Unoffical empeg BBS

Quick Links: Empeg FAQ | RioCar.Org | Hijack | BigDisk Builder | jEmplode | emphatic
Repairs: Repairs

Page 2 of 5 < 1 2 3 4 5 >
Topic Options
#277762 - 19/03/2006 16:41 Re: Stock Market [Re: n2toh]
bonzi
pooh-bah

Registered: 13/09/1999
Posts: 2401
Loc: Croatia
Quote:
Ok then how would such a ploy work on this game where rollovers happen all the time?

It would work. The recipe is simple: play only those rounds where the expected payback is larger than total amount paid for tickets (including yours, of course). Against whom you play (i.e. whose money are you getting)? Those who play in low-jackpot rounds. I think I remember there was a round of Powerball or something similar where the price of enough tickets to guarantee the jackpot was lower than the jackpot, and someone collected enough money to go for it (the main obstacle, IIRC, being the requirement to fill the tickets in manually).

Boy, I forgot all my statistics. Can anyone quickly calculate how many different unordered combinations of 6 out of 43 are there? Ah, 175711536, apparently. So, you will have to wait for several more rollovers... If you pay those 175M$, you are guaranteed to hit the jackpot, but might have to share it with someone else. That's why jackpot has to be higher than total amount paid.
_________________________
Dragi "Bonzi" Raos Q#5196 MkII #080000376, 18GB green MkIIa #040103247, 60GB blue

Top
#277763 - 19/03/2006 18:26 Re: Stock Market [Re: FireFox31]
gbeer
carpal tunnel

Registered: 17/12/2000
Posts: 2665
Loc: Manteca, California
Quote:
You know, in some states, lottery funds go to schooling for under privileged 3 and 4 year old children. Let's tell those MIT guys to back off raking the lottery systems.... which rake so many people.


Huh? The California Lotto is used to put additional funding into schools, but that money comes off the top, before anyone is paid a single jackpot. The other thing about the Ca Lotto is that it seems to pay the top jackpot too frequently to make raids profitable.

Top
#277764 - 19/03/2006 18:37 Re: Stock Market [Re: FireFox31]
bonzi
pooh-bah

Registered: 13/09/1999
Posts: 2401
Loc: Croatia
Quote:
Let's tell those MIT guys to back off raking the lottery systems.... which rake so many people.

The scheme of playing for huge sum when the jackpot is large enough works only when just one team is doing it (more precisely, another participant makes the treshold much higher). So, the system is self-regulatory. Actually, MIT-like efforts are likely to make significant jackpots more frequent, making the game more popular => more money for kids.
_________________________
Dragi "Bonzi" Raos Q#5196 MkII #080000376, 18GB green MkIIa #040103247, 60GB blue

Top
#277765 - 19/03/2006 18:51 Re: Stock Market [Re: FireFox31]
n2toh
journeyman

Registered: 29/01/2001
Posts: 89
Loc: New Jersey, United States
Quote:
HAHA, New Jersey, where the real "getting nothing for something" gamble is paying your taxes... to corrupt politicians' pensions. Oh, I should watch what I say. Their pending bill (real link broken) to force Internet message board posters to be fully identifiable with name and address (second paragraph says it all) may help The Man track me down for such slander.

You know, in some states, lottery funds go to schooling for under privileged 3 and 4 year old children. Let's tell those MIT guys to back off raking the lottery systems.... which rake so many people.


bills like that are typical for NJ, if you want a good laugh or cry go here and Search by Keyword in Synopsis for "firearm". If A812 or anything like it passes is the day I pack my bags and goto PA.
_________________________
The only difference between science fiction and reality is about 60 years.
100GB MK2 Green 080000171 + OEM tuner
v3.00a11 hijack v450 jEmpload v70

Top
#277766 - 19/03/2006 18:57 Re: Stock Market [Re: bonzi]
TigerJimmy
old hand

Registered: 15/02/2002
Posts: 1049
Quote:
The recipe is simple: play only those rounds where the expected payback is larger than total amount paid for tickets (including yours, of course).


This is not the correct recepie. It is possible to have a +EV gamble on rollover lotteries. Like any gambling transaction, it is +EV if the payout odds are larger than the odds against winning the payout. The number of tickets sold is not a factor in rollover lotteries because its possible for nobody to win, which was why there was a rollover in the first place. Your odds of winning are 1 in however many combinations of numbers there are.

Your payout is a bit more complex to figure out, because there are payouts in addition to the jackpot in most lottieries.

You will also need to factor in taxes. In powerball, the break-even after paying US federal tax is somewhere around $380M. However, it is possible for more than one person to win, so calculating EV needs to calculate the liklihood that you win, but only win half. (Interestingly, you need to do this in Hi-Low split poker too, like the Omaha/8 we were talking about in the other thread).

Lotteries are high variance games, to put it mildly. While you may have a *theoretical* positive expectation, its unlikely that anyone has a bankroll large enough to handle the downswings.

Jim
Edit: I think Bonzi is referring to the total summation of all the tickets purchased since the last jackpot hit. This never changes your odds of winning, however. As he says later in the post, that is related to the combinations of numbers. In the line I quote at the top of this post, both things being compared are related to the payout, not your odds of winning.


Edited by TigerJimmy (19/03/2006 19:00)

Top
#277767 - 19/03/2006 19:01 Re: Stock Market [Re: bonzi]
TigerJimmy
old hand

Registered: 15/02/2002
Posts: 1049
Yeah, because you are much more likely to be "playing for half the pot."

Top
#277768 - 19/03/2006 19:17 Re: Stock Market [Re: TigerJimmy]
wfaulk
carpal tunnel

Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
Okay, so people say that it's because of dividends, and I'm willing to assume that dividends were common, if not universal, in the early days of the stock market.

But let's look at it in the present:

Quote:
The whole reason you bought it was to participate in the exchange, precisely because it has no intrisic "utility" value.

But if it has no intrinsic value, why would I buy it in the first place? Because someone else wants it, right? But why do they want it? Because someone else wants it. It's like a closed loop. Basically, people want it because other people want it. There's no ultimate exit strategy. If, for some reason, everyone lost interest in this trading game, the people left holding the stock certificates would have nothing of value.

As far as I can figure, they have slightly less intrinsic value than baseball cards.
_________________________
Bitt Faulk

Top
#277769 - 19/03/2006 19:19 Re: Stock Market [Re: tonyc]
wfaulk
carpal tunnel

Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
I'm totally down with the abstraction of real value. But it seems that, ignoring dividends and potential controlling interest, stocks lose their connection with those real values as soon as the company sells them.
_________________________
Bitt Faulk

Top
#277770 - 19/03/2006 19:31 Re: Stock Market [Re: wfaulk]
TigerJimmy
old hand

Registered: 15/02/2002
Posts: 1049
Why are we ignoring those factors? They are what gives the stock value in the secondary market.

Dividends are secondary, and my understanding is that they always have been. The fact that a business has value as an asset is the major factor in stock appreciation. The business reinvests its profits, becomes more valuable, and becomes more expensive for someone to purchase. The stock price is just the price tag of purchasing the business, with the cool idea that you can purchase part of it, so that groups can go in together to buy the whole thing.

Forget about stocks. Say you started a laundromat. You wanted to buy new washers and dryers but didn't have the cash. So you sold me half the business for $100k, and we bought all of this new capital with the proceeds. Let's say, because of our improvements, our business became TREMENDOUSLY profitable. So profitable, in fact, that it generated so much cash in excess of operating expenses that our company was able to build 10 more laudromats in the state. Clearly, the company is more valuable, and my half of it would be worth much more than $100k by now. In fact, maybe I trusted you so much as a manager, that I just bought half the interest and let you manage the business and you accomplished this great success all by yourself. If I wanted to sell my half of the business to someone else, I could, and I would expect to get more than $100k for it. This whole thing has NOTHING to do with dividends. You never paid a dividend. You made the business more valuable instead. The fact I could sell my half of our laundry business is about the appreciation of the business as an ASSET.

Now, just do that same thing, except instead of getting money from one investor, you get it from thousands. To keep track of it all, purely for administrative reasons, you issue stock certificates.

That's all that is going on. The motivation for stock appreciation independent of dividends is that the stock IS tied to the company and the company has intrinsic value.


Edited by TigerJimmy (19/03/2006 19:51)

Top
#277771 - 19/03/2006 19:33 Re: Stock Market [Re: wfaulk]
TigerJimmy
old hand

Registered: 15/02/2002
Posts: 1049
Everything you say here could be said of $100 bills. It is a social convention because trading things that have real "intrinsic" value, like goats or cars or houses, is too difficult. The fact that the system is vastly superior to barter is what keeps the whole thing going and keeps people from losing interest.

Why you want something with no intrinsic value is because others do, yes. Because we've all agreed to trade those things for other things that do have intrinsic value. You want the stock, not for itself, but for what it represents should you choose to exchange it for something you want.


Edited by TigerJimmy (19/03/2006 19:36)

Top
#277772 - 19/03/2006 20:14 Re: Stock Market [Re: TigerJimmy]
wfaulk
carpal tunnel

Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
That's an incomplete analogy.

Lets say a potential business partner wanted to start up such a business. Would you invest your money in it? What if he told you that the only thing he would ever give you (or anyone you sold your interest to) for reimbursement was a piece of paper that said you "owned" 49% of it?

Quote:
The fact I could sell my half of our laundry business is about the appreciation of the business as an ASSET.

My question is, under my example above, which seems to be a fairly accurate description of the current stock market, at least from my point of view, why would anyone want to buy it?
_________________________
Bitt Faulk

Top
#277773 - 19/03/2006 20:23 Re: Stock Market [Re: TigerJimmy]
wfaulk
carpal tunnel

Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
Again, I understand the idea behind paper money. It represents some physical asset. My point is that when you buy stock in a company, you give them money, they give you a piece of paper, and they laugh all the way to the bank. They are not obliged to buy it back from you at any price. It becomes completely disconnected with any sort of wealth.

Let's look at it this way. Let's say I sold you a piece of paper that was worth 1% of me for $100. Then, let's say, I become a kajillion-aire. Not only do I not need to pay you 1% of my worth, I don't even have to give you back the $100. You're free to continue "owning" 1% of me, but that ownership will never see liquidity.
_________________________
Bitt Faulk

Top
#277774 - 19/03/2006 21:45 Re: Stock Market [Re: wfaulk]
bonzi
pooh-bah

Registered: 13/09/1999
Posts: 2401
Loc: Croatia
Quote:
You're free to continue "owning" 1% of me, but that ownership will never see liquidity.

It will, if someone wants to buy the whole of you.
_________________________
Dragi "Bonzi" Raos Q#5196 MkII #080000376, 18GB green MkIIa #040103247, 60GB blue

Top
#277775 - 19/03/2006 21:48 Re: Stock Market [Re: wfaulk]
mlord
carpal tunnel

Registered: 29/08/2000
Posts: 14496
Loc: Canada
Quote:
My point is that when you buy stock in a company, you give them money, they give you a piece of paper,


In this case, you are buying a share of the company. Which makes you a part owner, and carries an entitlement for you to receive a share of the profits. They don't have to buy your share back if you change your mind, but they do have to share out the profits [EDIT] equally to you and any other share holders. Many companies prefer not to release profits to their owners, and to simply hang onto the cash (retained earnings) instead. It is up to the shareholder representatives ("the board of directors") to police this.

Cheers


Edited by mlord (19/03/2006 21:51)

Top
#277776 - 19/03/2006 21:49 Re: Stock Market [Re: TigerJimmy]
bonzi
pooh-bah

Registered: 13/09/1999
Posts: 2401
Loc: Croatia
Hm, yes, I will have to think this through a bit better...
_________________________
Dragi "Bonzi" Raos Q#5196 MkII #080000376, 18GB green MkIIa #040103247, 60GB blue

Top
#277777 - 20/03/2006 03:36 Re: Stock Market [Re: bonzi]
TigerJimmy
old hand

Registered: 15/02/2002
Posts: 1049
It doesn't see liquidity because you don't sell enough of yourself. Put more than 50% of you on the marketplace, and set up laws that say you need to do whatever the plurality dictates, and then you have a different situation. Liquidity comes from the exchange, not from the issuing company. I don't understand the details of how the exchanges work, but I know they have mechanisms to ensure liquidity (specialists). You won't get listed on an exchange if you only sell 1% of yourself.

Alternatively, part of the contract of me buying 1% of you could stipulate that all of your income will be distributed via dividend and you are not allowed to retain any earnings.

The bigger point, though, is that companies don't just issue 1% of their equity. Enough equity is sold on the secondary market that there is liquidity.

Top
#277778 - 20/03/2006 11:52 Re: Stock Market [Re: julf]
Tim
veteran

Registered: 25/04/2000
Posts: 1529
Loc: Arizona
Quote:
Quote:
Are you saying stocks in other markets tend to actually pay dividends?


Traditionally, yes. But that has changed quite a bit in most markets.


I was under the impression that most stocks still pay regular dividends except in the computer fields. What I mean is that Microsoft was the first one I remember hearing of that didn't pay dividends, but all (or almost?) other companies still pay dividends. Coke, Pepsi, IBM (as of 2000), Northrop-Grumman, Lockheed-Martin, Boeing, etc all still pay quarterly dividends.

-- Tim

Top
#277779 - 20/03/2006 13:24 Re: Stock Market [Re: TigerJimmy]
wfaulk
carpal tunnel

Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
Fine. 49%. Whatever. I think you're totally missing my point.

My point is not that there aren't people willing to buy the stock once it's out there. My point is that those people are insane.

Okay, that's not really true. There are enough people out there that the whole system has an internal consistency that allows for liquidity.

But the money used to buy stocks never comes back out of the stock market. I cannot sell off my interest without someone coming in to fill my place. At a casino, to take an example not intended to be a gambling comparison, I buy chips from the casino to gamble with. At the end of my day, I sell those chips back to the casino. If the casino worked like the stock market, I'd have to find some other individual to buy my chips from me instead.

I guess what I'm saying is that you never really get out of the stock market until you find some sucker to take your place.

I realize that a lot of these arguments do apply to government-issued money, too. But that's an argument that I'm going to wait on for now, and, at this point, assume that US Dollars are real money.

And I'm not being dense. I know how people currently make money in the stock market. I'm not denying its existence. The problem is that no one has yet shown me how a stock is not virtually completely divested from the company that issued it.
_________________________
Bitt Faulk

Top
#277780 - 20/03/2006 13:28 Re: Stock Market [Re: wfaulk]
pgrzelak
carpal tunnel

Registered: 15/08/2000
Posts: 4859
Loc: New Jersey, USA
But companies do, on occasion, buy back their own stock. Granted, not frequently, but it does happen.
_________________________
Paul Grzelak
200GB with 48MB RAM, Illuminated Buttons and Digital Outputs

Top
#277781 - 20/03/2006 13:49 Re: Stock Market [Re: pgrzelak]
wfaulk
carpal tunnel

Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
Perhaps. But they buy it back at market value, so they just become another stock market investor. Even if you argue that my point is invalid (and you can certainly make that argument), that happens so infrequently as to be negligible.

I guess that part of my point is that the market value isn't even fixed on how much the company is worth, but on subjective assessments of how much the company is worth. (And then on top of that lies my main point that it doesn't seem to actually make any difference how much the company is worth at all, since none of the money you ever receive from the stock is based directly on the company's worth.)
_________________________
Bitt Faulk

Top
#277782 - 20/03/2006 14:21 Re: Stock Market [Re: wfaulk]
JeffS
carpal tunnel

Registered: 14/01/2002
Posts: 2858
Loc: Atlanta, GA
Quote:
But they buy it back at market value, so they just become another stock market investor.
Not really- and especially not in the case of a hostile takeover. At that point the buyer really does consider whether the cost incurred to purchase the stock is worth payed in order to gain controlling shares of a company.

I know this much- my brother in law's company got bought out by a larger company (not a hostile takeover) and everyone who had stock got paid off when it happened. Some of the employees who'd been there for years had quite a bit of stock and got handed checks for 200K-300K. I'm sure the purchasing company would not have paid that amount to the shareholders if it was just a matter of perceived value. He said it was crazy that these NOC employees all came to work the next week with new cars- including one who purchased a Lotus.
_________________________
-Jeff
Rome did not create a great empire by having meetings; they did it by killing all those who opposed them.

Top
#277783 - 20/03/2006 15:17 Re: Stock Market [Re: wfaulk]
DWallach
carpal tunnel

Registered: 30/04/2000
Posts: 3810
You have to always remember that stock shares represent not only profits but control. Small-time investors don't have very much power, but big-time institutional investors get seats on the board of directors. Likewise, when one company acquires another, stock may be acquired or swapped or whatever else.

Further, you have to look at the long-term value of a share of a company versus other sorts of long-term investments. You can keep your assets directly as dollars or euros, but then inflation will reduce the value of your holdings over time. You can keep your assets in a money market account, which means you really own treasury bills (i.e., government-issued bonds). You can keep your assets in real estate, which may or may not appreciate over time, and which can have ongoing maintenance costs. You can keep your assets in precious metals or oil or whatnot, but those have volatility that may not be appropriate for most investors. Stocks, by and large, have no maintenance costs, can be selected for desirable volatility, and tend to outperform inflation over the long term.

Given that you need to park your assets somewhere, and pretty much any asset you might own is going to be abstract, why not have a big chunk of your assets in stock?

Top
#277784 - 20/03/2006 16:13 Re: Stock Market [Re: wfaulk]
Ezekiel
pooh-bah

Registered: 25/08/2000
Posts: 2413
Loc: NH USA
Quote:
My point is that those people are insane.


I think Bitt's angling for a title change to 'Wonko the Sane'.



-Zeke
_________________________
WWFSMD?

Top
#277785 - 20/03/2006 16:43 Re: Stock Market [Re: JeffS]
tanstaafl.
carpal tunnel

Registered: 08/07/1999
Posts: 5549
Loc: Ajijic, Mexico
Heck, getting a college education could be considered betting (paying tuition) on a certain outcome (making more with an education than without). While that's a pretty good bet, I'm sure it's not 100%.

Darn right it's not.

Not too long ago I paid an electrician $3400 to replace my breaker box and extend power over to my new detached garage. He was so heavily booked that I felt lucky to get him at any price, and the work had to be done by a licensed electrician to meed building code.

He had about $400 in materials, and a day and a half of his time invested in the project.

I do have a college education, and I'm not making even 10% of what that guy made on an hourly basis.

tanstaafl.
_________________________
"There Ain't No Such Thing As A Free Lunch"

Top
#277786 - 20/03/2006 20:32 Re: Stock Market [Re: DWallach]
wfaulk
carpal tunnel

Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
Quote:
Small-time investors don't have very much power, but big-time institutional investors get seats on the board of directors.

I will admit that I'm looking at this from the viewpoint of the small investor. At the same time, the reason that that power is important is to protect your huge investment in the company. So now you're paying money to get a job to protect the money that you spent to get the job, ad infinitum. And it still doesn't show me the connection between the company's value and the stocks.

Quote:
Likewise, when one company acquires another, stock may be acquired or swapped or whatever else.

Yeah, but that's effectively just someone buying your stock. Not really much different than the normal case, although it does pull in that edge case of actually using stock for power, which is where my argument breaks down.

Okay, so assuming that the only times that your stock is actually worth anything is when someone takes over the company (hostilely or not), then isn't buying stock a hope that the company will get bought out?
_________________________
Bitt Faulk

Top
#277787 - 20/03/2006 23:31 Re: Stock Market [Re: wfaulk]
JeffS
carpal tunnel

Registered: 14/01/2002
Posts: 2858
Loc: Atlanta, GA
Quote:
So now you're paying money to get a job to protect the money that you spent to get the job, ad infinitum.
No, you're paying money to get a job to make more money, which could be realized in dividends, the buyout of your shares, or selling to another investor at a higher amount (obviously the most likely scenerio).

And certainly spending money to make money is not a new concept. It's the reason people are in business at all.

Quote:
Okay, so assuming that the only times that your stock is actually worth anything is when someone takes over the company (hostilely or not), then isn't buying stock a hope that the company will get bought out?
That potential is what gives the stock its value. If you invest in land that you don't live on or use, you are purchasing on the hope that its value will go up and someone will buy it from you. That person may or may not want it for personal use- it could be another investor. The point really doesn't matter, since you're buying it as an investment to being with, but the end potential for use is what gives it its value. The value of stock is a share in the value of that company- realized when someone decides it is important to own a controlling share of that company (which could be the company itself). Whether you experience this yourself, that potential allows you to purchase stock as an investment and sell it at a gain if the value of the company goes up (making purchasing a controlling amount of stock that much more enticing).
_________________________
-Jeff
Rome did not create a great empire by having meetings; they did it by killing all those who opposed them.

Top
#277788 - 20/03/2006 23:36 Re: Stock Market [Re: wfaulk]
matthew_k
pooh-bah

Registered: 12/02/2002
Posts: 2298
Loc: Berkeley, California
Quote:
Okay, so assuming that the only times that your stock is actually worth anything is when someone takes over the company (hostilely or not), then isn't buying stock a hope that the company will get bought out?

No, your stock is worth something because it represents a share of the company For richer or for poorer, you own a fraction of the company. Ownership isn't a new concept, we brought it over on the mayflower and it's been thriving in North America ever since.

Your problem with the stock market seems to be that you're never going to end up with a controlling stake in the company, so you'll always be at the whim of the other larger investors. But, seeing as they're larger investors, they're going to have their best interest at heart, which conveniently enough is your best interest. There of course arise situations where their best interest may not be your best interest. The SEC exists to prevent this from becoming an issue.


Matthew

Top
#277789 - 21/03/2006 02:13 Re: Stock Market [Re: JeffS]
JeffS
carpal tunnel

Registered: 14/01/2002
Posts: 2858
Loc: Atlanta, GA
Another thing to consider against your claim that the tie-in between stock value and company performance is imagined- consider what would happen if a large, successful company had stock valued at a fraction of a penny. In fact, say you could buy a controlling amount of stock in an IBM sized company for $100,000. That would obviously be a worthwile investment, as you could then do whatever you wish with it and pocket as much of the profits as you wanted (remember, this is a successful company well in the black). Of course, that wouldn't ever happen because the moment a successful company got anywhere near that, it would be snatched up by hungry investors. No one would ever let it get that low because the value IS tied to the performance of the company. The other extreme would be owning a controlling share in a lousy company and trying to sell it for a premium price. It isn't going to happen because no one wants any piece of a company losing money.

That's not to say I don't agree with a lot of your point- it seems that stock prices rise and fall more at the whim of investors than because of real value fluctuations in the worth of a company. The value of Microsoft is probably not changing drastically from day to day, but its stock price is probably a different story (though I wouldn't know, not following Microsoft stock). Having said all of that, owning stock IS ownership in a company, and it does carry with it some degree of controlling how that company can make you money, including issuing profits to your pocket. Unforutnatly, you'd have to own quite a big piece to really have any reasonable control over these things. That doesn't change the fact that buying stock is buying something of value, as little value as it may be in the grand scheme of things.
_________________________
-Jeff
Rome did not create a great empire by having meetings; they did it by killing all those who opposed them.

Top
#277790 - 21/03/2006 03:26 Re: Stock Market [Re: matthew_k]
wfaulk
carpal tunnel

Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
Okay, from my point of view, everyone keeps using the same arguments, none of which even begin to show me how you actually make money from the ownership (not the selling) of stock, outside a few edge cases.

At this point, I'm just gonna take my ball and go home while the rest of you keep drinking the Kool-Aid.
_________________________
Bitt Faulk

Top
#277791 - 21/03/2006 04:11 Re: Stock Market [Re: wfaulk]
TigerJimmy
old hand

Registered: 15/02/2002
Posts: 1049
This is a silly statement. You make money by buying and selling the stock -- by participating in the exchange.

How do you make money from mere ownership, without participating in the exchange? You don't. But markets exist. Its like saying that a car doesn't have any value if you don't drive it. Well, duh.

You started this conversation asserting that the stock did not have value that is tied to the compnay. I believe we have explained in detail that it does, and that it is tied to the company, within the context of a marketplace of other investors. If you can sell it on the exchange, it has value, and that value is based on the company.

Nothing has monetary value if you refuse to sell it. That's just a silly strawman.

You are entitled to argue your point in this way, but please don't accuse us of being the Kool-Aid drinkers.

Top
Page 2 of 5 < 1 2 3 4 5 >