads-tails-heads-tails-heads-tails-heads-tails-heads-tails........

I'm actually quite shocked it turned out like this.

[/ QUOTE ]
Haha awesome.

Re: I flipped 100 coins

Nielsio, if you used american money, you did not run a fair test due to the coin not being equally weighted on both sides. I think this test needs to be redone with european money before I believe in it

Re: I flipped 100 coins

Sounds like a sweet way to spend a Saturday night.

Re: I flipped 100 coins

This post is much more important than people seem to realize.

I'm sure most of us have heard of the "Gambler's Fallacy." It basically means that a little bit of statistics is a dangerous thing. People know that a "fair coin" will flip heads as often as tails. So when they watch a coin flip heads-heads-heads-heads-heads they KNOW that the coin is "overdue" for tails, and they begin to expect that tails will come more often for awhile to "catch up," because that's what coins do. As savvy gamblers we should know that coins, dice, and cards have no memory. They don't know that they've cheated you the last six times, and they don't feel that they owe you a win now. They ALSO don't know that they've let you suck out the last six times, so they're not going to punish you this time. Each coin flip is an independent event, and should be judged on its own merits, rather than on the past history.

Luckily, ordinary gamblers are NOT savvy about statistics. Case in point: several years ago, casinos began adding a counter to their roulette wheels that showed the last dozen or so spins of that particular wheel: what the number was and whether it was red or black. After putting in those counters, the casino profits from the roulette tables increased over 25% basically overnight, as people began betting on the roulette wheels that were "due" to hit a particular number or color.

Another point is that we, as human beings, have VERY little idea of what a "random" process actually looks like. We see streaks of 5 or 6 or 7 or 8 heads (or tails) in a row and immediately assume that something odd is happening:

- Raptor Christ hates me, because NOBODY could be this unlucky
- the casino is rigged, because I couldn't POSSIBLY lose this many coin flips in a row
- someone is cheating or has figured out the RNG for the casino, because they run MUCH hotter than is possible

etc.

Take a real look at the numbers Nielsio posted. Look at those streaks! Nobody would consider that truly random, but that's what random REALLY looks like. I remember hearing about a statistics professor that used to do an experiment in class: he'd select two teams of students. One would take an actual coin and flip it 100 times, writing the results in order on the board. The other team would invent their OWN series of 100 random-looking coinflip results on a different board. The professor would leave the room while they did their experiment, then would return to the room and tell them which list was which. He has never been wrong. When asked how he did it, he said it was quite easy: people making what they think are random lists actually put WAY too much volatility into it; rarely would a group of students have a streak more than four heads or tails long in their invented list. The coin, on the other hand, will USUALLY have a streak of seven or eight in a row at one point or another.

So, the lessons to be learned from this:

1. Cards have no memory.
2. Random doesn't mean what you think it means.
3. Just because you've won/lost the last xxx coin flips doesn't mean youre going to lose/win this one.
4. CARDS HAVE NO FREAKIN' MEMORY.
5. The long run is longer than you think.
6. Yes, it really is possible that you are running that hot/cold. No, you haven't necessarily discovered some secret coin-flipping theory that's giving you an edge. Yes, starting from now you're most likely to have a break-even outcome on your break-even bets.

Re: I flipped 100 coins

[ QUOTE ]
I bet if FGators did the flips it would come out like 17/83, man that guy runs bad.

[/ QUOTE ]

five things made me lol in this thread, but this was the best

seriously wtf? flip a coin a million times, then we'll talk.

Re: I flipped 100 coins

Who knew that Nielso and Pokey would tag team level ssnl?

Re: I flipped 100 coins

iuaewradiughakfghaksjfgsadl;kgjskafljgh
k done

Re: I flipped 100 coins

Hi, I'm trying to learn what is random and what isn't random. Can someone tell me if these are random? I only had time for 3 sets of 10 flips each.

First time:
h
h
h
h
h
h
h
h
h
h

Second time:
t
t
t
t
t
t
t
t
t
t

Third time
h
t
h
t
h
t
h
t
h
t

Thanks in advance, imo.

Re: I flipped 100 coins

Did that coin come from FTP?