You flip a coin 50 times a day. How long would it take to get 43/50 heads?

[TruthIsAll]

You flip a coin 50 times a day.
How often would you EXPECT that it would take, ON AVERAGE, to get 43 heads?

This is a very simple exercise, if you know the Excel formula.

We all know that the probability of getting heads on any flip, assuming a FAIR coin, is .50.

The probability of getting at least 43 heads in 50 flips is:
Probability = 1 - BINOMDIST(42,50,0.5,TRUE)
Probability = 0.0000001049

Therefore, ON AVERAGE, it would occur ONCE in 9,529,811 daily trials (1/0.0000001049).

Yes, it could occur today. Or next week Just like you COULD win Powerball today or next week. Or next year.

But you could only expect it to occur ONCE every 26,109 years, ON AVERAGE.

Similarly, one WOULD EXPECT that ON AVERAGE, that it would take 9,529,811 national elections (or ONCE every 38 million years) for a candidate's votes to exceed his exit poll numbers in at least 43 states.

This assumes an unbiased exit poll AND a fair vote count in all elections. If random, the odds are 0.50 that the vote count would deviate to either candidate - that is, each has an equal chance.

[7th_Sephiroth]

1. 43 actually

i am the Diebold of coin flipping

[TruthIsAll]

30. CORRECTION: It was 42 states (heads). On AVERAGE, ONCE every 4,700 YEARS

Probability of at least 42 heads (states):
= 1-BINOMDIST(41,50,0.5,TRUE)
= 0.00000058178
The odds: 1 in 1,718,869

So, the answer is:
1,718,869 days
4,709 years

Or:
1,718,869 elections
over 6,875,476 years

[7th_Sephiroth]

31. i can still flip a coin and make it land on heads

as much as i feel like it

[MikeDuffy]

48. Restated in another way:

Probability of at least 42 heads out of 50 tosses =
 [(50) (50) (50) (50) (50) (50) (50) (50) (50)]
 [(42)+(43)+(44)+(45)+(46)+(47)+(48)+(49)+(50)]*(1/2)^50 =
[536,878,650+99,884,400+15,890,700+2,118,760+230,300+19,600+1,225+50+1]*(1/2)^50
=.00000058178

         (50)
where by (42) I mean "the combinations of 50 things taken
42 at a time" = 50!/(42!8!)

     

[bleever]

2. Great explanation, easy to share.

[Joe Chi Minh]

11. Yes

and 7th-Sephiroth's too!

[dsc]

3. That isn't what probability means

It means that on average one can expect that one out of every 9,529,811 daily trials will have exactly 43 heads but it doesn't mean that it would take 9,529,811 daily trials for that to occur. It could take less it could take more. To see the mistake you made replace 43 out of 50 with 1 out of two. On average, half the days should see 1 out of 2 coin flips be heads but that doesn't mean it would take two days for that outcome to occur.

[eg101]

4. Wrong!

It might happen first try, or it might NEVER. All you did was calculate odds. Such an event could happen right way, but the odds would be astronomical, or it might never happen, although, again, the odds would be very much against that happening.

[TruthIsAll]

7. YOU KNOW WHAT I MEANT. ONCE ON AVERAGE, EVERY 26,109 TRIALS

I thought that was understood.
But I made the change in wording.

I guess you caught me.

[dsc]

9. even that is wrong

The expected value is once every 26,079 years but again it could happen sooner or later. Words have meaning here.

[TruthIsAll]

14. Words do have meaning. But I think you'e nitpicking. The calc is CORRECT.

But it is not very professional on your part to refer to it as junk math, as you did.

Come on, dsc, take that chip off.

[dsc]

25. As I said below

math is more than putting numbers into a calculator, or at least it should be. Given a reasonable amount of time I could get any high schooler to perform the calculation you did. The math comes in in the explanation.

[rdmccur]

29. Depends on your

philosophical preference for what mathematics is.
I would rather say you are talking metamathematics or meta-metamathematics. I would not bet my money, if say the minimum bet were $1000, regardless of the potential reward (say 1 million dollars) that it would happen in my lifetime, even if ten parallel trials could take place simultaneously. But then I'm not a gambling type.

In other words, I think the argument here is philosophical not mathematical.

Another mathematician

[genieroze]

19. Isn't this the third time this happened? 2000, 2002, 2004 and most

likely 2006 unless the Dems get off thier butts and do something.

[ladjf]

5. One hellofa good post. Great perspective or conceptulazation.

[Psephos]

6. Good thought but not so good math

Your calculation pinpoints only how long, on average, it would take for the likelihood of the event to approach certainty, when looking at the entire aggregate of trials. In other words, one might expect the event to have happened after running that many trials. However, you wouldn't know whether it would be on the third run or the fifty thousand one hundred and third run. Each run would have equal probability of being the "one."

Read some of John Allen Paulos' books (Innumeracy is one of the best) for entertaining and insightful debunking of mathematical misconceptions common in politics and general life.

[smartvoter]

8. Overthinking. The point is improbability. nt

[dsc]

10. No he is being accurate

Junk math is junk math no matter who is purveying it.

[TruthIsAll]

13. What do you mean, junk math, my friend? Do you dispute the calculation?

tia

[dsc]

17. I don't dispute the calculations

I do dispute, as I plainly said, your interpretation of what the calculations meant. Misinterpreting math is still junk math. Math isn't just plugging numbers into a calculator or computer and getting numbers out. It also is interpretting those numbers correctly.

[davidgmills]

28. We know what he meant

Sure it could happen the first day. It could even happen two or three times in 26,109 years.

But you know good and well it is not likely to happen today and it is not likely to happen in my lifetime or yours.

[smartvoter]

15. Why is it junk? It's a legitimate illustration. nt

[dsc]

22. No it isn't

when within the illustration one of the most perniciously common falacies of probability is being put forth. I am literally teaching this in my class in a couple of weeks and anyone who gives me that kind of answer to a probability question will be serverly marked down. He has fixed it to some extent which helps.

[Joe Chi Minh]

16. Wrong!

Do you think the computations of actuaries working for insurance companies are worthless and do not have the most eminently safe and practical applications? And DNA profiling statistics, are they worthless?

What's more, the odds of the latter cases, are, of course, much lower than the likelihood of the occurrence of such unfathomable(?) deviations. The Junk thinking is yours, dsc.

[smartvoter]

18. Too much picking around here sometimes. The illustration is valid. nt

[dsc]

20. They do

but they also have limits. To take one example, I pay much less for life insurance than my grandmother would. That is because in most cases people like me will out live people my grandmother's age. But that doesn't mean that I will definately out live her. I presumedly will but I also could get hit by a bus tomorrow.

[smartvoter]

21. Hence the point of the whole exercise. nt

[dsc]

23. He has fixed his example

but I stand behind the fact that without that fix his example was not at all a helpful thing.

[Joe Chi Minh]

27. Precisely.

It's extreeeemely practical. Just about *the* most practical resource technical people have available to them.

[TruthIsAll]

24. Thanks. You got it right That is EXACTLY the point. n/t

I do not write these posts to ruffle feathers.
The fact is, no one else here has done it. I don't know why.
So I do it.

I thought, by putting the numbers in context, the analogy would dramatize the facts of this election. The outrageous odds could be better appreciated.

Of course, others did not see it that way.
Junk math, one called it.
Well, what does THAT tell you?

True, the wording was not as clear as it should have been.
And I fixed it.

Oh, well, such is life.

[bear425]

26. TIA, want you to know that I appreciate all your efforts here

I wish I had half the talent you have mathematically/statistically. I would gladly help in your efforts, but I barely got through college algebra and statistics.

I just hope that the Powers That Be get to see your work, then we will ALL benefit from the fruits of your labor. Including the naysayers.

Again, thank you.

[TruthIsAll]

12. The math IS correct, the wording was NOT precise. I fixed it. n/t

tia

[MadisonProgressive]

49. It seems awfully fishy to me that the 43 out of 50 just happened

to come on the day of the most important election the world has ever witnessed...

[Pooka Fey]

32. Not so good reading of original post.

I don't know math, but I do know language.
Here's what you said: "you wouldn't know whether it would be on the third run or the fifty thousand one hundred and third run. Each run would have equal probability of being the "one."

Here's what TIA said:
"Yes, it could occur today. Or next week Just like you COULD win Powerball today or next week. Or next year. But you could only expect it to occur ONCE every 26,109 years, ON AVERAGE."

You obviously want to challenge TIA, but you need to know that you've been unsuccessful.

[Psephos]

35. Pooka, I did read the original post...the version you read has been edited

But here's a more important question. Why the ruffled feathers?

If we don't police our own logic and math here, then that just means some wingnut will do the job instead, and discredit the entire argument.

Sometimes, it seems like people here are looking for reasons to get mad at each other. Let's remind ourselves to assume the best about each other's intentions, not the worst.

[Pooka Fey]

36. Re: edited post - sorry about the misunderstanding then.

And yes - questions/input are absolutely necessary to ensure that all our argument are ship-shape.

The ruffled feathers come from about 10 days worth of name-calling on TIA's posts from various new DUers - people questioning his degrees, demanding references, making statements like "he uses junk math", and trying to discredit his analysis without backing up their statements with their own analysis. My experience since the election is, sadly, we can't assume the best about each other's intentions here. No hard feelings, I hope.

[Psephos]

38. No offense taken; all in the spirit of discussion

Sorry to hear TIA's been hammered lately, too. I can certainly relate to your own post-election experience, too.

I'm all for scrutinizing someone else's arguments, but am chagrined when this passes into slamming the person who makes them. TIA, if you're reading this, keep up the good posting. We'd all do well to remember that in anonymous online forums it's easy to indulge the impulse to call other people names or make them feel bad, simply because there's no real-world, real-time feedback. I'll bet most of those who've hammered TIA would be far more civil if the discussion took place over a cafe table.

[TruthIsAll]

34. You state the obvious. And you totally miss the point. n/t

.

[Igel]

33. And, like many other things, coin tosses aren't random.

There's a systematic bias, presumably caused by the difference in shape (aerodynamics) and distribution of mass in real coins. It's slight, but there nonetheless, and depends on the coin. I think it turns up heads more often than predicted, but they only tested one or two coins.

Yes, years ago somebody actually decided to test the stats; it was a Science News blip maybe 4-6 years ago. They found out why the stats mis-modeled reality: they assumed an idealized coin. In other words, the assumptions in deriving the probabilities were slightly wrong.

Still, if you file the burrs off of the metal bits that used to seal off holes in wall outlet boxes, and make sure they're properly balanced and neither side produces more drag, then *that* should be close enough to being the idealized coin to adequately satisfy the assumptions in the typical coin-toss calculation.

[rdmccur]

37. You've pointed out a

bias which is based on geometry, mass distribution, etc., which constitutes the deviation (if you will) from toin cossing being random.
I think what TIA is trying to show (and I may be wrong here TIA) is that it is very unlikely that one would expect the Bush-Kerry apportionment of vote totals in the collection of constituent states presented here, given no bias. Thus there was, in all likelihood, bias. As Freeman has discussed fairly extensively, there is enough likelihood (given the statistical analyses done) for bias that both the exit poll analysis and the election process, itself, should be investigated to find out what caused this bias. Given the multitude of other evidence that various types of voter disenfranchisement (e.g. voter suppression), machine tabulation problems (whether 'accidental' or deliberate), tabulation inconsistencies (based on party registration, % turnout, etc.), and other problems I can't recall to enumerate here; I believe it is the election vote count that should receive the closest scrutiny. Furthermore I believe Kerry, if the vote recording and tabulation were done without fraud, would be the president elect.

[TruthIsAll]

42. I said a FAIR coin. But of course, irrelevancies had to be brought

Bad coin? Trick dice?
It only serves to ignore the REAL issue with philosophical jargon.

I said flip a FAIR coin.
So turning up HEADS or TAILS is a RANDOM event.
THE COIN HAS NO NO MEMORY.

It's no different than vote deviations from exit polls.
The deviations should have NO MEMORY and be a sequence of random events.
It's either Kerry or Bush.
It shouuld be around 50/50.

LIKE A FAIR COIN, THE DEVIATIONS SHOULD HAVE NO MEMORY.
But it wasn't anything near random.

That is the issue.
Everything else is just smoke.

[rdmccur]

43. BTW I'm NOT

disputing what you have done in any way.
Let me rephrase what I said before another way.
If someone I did not know (but had heard was a scoundrel) took an ordinary nickel and said that after flipping it 50 times they got, say 43 heads to win a bet, I would be incredulous and not believe them.
If addition they had refused to have a credible verified witness for their coin flipping exercise, I would definitely not believe them.

[TruthIsAll]

53. rdmccur, I was referring to the poster you replied to. No dispute with you

.

[Igel]

47. A "fair" coin to me is one that hasn't been rigged.

Just like a "fair die" would be one that's not weighted.

Maybe a "fair coin" is a round piece of metal with identical markings and mass distribution on both sides. In which case the US mint doesn't produce any fair coins. If that's the generally accepted definition, I stand corrected, but it's a usage I've never heard. Still, I don't gamble.

In any event, I don't think any coin has a memory. Even a rigged one. (I guess one could construct a die that has a crude very short-term memory.)

[Yupster]

39. Interesting Igil

So are we getting an exit poll that is not random?

Since the responders can respond or not respond depending on how they're feeling that second, are we getting a systematic bias?

What if Republican voters are just unfriendlier than Democratic voters and they turn down the opportunity to answer the exit poll more frequently. That would explain why Democratic candidates seem to often do worse than their exit poll predictions say they will.

[TruthIsAll]

40. Still pushing that canard? Repubs not as friendly as Dems?

Yup, that's a possibility. NOT.

[Yupster]

50. Well, It would certainly explain the numbers

and it fits with my own experiences.

People with Democratic values are generally more friendly and open than people with Republican values. That sure seems logical to me.

All the really rude or angry people I know who would blow off exit pollsters are Republican types, usually older white men with NRA stickers and "Rush is Right" bumper stickers.

However TIA,

I didn't address one of your posts on purpose because I realize that you have so much invested in your effort that you cannot change your opinion now. You will likely go to your grave believing there was a giant conspiracy to change millions of votes, and any theory against yours will be ridiculed or dismissed and any evidence against it will just go to show the conspiracy was even bigger than you thought.

I read others' opinions, but I gave up on yours' when you used the Pew Poll to show that the final pre-election polls showed Kerry ahead. Of course when I went to the Pew Poll, it showed Bush ahead 51-48, the exact final result. When I asked you for an explanation, you said for that poll you were using registered voters rather than likely voters. Well, that was it for me as in a close election if someone is that willing to cherry pick their data, then one could prove anything they want. I wasn't interested in that level of manipulation though, so that was the end of paying attention to you for me.

You have enough people lauding your work. There are dozens of people on this thread who want to hear from you. Why don't you kindly cross me off your list. ;) Thanks.

[TruthIsAll]

54. And I explained why RV polls are better when there are many NEW voters

Maybe you didn't read my explanation; it was a reply to another DUer.

There were 15-20 million new voters in THIS election, the majority of whom voted for Kerry. They would NOT have been polled as LV's, but they would be as RV's. And why shouldn't they be polled?

If I cherry-picked the RV polls it's because I used a little common sense. It is very logical to assume that including RV's in the poll would give a better result. And they did just that, because the RV polls were right on the money.

So your whole argument is false and misleading.

I have no lists. I don't cross anyone off. If you mean that I should put you on my ignore list, I won't do that.

Because otherwise, I won't have the opportunity of rebutting your rebuttals.

[banjosareunderrated]

41. Nitpickers

It seems every time TIA posts, there are those who try to dispute what he is saying. However, you nitpickers seem to be missing one glaring fact: we already have evidence that the election was stolen. Not to rehash it all, but from the "challengers" to the deliberate redirection of voters in key democratic precincts to the whole "weight of the paper" registration fiasco. There is clear, solid, indisputable evidence that the Pukes stole this election. It's not as if we have a feeling that the election was stolen and are looking to people like TIA to find the proof. We already HAVE proof. TIA, in my opinion (and I don't want to speak for you), is simply using the numbers to show that fraud was more rampant than we may think. It wasn't only confined to Ohio or NM.

TIA, you put the rock in the roll. Thanks.

[The Straight Story]

44. What are the odds that it will not be 50-50

Any given day? Or the odds that it WILL be 50-50 each day for a week, etc?

Point is, calcultating for one single event can be misleading. It might be better to calculate for a group of events (thinking lottery if you will, what are the chances the number you picked will be part of a set like 6 numbers all sequential or 2 apart, et al - and what is the likelihood that some number from that set will appear).

[TruthIsAll]

45. Your story is not very straight. It makes no sense. You are

introducing bogus complications which totally camouflage a very simple math problem.,

I suggest you pick up a stat book and read up on the binomial distribution.

And, please, please, do not go to Vegas.

But you can keep buying those lottery tickets.
I have no idea when you may win.
It could happen next week. But I doubt it.

Just don't expect to win anytime over the next thousand years.

Here's a prposition for you.
Flip a coin 50 times a day, just like the example.
Keep a record of how many turn up heads.

Don't stop until you get 42 heads.
I hope you live a long, very long life.

[The Straight Story]

46. I understand your experiment quite well

The point is you are using a singular event, the odds of exactly that one event happening, after it has occured to prove that the only way that event could have 'reasonably' occured was through a rigged game. Fair enough.

Had someone come out and predicted that 43 states would have exit polling data that was not what it should be beforehand and offered a bet that would be a hard one to take, versus if they had a point spread of states (ala a set). Then one would have to look at a lot of other factors:
1. How many times in history have states' exit polls not matched, what was the percentage of difference, how many states, et al.
2. Is exit polling forced or do people (who have been in line hours already) simply ignore the exit polling, does weather play (or has it played) a factor, who was polled where the most (ie were the respondents more likely to be in a certain demographic, et al). What factor does lying and psychology play.
3. Is the exit polling designed to verify votes or cover a larger range of topics - ie, what is the goal nationally for exit polling (simply to project or to supercede the actual votes. You cannot recount exit polls - or diebold for that matter)

From a purely mathematical aspect, yes it is an accurate descpription to say that getting 43 heads would take X years or so many throws, et al. But this was not a purely mathematical exercise - there were many more factors involved in the outcome much of which was based on people, participation, and other things which could skew how the toss turned out (ie - it was not a perfectly weighted coin).

That is not to say that exit polling is worthless, and it can indicate problems - problems which proper counting of the votes with a verifiable trail could fix. As I said, my main problem is that this in not a perfectly weighted coin.

As for the set theory and lotto thing :) - The idea was that IF you're going to play the lottery on a regular basis, and you did an anlysis similar to yours on the odds, you would find that certain sets of numbers would get a hit more often than other sets - you would/could simply increase your odds over a time period which does not mean you would win, just increase the odds because you have narrowed the set from which you would be choosing numbers to a set which has a better pure mathematical chance of having a hit within that set (whereas picking a number like 1,2,3,4,5,6 which is based on a smaller set of sequential numbers over time would give you less odds).

[TruthIsAll]

56. Have you heard of Gambler's Ruin: The Martingdale Betting strategy?

There is no formula. If there is one, tell us.
Maybe we should play it.

We must assume a random event. All combinations are equally likely.

It's like the old gamblers ruin Martingale.

Place a UNIT bet. Lose.
Double your previous bet in the hope that you will win it back and gain ONE unit. But you lose. So you double again.
And so on....

You keep doubling your bet because you feel you are "due" to win.
That's a fallacy.

True, you may win at any time.
But eventually, if you adhere to the strategy, you will no longer be able to double your bet.
Because at some point you will lose N bets in a row.
You will be out of money.

Picking 1 2 3 4 5 6 is just as good a bet as picking 1 4 6 14 39 42 (which I always did- those are the old Brooklyn Dodger uniform numbers).

My aunt has won lotto a number of times by always playing 1 1 1.
Is that any more likely than 4 7 9 ?

I doubt it. But then, who can remember 4 7 9?
We can easily remember 1 1 1.

To place future bets based on a "pattern" from hundreds of winning lottery combinations when there are millions of combinations is ridiculous.

[Shalom]

51. To Be Fair to Bushitler, Calculate Likelihood of at LEAST 43 Heads...

We are not calculating the likelihood of Bushitler getting exactly 43 heads in 50 trials, but the likelihood of getting 43 heads or MORE.

Excel allows you to set the flag to a "cumulative" calculation.

By ending over backwards to be fair to Bushitler (which the creep does not deserve), we will still end up with an ASTRONOMICAL impossibility that the shithead was elected fairly.

[TruthIsAll]

52. I am calculating the probability of at least 42 heads.

Forty-two states deviated to Bush, not 43.
I fixed that.

I said 42 heads, you took it to mean exactly 42.
I meant at least 42.
That is what I computed.

Look at the Excel Function.
The TRUE parameter means cumulative.
The probability of AT MOST 41 heads is = BINOMDIST (41,50,.5, TRUE)

So the probability of AT LEAST 42 heads is:
Prob = 1 - BINOMDIST (41,50,.5, TRUE)

[Shalom]

55. Right You Are, and Yet All Has Turned Out Wrong ! ;-(