Take Out Thought.

[thoroughbred]

Here, perhaps, is an interesting thought about "Take Out."

IF:

1. There were no take out at all,

AND,

2. The betting public always caused the odds to be the exact, correct odds,

THEN:

Everybody would break even in the long run.

[alysheba88]

Not at all. While I dont agree with the idea of "correct odds" I'll go along with the supposition at least. But what isnt factored in is the HUMAN element. The pyschology of betting. Knowing how to bet, and keeping your emotions under control determines who wins and who loses far more than handicapping skill. Players spend their whole lives searching data bases, reading every book, etc for the "Hold Grail". Spending 95% of their time on handicapping. And little on betting. Have been guilty of this myself.

[Whirlaway]

I don't think that anyone would suggest that the public odds are perfectly efficient. The problem for the bettor is that broadly speaking they're efficient to within 5-10%, while takeouts are 15-20% (and up). If there were no takeout, a reasonably profficient handicapper could expect to make a 7-10% profit betting every race, which is probably impossible at current takeout levels.

[hurrikane]

whirl

I don't think that anyone would suggest that the public odds are perfectly efficient

I guess you haven't met Joe. lucky you

[formula_2002]

QUOTE] originally posted by thoroughbred
Here, perhaps, is an interesting thought about "Take Out."

IF:

1. There were no take out at all,

AND,

2. The betting public always caused the odds to be the exact, correct odds,

THEN:

Everybody would break even in the long run. [/QUOTE]

Thank you...
The one of the operative words is the long run...but even then, as long as one keeps playing it’s impossible to breakeven...

Regarding the simple flipping of a coin, according to John Allen Paulos, “ ..It’s considerably more likely that one could be ahead (or behind) more then 98% of the time, say, than one be ahead between 49 and 51% of the time.”
And that is for fixed 1-1 odds with no take-out.

[formula_2002]

actually, impossible to break even after but one flip of the coin.
proving ofcourse the flipped coin returns a heads or tails...

Joe M

[Holy Bull]

The answer is no. From a purely mathematical standpoint, there is a theorem in random walks that the longer you "Walk", the further you on average will be away from the expected place (in this case, breakeven). I believe the function for this distance is a function of the square root of the # of trials which would make sense (in this case everyone's ROI would be pulled back to 1.00 but from a raw win/loss would drift further and further away from break even).

[Lefty]

Let's take that coin toss; me and you $1 a shot even steven. Oh, you have $10 and I have a $100. Who do you think will win and all with no "takeout".
There are slot machines in Vegas that return 100% over the long run, yet the casinos make big bucks with 'em.

[superfecta]

Originally posted by alysheba88 (MW)
Not at all. While I dont agree with the idea of "correct odds" I'll go along with the supposition at least. But what isnt factored in is the HUMAN element. The pyschology of betting. Knowing how to bet, and keeping your emotions under control determines who wins and who loses far more than handicapping skill. Players spend their whole lives searching data bases, reading every book, etc for the "Hold Grail". Spending 95% of their time on handicapping. And little on betting. Have been guilty of this myself. Hope this doesn't catch on,keep this to yourself OK?;)

[hurrikane]

alysheeba,

this is one thing that makes it possible to beat the hores.
Unlike flipping a coin where you will always have a 50/50 chance of winning and you know you should get 1-1 odds (unless you can find an idiot to give you 2-1).

There is not one race that is exactly the same as another. Even with the exact same horses running things will not be the same.
Knowing when to pull the trigger is just as important as knowing the speed, class, track, etc. In fact more important. We all have the same data. So what seperates the winners from the Joes in the world. Fearless, patient, hard work, and the ablilty to believe in what you are doing even when the losers of the world say it can't be done.

What a great friggin way to make money! I love it!

[keilan]

Kane – is calling heads or tails really a 50-50% chance.

Little experiment -- have someone flip a coin 10 times and you call whether it lands heads or tails. The guy calling doesn’t have a 50% chance of calling it right. Do this exercise 5 times (50 flips) I know small sample but it will get you thinking.

By now some of you are thinking Keilan has lost his mind. Now your standing at the teller getting ready to purchase a win ticket and you’ve narrowed your selections down to two horses –choose one, do you have a 50% chance of winning? I don’t think so.

Little tip when flipping a coin to see who buys coffee/picks up the tab etc – have the other guy call, it will save you some $$$ over the long haul.

[hurrikane]

I'm not following you're thinking here Keilan..you're going to have to work real hard with me on this one. :D

[keilan]

-- humor me, try the experiment. Post the results. I have some appointments but will be back later okay.

Sample #1 flipper won 6 – caller 4
Sample #2 etc.

[hurrikane]

I don't have anyone handy that I could ask t flip a coin..and most I know would think I was a nut(most already do).

But I can't flip it myself, that wouldn't be the same as what you are saying. If what you are saying is true(which I doubt) then it is because the coin is not being flipped faily each time.

If a machine were flipping the coin and I was calling the flip you are saying I wouldn't have a 1-1 chance of winning(or losing).

Something tells me this is not going to be fun. you're pulling my leg, right? :D

[MarylandPaul@HSH]

I'll play. I call "Tails" every time. Just pretend I'm there. ;)

MP

[Show Me the Wire]

hurrikane:

It is the effect of randomness and adding variables. Over the long run the odds would be 1 to 1, if you called heads or tails every flip, but randomness will influence the run no matter your consistency. However, if you add a variable by calling heads or tails on an unequal basis, have you not compounded the odds to make it something more than 1 to 1?

Sort of like favorites lose 66% of the time.

Regards,
Show Me the Wire

[Whirlaway]

Here's (http://www.agribiz.com/merchdiz/cointoss/cointoss.html) a coin toss simulator for anyone interested in the subject.

[GameTheory]

Keilan seemed to be implying that the flipper actually had an advantage, and that the caller would be right less than 50% of the time. That would not make sense.

In a series of samples, you should see a normal distribution (bell curve) centered around 50%. In some samples, the flipper will win (a series of flips), and in others (same proportion) the caller will win. Once in a while they will exactly tie, assuming an even number of flips in the series.

When doing a long series of flips (random walk) and counting +1 for right and -1 for wrong, the sum will move away from zero as the number of flips increases. However, at the same time, the percentage of correct guesses will converge closer & closer to 50%. There is no contradiction there.

[hurrikane]

ok
h-t
5-5
4-6


Maryland....where do I send your 50 cents. (damn it! next time I'm flipping a penny) :D

SMTW, yes, I understand what you are saying. But it sounded like Keiland was saying the person calling the flip had an advantage.
That sounds a little funny.

for the odds to remain 1-1 you would have to call the same thing every time.

However.

The point I was making so poorly is that at the call you have a 50/50 chance of winning regardless of what you call.

Contrary to the odds worshipper on the site...every 5-1 horse is not really a 5-1 horse. I'm sure you would agree understanding this is paramount to winning.

Even Karl and Kenwoodall can't win betting $40.00 on 5-2 horses that should really be 10-1.

[keilan]

– remember what I’m asking, the caller has to call whether each outcome is either heads or tails. It is because the caller has to make the correct choice while the coin is in the air he will be correct less than 50% of the time.

Please take 5 minutes, grab your wife and conduct the exercise, honest guys this is for real. And no Kane I’m not pulling your leg.

Thanx for playing along – fffast has an adjustment for this I think!

I will be back – couple more appointments.

[GameTheory]

Originally posted by keilan
– remember what I’m asking, the caller has to call whether each outcome is either heads or tails. It is because the caller has to make the correct choice while the coin is in the air he will be correct less than 50% of the time.



Sorry, still doesn't make sense. With a fair coin, it doesn't matter what the caller calls. Maybe you should try it -- I'll take tails every time.

[superfecta]

Originally posted by keilan
– remember what I’m asking, the caller has to call whether each outcome is either heads or tails. It is because the caller has to make the correct choice while the coin is in the air he will be correct less than 50% of the time.

Please take 5 minutes, grab your wife and conduct the exercise, honest guys this is for real. And no Kane I’m not pulling your leg.

Thanx for playing along – fffast has an adjustment for this I think!

I will be back – couple more appointments. Good exercise in how statistic truths are not always what we think they are....I always like to say to the stat guys at the racino ,"yes you can prove your stat is true,but that doesn't make it right"and they always look at me funny,and I don't bother to expand because its a waste of time and effort.

[keilan]

Maybe I should have stipulated earlier that one could not choose either just heads or just tails but they should randomly select either heads or tails based on what they thought would occur on each flip of the coin.

The flipper has the clear advantage because the caller has to call the correct outcome. SMTW is correct about adding a variable to the mix.

Didn’t mean to turn this into anything other than that.

When you flip for coffee or the tab, the odds are in your favor if you have paid attention. When you win the flip thank “keilan” when you lose (or is it loose) pay the bill.

Hell what do I know “I’m a horseplayer”. Where’s anotherdave? -- still on sabbatical.

[GameTheory]

Originally posted by keilan
Maybe I should have stipulated earlier that one could not choose either just heads or just tails but they should randomly select either heads or tails based on what they thought would occur on each flip of the coin.

The flipper has the clear advantage because the caller has to call the correct outcome. SMTW is correct about adding a variable to the mix.


Still don't get it. If I as the caller pick all heads, all tails, alternating heads & tails, random heads or tails, or even heads 80% of the time & tails 20% of the time doesn't matter -- probability of getting it right is exactly 50% every time.

Can you explain how it would be otherwise? What amount of time do you think the caller would get it correct? I'm interested to hear your reasoning.

Here is mine: the coin is either (going to be) heads or tails. So I call heads or tails. Half of the time what I call will match up with the coin. Doesn't matter what I call, and doesn't matter what I called the last 100 times because each flip is an independent event. Whatever I call has a 50% chance of being a match as long as the coin is fair. That is, as long as the coin has a 50/50 chance of being heads/tails, then that's all you need to know. The only way I could lower my probability is to call "lands on the edge" or something like that.

There is nothing tricky about this. I think if coin flips were not fair we would have heard about it by now. This place really has gone crazy. This is the sort of thinking that gets people to think the favorite is "due" because 8 non-favorites have lost in a row...

[GameTheory]

Correction: when 8 favorites, not non-favorites, have lost...

[thoroughbred]

Reading the messages here, points out what many have observed, i.e., the human mind has difficulty understanding probabilities.

Some think that the mathematics of probability is separate from reality, when in fact, it represents reality.

Here is an example that illustrates that most of us will have difficulty with probability.

Marilyn Von Savant, in her column, posed the following puzzle:

You are a contestant on a TV game show.
The TV host places you in front of three closed doors.
You are told that behind one of the doors is a Mercedes-Benz, and behind each of the other two there is a goat.

At this point you choose one of the doors.
But before your door choice is opened, the TV host opens one of the OTHER doors showing you a goat. (He can always do this because there are two doors with goats, and he knows where they are.)

Now, you are in front of two closed doors, the original one you chose, and the other remaining closed door.

You are now given the opportunity of either sticking with your original choice, or switching to the other closed door.

What decision would be the best one for you to make and why?

a. Stick with your original choice.
b. Switch to the other door.
c. It doesn't matter.

[hdcper]

Seems simple enough to me, always switch to the other door!!!

In otherwords, at random my first choice will only be the Mercedes 1/3 of the time.

But the 2/3 of the time I happen to pick a goat, the switch guarantees I am driving a new Mercedes.

Now if I could only get someone to show me a goat that has more than the take invested on it, this game would be easy!

Bill

[thoroughbred]

Originally posted by hdcper
Seems simple enough to me, always switch to the other door!!!

In otherwords, at random my first choice will only be the Mercedes 1/3 of the time.

But the 2/3 of the time I happen to pick a goat, the switch guarantees I am driving a new Mercedes.

Now if I could only get someone to show me a goat that has more than the take invested on it, this game would be easy!

Bill

hdcper:
You are not correct when you say that the switch guarantees you will be driving a Mercedes. After all, there are still two closed doors and only one of them has the Mercedes.

[hdcper]

hdcper:
You are not correct when you say that the switch guarantees you will be driving a Mercedes. After all, there are still two closed doors and only one of them has the Mercedes

Sorry but I tend to disagree. It is clear that only 1/3 of the time I will happen to select the Mercedes on my first choice of a door. Thus, 2/3 of the time I will select one of the doors with a goat behind it. So on this 2/3 probability of happening to pick a door with a goat behind it, the host will open the other door with a goat behind it(since he knows which one it is). Therefore, on these 2 out of 3 times I happen to pick a door with a goat, I am guaranteed the Mercedes by switching doors!!!!

Hopefully that is somewhat clearer,

Bill

[MarylandPaul@HSH]

I'd say it doesn't matter. The first decision, choosing one of three doors, was a non-event since they never opened that door. There was no payoff, right or wrong.

MP

[Derek2U]

IMHO .... In Keilan's coin flip the LONG TERM heads-tails will be
50-50 no matter what. And, the more flips, the closer to 50-50.
Agreed? Thank Budha for coin & card problems that simplify Pr.
But in the real world, who cares --- especially with puters &
the Pr software. But a while ago someone mentioned using
Bayesian Pr ---- now thats more to the point. Whats the Pr
that my grandparents will OverStay when they visit? 100%.
hehe .... When we make Pr estimates our brains use data that's
impossible to quantify .... but it works. With Bayes stuff you can
set Pr estimates .... and Voila then do the math. It's more fun.

[keilan]

Question – if someone or machine flipped a coin 1 million times the probability of it landing heads or tails is 50%. But I’m not really talking about that.

Lets say from a sample of 954 coin tosses the caller randomly selects heads 620 times or 65% of the time or he randomly selects heads exactly half the time (477). Remember I asked that the caller select either heads or tails based on what they thought would occur on each flip of the coin Are you telling me that at the end of 954 flips the flipper and the caller will be tied at 477 wins apiece. Don’t think so boys.

[GameTheory]

Originally posted by keilan
Lets say from a sample of 954 coin tosses the caller randomly selects heads 620 times or 65% of the time or he randomly selects heads exactly half the time (477). Remember I asked that the caller select either heads or tails based on what they thought would occur on each flip of the coin Are you telling me that at the end of 954 flips the flipper and the caller will be tied at 477 wins apiece. Don’t think so boys.

The chance that they will be exactly tied is the *most* likely event, yes. But in the space of all possible outcomes, it will only happen a small amount of time. What I am saying is that the caller & flipper have equal chances of coming out ahead.

You seem to be saying the flipper has an advantage. Absolutely not true.

I can even prove it. It is elementary stuff. Would you like to see the data?

I'm most interested in hearing why you think either side would have an advantage...


Regarding the Mercedes & the goats -- yes you should always switch doors. You will get the car 2/3 of the time.

[keilan]

Are you telling me regardless of whether someone chooses heads 65% or tails 65 % of the time at random that they will be exactly tied as the most likely event?

Have you tried this little exercise with someone yet?

[Chico]

Originally posted by MarylandPaul@HSH
I'd say it doesn't matter. The first decision, choosing one of three doors, was a non-event since they never opened that door. There was no payoff, right or wrong.

MP

Sorry, MP, but you are wrong.
The first decision WAS an event. If you selected door #1 initially you would be correct 1/3 of the time. If you stick with it you will win 33 of 99 events. If you switch, since the game show host can't show you a winning door initially, you are guaranteed to win 66 of 99 events. It all has to do with a mathematical principle called "the rule of restricted choice."
Regards,
Chico

[Chico]

Originally posted by formula_2002
QUOTE] originally posted by thoroughbred
Here, perhaps, is an interesting thought about "Take Out."

Everybody would break even in the long run.

Thank you...
The one of the operative words is the long run...but even then, as long as one keeps playing it’s impossible to breakeven...

Regarding the simple flipping of a coin, according to John Allen Paulos, “ ..It’s considerably more likely that one could be ahead (or behind) more then 98% of the time, say, than one be ahead between 49 and 51% of the time.”
And that is for fixed 1-1 odds with no take-out. [/QUOTE]

With no takeout it becomes a "zero sum" game and
from the very first race through the very last race it is an exactly 50.0000% - 50.0000% proposition for the public.
Regards,
Chico

[GameTheory]

Originally posted by keilan
Are you telling me regardless of whether someone chooses heads 65% or tails 65 % of the time at random that they will be exactly tied as the most likely event?



Yes, that is exactly what I'm telling you. The caller could call a heads tails split 65/35, 80/20, 90/10, 15/85, 50/50 and it doesn't matter a bit. IT DOES NOT MATTER WHAT THE CALLER CALLS.

When I say most likely that doesn't mean it will happen all that much (something that has a 1% chance of happening can still be the most likely outcome if every other outcome has less than a 1% chance of happening). I'm also saying it is the most likely EXACT outcome -- more likely than any other single exact score: 478 to 476 for example.

But if we forget about the ties, and group all other outcomes into "flipper wins" or "caller wins" each group will be roughly the same size.

Bottom line: neither side has an advantage, and it doesn't matter what the caller calls.


And no, I haven't tried it in the sense that I've sat here and flipped a coin over & over. It would take hours for one thing. I could prove my point with a computer simulation if you like, unless you are saying there is a difference between what would happen in reality and what the computer would show. In which case you would be playing with an unfair coin in real life or the caller would be psychic.

What do you think about the 3 doors? Would you switch? You should.

[Derek2U]

hehe that math nerd knows what? he just wrote a new book
Explaining Why he dropped a bundle in the stock market --- where
BEFORE he lost that small fortune, he Wrote about how he uses
math to spot undervalued stocks. Now lets really beleive his
math ability.

[Tom]

Originally posted by keilan
Question – if someone or machine flipped a coin 1 million times the probability of it landing heads or tails is 50%. But I’m not really talking about that.



But, more to the point, what is the probability that the machine will function correcctly 1 million times in row, without breaking down?
Inquiring minds want to know!

[keilan]

GT – if you can duplicate a real life simulation with a computer I would like to view the results based on 954 coin tosses. Each at 477 random selections of heads then tails please. I would prefer you actually flipped the coin though – it would keep you off this thread for a while HAHA.

If it’s to time consuming I will take your word for it. I really have to handicap a few races today and this is slowing me down “posting”.

[GameTheory]

It is very easy. 954 times in a row (where did we get 954?) I ask the computer to pick a random number -- either 1 or 2. That's the caller. Then I ask for a second random number, also 1 or 2. That's the flipper. (Reverse them, same thing.)

If the two numbers match (both heads or both tails) then that means the caller got it right and that is one point for the caller, otherwise the flipper gets the point.

Here are the results for 10 runs (954 flips each):


Caller Flipper Winner
464 490 FLIPPER
480 474 CALLER
473 481 FLIPPER
505 449 CALLER
478 476 CALLER
477 477 TIE
491 463 CALLER
465 489 FLIPPER
483 471 CALLER
443 511 FLIPPER



The caller won 5, the flipper won 4, and 1 tie.

Now let's have the caller call heads 2/3 of his calls:


Caller Flipper Winner
491 463 CALLER
490 464 CALLER
480 474 CALLER
467 487 FLIPPER
475 479 FLIPPER
481 473 CALLER
473 481 FLIPPER
470 484 FLIPPER
484 470 CALLER
476 478 FLIPPER


Caller 5, Flipper 5


See?

Now can explain why you thought the results would be otherwise? I'm much less interested in "being right" then in understanding how people think...

[keilan]

Thanks GT, for showing me the light.

Those friggin smart guys, probably plays chess to – and you really don’t want to know how I think!

Oh Andy, any idea who wins the 5th at Churchill today?

[thoroughbred]

HCPR

From your latest, I can see where you have gone astray.

You have ignored the case, which happens 1/3 of time where you happened to have chosen the Mercedes door on your first choice of doors.

Clearly in this case, if you switch doors, you will not be getting the Mercedes.

[thoroughbred]

Originally posted by MarylandPaul@HSH
I'd say it doesn't matter. The first decision, choosing one of three doors, was a non-event since they never opened that door. There was no payoff, right or wrong.

MP

Maryland,,,,,,

Sorry not correct.

I'll post the correct answer after others have a shot at giving the answer.

[GameTheory]

Originally posted by keilan
Oh Andy, any idea who wins the 5th at Churchill today?

If stays on turf,

#9 -- Soldier Song (ML 6/1)

or

#8 -- Trial By Jury (ML 5/1)

[Derek2U]

Im hangin w/ Keilan in the WR & I gotta tell u guys that he just
finishd his 250,000 coin flip & he got 249,000 heads. I told him
to go for 500K more.

[keilan]

D2U sometimes I could just choke you (a little) PA can I -- can I

PA I would own ya one!

[GameTheory]

Well, #8 won but they took him down! What are the chances of that happening?

[hdcper]

T-bred,

Seems you misunderstood my explanation of my reasoning, and thanks for the email (but couldn't respond to your email to explain what I was thinking further).

Hopefully, you realize I was basically saying that 2/3 of the time you would win the Mercedes by switching doors everytime. Guess I thought my wording was expressing that but when I said guaranteed it confused the issue.

Anyway thanks for the problem, I am sure my algebra students next year will find it challenging.

Bill

[BillW]

Guys,

Lots of coverage of this on the web ...

For instance:

http://shomenuchi.hippopotamus.com/CarGoatSolution.htm


Try a google search for "goats and car" or something similar. You get a fair amount of noise, but a surprising number of relevant hits.


Bill

[GameTheory]

It is generally known as the "Let's Make A Deal problem", and if you search for that you'll find lots of stuff...

[thoroughbred]

O.K. The answer has been revealed by others and BillW gave us a link to web sites that discuss the problem and give the correct answer, i.e., that it is better to switch because it increased your probability of getting the Mercedes from 1/3 to 2/3.

That saves me from the task of explaining why it is better to switch.

I will, however, show, how, intuitivelly, you can see why it is better to switch. It becomes very clear, if we increase the number of doors, to, say, one million. (I pick this large number to make the point; the principle remains the same.)

So now the puzzle is:

You are faced with 1,000,000 closed doors. Only one of the doors has a Mercedes behind it, the other 999,999 closed doors each has a goat behind it.

After you pick a door, the host who knows where the goats are, opens 999,998 doors showing you the goats. That leaves just two closed doors; the original one you chose, and one other.

Now it is absolutely clear, that if you are given the option of switching, you should because your chances of having guessed right at first were one in a million, while the chances of the car being behind the other closed door are 999,000/1,000,000.

It would be ludicrous to say, that because you are faced with two closed doors, that the odds are 50-50. With such a large number of doors to begin with, you are almost absolutely certain that the Mercedes is behind the remaining closed door.