vpFREE2 Forums

Best Randomness Analogy Contest

#21

Gee, Frank, did you think that the religion aspect would turn out to be the definition of randomness?

And sometimes it refuses to see patterns based on preconceived assumptions.
http://www.livescience.com/animals/pigeons-monty-hall-problem-100304.html

So, in the Monty Hall problem, can we perceive a pattern in the remaining two doors? When 1 and 2, more likely to be 1, when 2 and 3 more likely to be 2, etc.? I don't think the pigeons did - they learned to make a choice based on probability, not patterns, and I didn't see evidence that they then chose the correct door with any edge.

American Coin scandal, the machines would still be operating today.

American Coin involved gaffed machines - no randomness there.

even coin flips are up to dispute:
http://www.npr.org/templates/story/story.php?storyId=1697475

Diaconis' work proved that if we flip a coin, with the same initial conditions, we can predict, nay, control, the outcome - similar to placing a coin in our palm and turning our palm over - the coin still "flipped" - with predictable results - until we lose muscular control. This is not randomness.

http://en.wikipedia.org/wiki/Hardware_random_number_generator

Do certain hardware (and pseudo) random number generators decay? Yes, pseudos will even repeat. Do they all? I don't know - counting neutrino arrival rates, e.g., may not. Even with decay, and absent of knowledge of initial conditions, I say such devices produce sequences that are random as far as we can tell. Do we think that we can track past output from such devices and discern a future pattern? I don't.

I think that's Frank's question - 3 reds in a row so now bet black (or red)?, trip 6s in a row so now hold a single 6?

···

--- In vpFREE@yahoogroups.com, David Silvus <djsilvus@...> wrote:
--- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <nightoftheiguana2000@...> wrote:

#22

Heres a great game to play. Grab a deck of cards and sit down at the kitchen table. This is gonna take a while so quit your job.

You're gonna shuffle up and deal out five cards then replace up to five cards just like on a machine. No Cheating (no peeking, no base dealin', no dealin' seconds, I don't want to see a mechanics grip). And you're gonna use computer perfect strategy for 9/6 Jacks.

You're gonna play a few thousand hands. While you're playing along look for the patterns. You know, hot streaks, cold streaks. Be honest with yourself. You notice you go thru spurts where you seem to be hitting the pay hands at about the frequency it calls for. But then you also go through periods where the deck is colder than a well diggers ankle in Idaho, you can't seem to hit a pay hand. You also experience spurts where the deck is hotter than a pistol, you seem to hit a pay on almost every hand. Hot Streak, cold streak, medium streak, cold streak, medium streak, cold streak, hot streat, medium streak, hot streak, etc.

Also notice theres some other weird stuff going on. You hit a couple of full houses within a few hands of each other. But then you go 250 hands without seeing one. Same thing with the straights and flushes but sometimes they come at about the right speed they should be.

What you wanna do is play at least a few thousand hands so you can get all these patterns ingrained in your head. Then set the deck down on the table and stare at it saying to yourself "Yep, just what I thought. That deck of cards is pre-programmed with hot streaks and cold streaks! I wonder how they do that."

The great benefit of doing all that is so when you are out playing video poker and see similar patterns you can say to yourself "This machine is rigged just as bad as that deck of cards I got back home."

#23

Mickey,

This is a truly outstanding suggestion for new players and the open minded to experience randomness with a simple test that is under their own control. Unfortunately many people are not able to put their irrational beliefs to a test or even acknowledge any evidence that disagrees with their beliefs. The hard part for many is your advice, "Be honest with yourself."

Chris

···

--- In vpFREE@yahoogroups.com, "Mickey" <mickeycrimm@...> wrote:

Heres a great game to play. Grab a deck of cards and sit down at the kitchen table. This is gonna take a while so quit your job.

You're gonna shuffle up and deal out five cards then replace up to five cards just like on a machine. No Cheating (no peeking, no base dealin', no dealin' seconds, I don't want to see a mechanics grip). And you're gonna use computer perfect strategy for 9/6 Jacks.

You're gonna play a few thousand hands. While you're playing along look for the patterns. You know, hot streaks, cold streaks. Be honest with yourself. You notice you go thru spurts where you seem to be hitting the pay hands at about the frequency it calls for. But then you also go through periods where the deck is colder than a well diggers ankle in Idaho, you can't seem to hit a pay hand. You also experience spurts where the deck is hotter than a pistol, you seem to hit a pay on almost every hand. Hot Streak, cold streak, medium streak, cold streak, medium streak, cold streak, hot streat, medium streak, hot streak, etc.

Also notice theres some other weird stuff going on. You hit a couple of full houses within a few hands of each other. But then you go 250 hands without seeing one. Same thing with the straights and flushes but sometimes they come at about the right speed they should be.

What you wanna do is play at least a few thousand hands so you can get all these patterns ingrained in your head. Then set the deck down on the table and stare at it saying to yourself "Yep, just what I thought. That deck of cards is pre-programmed with hot streaks and cold streaks! I wonder how they do that."

The great benefit of doing all that is so when you are out playing video poker and see similar patterns you can say to yourself "This machine is rigged just as bad as that deck of cards I got back home."

#24

"So, in the Monty Hall problem, can we perceive a pattern in the remaining two doors? When 1 and 2, more likely to be 1, when 2 and 3 more likely to be 2, etc.? I don't think the pigeons did - they learned to make a choice based on probability, not patterns, and I didn't see evidence that they then chose the correct door with any edge."

What's the difference between "probability" and "pattern" though? The "pattern" is that your "probability" of reward is twice as great if you change your initial choice than not. If one group opts to change and ther other group opts to stand pat, the first group has recognized that pattern while the 2nd group has not.

Honestly, as addressed by someone else before, the term " pattern" really needs to be defined more tightly for this discussion. I readily agree that my usage of the term in the preceeding paragraph does not comport with its definition as used in mathematics. If that is the definition being used for the term, however, then the discussion becomes far less interesting on the macro and micro level (at least to me).

···

To: vpFREE@yahoogroups.com
From: allen-walker@sbcglobal.net
Date: Wed, 5 Jan 2011 21:18:28 +0000
Subject: [vpFREE] Re: Best Randomness Analogy Contest

Gee, Frank, did you think that the religion aspect would turn out to be the definition of randomness?

--- In vpFREE@yahoogroups.com, David Silvus <djsilvus@...> wrote:

And sometimes it refuses to see patterns based on preconceived assumptions.
http://www.livescience.com/animals/pigeons-monty-hall-problem-100304.html

So, in the Monty Hall problem, can we perceive a pattern in the remaining two doors? When 1 and 2, more likely to be 1, when 2 and 3 more likely to be 2, etc.? I don't think the pigeons did - they learned to make a choice based on probability, not patterns, and I didn't see evidence that they then chose the correct door with any edge.

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <nightoftheiguana2000@...> wrote:

American Coin scandal, the machines would still be operating today.

American Coin involved gaffed machines - no randomness there.

even coin flips are up to dispute:
http://www.npr.org/templates/story/story.php?storyId=1697475

Diaconis' work proved that if we flip a coin, with the same initial conditions, we can predict, nay, control, the outcome - similar to placing a coin in our palm and turning our palm over - the coin still "flipped" - with predictable results - until we lose muscular control. This is not randomness.

http://en.wikipedia.org/wiki/Hardware_random_number_generator

Do certain hardware (and pseudo) random number generators decay? Yes, pseudos will even repeat. Do they all? I don't know - counting neutrino arrival rates, e.g., may not. Even with decay, and absent of knowledge of initial conditions, I say such devices produce sequences that are random as far as we can tell. Do we think that we can track past output from such devices and discern a future pattern? I don't.

I think that's Frank's question - 3 reds in a row so now bet black (or red)?, trip 6s in a row so now hold a single 6?

[Non-text portions of this message have been removed]

#25

Heres a great game to play. Grab a deck of cards and sit down at the kitchen table. This is gonna take a while so quit your job.<snip>

The great benefit of doing all that is so when you are out playing video poker and see similar patterns you can say to yourself "This machine is rigged just as bad as that deck of cards I got back home."

Mickey,

Your post reminded me of when I first started to learn blackjack card counting about 15 or 16 years ago. Early on I went through a stretch where I had the absolute worst luck imaginable. Seemed like every single time I put out a max bet the dealer would blackjack, or the dealer would beat every big bet 20 with a multiple card 21. Double down and split hands - automatic losers. It was just mind-numbing. My results were so bad that I was almost 100% certain that I was being cheated, except....
... that I was dealing all the cards to myself at home.

In the long run this was probably a benefit to me. I learned a good early lesson in just how badly things can go south, even when we have the advantage.

EE

···

--- In vpFREE@yahoogroups.com, "Mickey" <mickeycrimm@...> wrote:

#26

I'm pretty sure pigeons don't know probability. Instead, they have a randomizing algorithm.

http://en.wikipedia.org/wiki/Randomized_algorithm

This allows them to discover that the grass is sometimes greener on the other side, in other words they discover a pattern in a random event, after all it's not guaranteed that there's always food in the other door, there's no direct and deterministic cause and effect, instead it's just more likely. Hence, for the pigeons, discovering a pattern in randomness is economically useful, not a folly as some might suggest. (I'm assuming the pigeons learned to increase their choice of the other door, but maybe they simply kept their randomizing ratio the same and weren't smart enough to learn).

What makes it more interesting is that the famous mathematician Paul Erdos, who thought he knew probability theory perfectly, was not at all convinced, until he looked at a Monte Carlo sim. A Monte Carlo sim is a brute force method, it simply spits out the possible results. The mathematician Paul Erdos instantly recognized a pattern in the random data, just as the pidgeons had recognized a pattern in the data they collected, namely that changing ones choice doubled ones odds, but Erdos was able to also correct the mistake he had made in his earlier judgement using probability theory. The moral of the story is that it is sometimes useful to run a Monte Carlo analysis, or simply start collecting data, and confirm that the patterns revealed are consistant with ones understanding of probability theory.

http://en.wikipedia.org/wiki/Monte_Carlo_method

Mickey's suggestion that one try dealing the cards to oneself first and watching the patterns is a form of the Monte Carlo method.

Other links that might be found useful:

http://en.wikipedia.org/wiki/Monte_Hall_Problem
http://en.wikipedia.org/wiki/Empirical_probability
http://en.wikipedia.org/wiki/Classical_probability
http://en.wikipedia.org/wiki/Determinism
http://en.wikipedia.org/wiki/Superdeterminism

···

--- In vpFREE@yahoogroups.com, David Silvus <djsilvus@...> wrote:

"So, in the Monty Hall problem, can we perceive a pattern in the remaining two doors? When 1 and 2, more likely to be 1, when 2 and 3 more likely to be 2, etc.? I don't think the pigeons did - they learned to make a choice based on probability, not patterns, and I didn't see evidence that they then chose the correct door with any edge."

What's the difference between "probability" and "pattern" though? The "pattern" is that your "probability" of reward is twice as great if you change your initial choice than not. If one group opts to change and ther other group opts to stand pat, the first group has recognized that pattern while the 2nd group has not.

Honestly, as addressed by someone else before, the term " pattern" really needs to be defined more tightly for this discussion. I readily agree that my usage of the term in the preceeding paragraph does not comport with its definition as used in mathematics. If that is the definition being used for the term, however, then the discussion becomes far less interesting on the macro and micro level (at least to me).

To: vpFREE@yahoogroups.com
From: allen-walker@...
Date: Wed, 5 Jan 2011 21:18:28 +0000
Subject: [vpFREE] Re: Best Randomness Analogy Contest

Gee, Frank, did you think that the religion aspect would turn out to be the definition of randomness?

--- In vpFREE@yahoogroups.com, David Silvus <djsilvus@> wrote:
>
> And sometimes it refuses to see patterns based on preconceived assumptions.
> http://www.livescience.com/animals/pigeons-monty-hall-problem-100304.html

So, in the Monty Hall problem, can we perceive a pattern in the remaining two doors? When 1 and 2, more likely to be 1, when 2 and 3 more likely to be 2, etc.? I don't think the pigeons did - they learned to make a choice based on probability, not patterns, and I didn't see evidence that they then chose the correct door with any edge.

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <nightoftheiguana2000@> wrote:
>
>American Coin scandal, the machines would still be operating today.

American Coin involved gaffed machines - no randomness there.

>even coin flips are up to dispute:
>http://www.npr.org/templates/story/story.php?storyId=1697475

Diaconis' work proved that if we flip a coin, with the same initial conditions, we can predict, nay, control, the outcome - similar to placing a coin in our palm and turning our palm over - the coin still "flipped" - with predictable results - until we lose muscular control. This is not randomness.

>http://en.wikipedia.org/wiki/Hardware_random_number_generator

Do certain hardware (and pseudo) random number generators decay? Yes, pseudos will even repeat. Do they all? I don't know - counting neutrino arrival rates, e.g., may not. Even with decay, and absent of knowledge of initial conditions, I say such devices produce sequences that are random as far as we can tell. Do we think that we can track past output from such devices and discern a future pattern? I don't.

I think that's Frank's question - 3 reds in a row so now bet black (or red)?, trip 6s in a row so now hold a single 6?

[Non-text portions of this message have been removed]

#27

Kudos to NOTI for clearing up some of the misconceptions about pigeons and the Monte Carlo problem. (Seriously)

What I want to offer up is that I think Frank introduced a red herring into the general topic when he suggested that "it's a bad idea to look for patterns in random events." Hell, scientists engage in queries all the time where they do just that. SETI is one of the most notorious examples.

The fallacy that I believe Frank desired to highlight was attributing meaning to patterns in random events without first having subject the phenomenon to appropriate statistical tests to evaluate the probability of such a pattern occurring "at random", as opposed through some distortion of natural odds.

When it comes to the belief that some have that they can improve their odds in the casino by strategically switching machines, it has to be conceded that the M.C. pigeon "switchers" were right on the money. But the math fully supports their call .. intuitively, they made the right choice.

But in some situations intuition is a poor play partner, and the casino "machine switch" has no such support in the underlying math. As I noted before, ideally, such behavior has no penalty (such as when the switch is to another equivalent machine and doesn't impact other aspects of play). But, in practice, I often see it give rise to sub-optimal choices that impact the player, and sometimes those around them.

#28

I think most folks fall prey to remembering only the "memorable" and forgetting the mundane. If you play VP full-tilt for 8 hours and lose a little, it's forgettable. You play for 15 minutes and hit 2 FH and Quads, it's memorable. 3 months later all anyone tends to remember is the latter, not the former.

I personally see more of the situational rationalization at the craps table since it's largely the same premise, but couched in a more public setting. I get loads of entertainment watching analytical types trying to explain to the hunch-player why hardways are bad bets and streaks are a myth and place bets have a larger house edge than pass+odds. Sooner or later someone hits 4 or 5 hardways and/or a bunch of 6's (or whatever number he's placed) and the hunch-player is (usually loudly) going on about how he "knew" shooter X or 6 "was due, KNEW IT!!!" And that's his "proof" against the analytical-type's premise. Said hunch-players conveniently forgets the other 10 shooters/numbers he "knew, KNEW!!!" were due but weren't. I've also noticed that the same guy is usually pressing everything on those bets and often finds himself muttering "one more [whatever] and I would have won some cash".

···

To: vpFREE@yahoogroups.com
From: harry.porter@verizon.net
Date: Thu, 6 Jan 2011 22:18:00 +0000
Subject: [vpFREE] Re: Best Randomness Analogy Contest

Kudos to NOTI for clearing up some of the misconceptions about pigeons and the Monte Carlo problem. (Seriously)

What I want to offer up is that I think Frank introduced a red herring into the general topic when he suggested that "it's a bad idea to look for patterns in random events." Hell, scientists engage in queries all the time where they do just that. SETI is one of the most notorious examples.

The fallacy that I believe Frank desired to highlight was attributing meaning to patterns in random events without first having subject the phenomenon to appropriate statistical tests to evaluate the probability of such a pattern occurring "at random", as opposed through some distortion of natural odds.

When it comes to the belief that some have that they can improve their odds in the casino by strategically switching machines, it has to be conceded that the M.C. pigeon "switchers" were right on the money. But the math fully supports their call .. intuitively, they made the right choice.

But in some situations intuition is a poor play partner, and the casino "machine switch" has no such support in the underlying math. As I noted before, ideally, such behavior has no penalty (such as when the switch is to another equivalent machine and doesn't impact other aspects of play). But, in practice, I often see it give rise to sub-optimal choices that impact the player, and sometimes those around them.

[Non-text portions of this message have been removed]

#29

Damn, I know that guy!

···

I've also noticed that the same guy is usually pressing everything on those bets and often finds himself muttering "one more [whatever] and I would have won some cash".

#30

Another point, the output of a slot is not purely noise, instead it's telling you a story of how it works with your particular strategy. An example for video poker: players should definitely at least track their straight flushes. If you're not getting the straight flushes you expected, it might not be just random noise, instead it might be you're missing some of the straight flush draws, which is easy to do in the poorly lighted and highly distracting arena of the casino. If you're missing some straight flush draws, that will show up in your results eventually. If you're real detailed in your tracking (there must be an ap for that, right?), you might notice a machine that does poorly for you, then if you go back and check that machine, you might find something wrong with it, such as sticky or bouncy keys or a spot light right on it that reflects into your eyes causing eye fatigue so you mistake a spade for a club and so on.

#31

I jumped off a Burlington Nortbern freight train one night in Spokane, Washington. I was looking to replinsh the ole' bankroll....which might have been maybe $25 at the time. I was gonna have to stop and work some day labor. I rolled my bag out beside those tracks.

I woke up the next morning and hit the McDonald's for a cheap breakfast and a newspaper read. No matter where you are at you simply have to run intelligence.

The headline in the paper was how they found a man, identity unknown, laying in his sleeping bag, right along the tracks, shot in the head and dead....in the same spot I had just spent the night in.

Okay, Mr. Random Man.

#32

The dead guy, whoever he was, was found the morning before the night I arrived to that spot. I was random coming into that spot. No one in Spokane could have known I was coming. The killing was probably random tramp shit. Killing a guy for his little money or food stamps...by a hard core FTRA.

···

--- In vpFREE@yahoogroups.com, "Mickey" <mickeycrimm@...> wrote:

I jumped off a Burlington Nortbern freight train one night in Spokane, Washington. I was looking to replinsh the ole' bankroll....which might have been maybe $25 at the time. I was gonna have to stop and work some day labor. I rolled my bag out beside those tracks.

I woke up the next morning and hit the McDonald's for a cheap breakfast and a newspaper read. No matter where you are at you simply have to run intelligence.

The headline in the paper was how they found a man, identity unknown, laying in his sleeping bag, right along the tracks, shot in the head and dead....in the same spot I had just spent the night in.

Okay, Mr. Random Man.

#33

I cannot imagine riding a freight train and sleeping in homeless camps without being armed. As I mentioned, I always wanted to ride one but never got the courage. And, of course, I've never been homeless either. But how can one put oneself in that situation without having a gun in his pocket?

Hey Mickey, what were the railroad police like? What was their job detail, and how did they deal with people riding the trains?

That reminds me of an old movie I saw many years ago. It was with Ernest Borgnine, and I think Lee Marvin. Do you know the movie I'm talking about? Borgnine was the railroad cop, and he was a mean son of a bitch. lol

···

--- In vpFREE@yahoogroups.com, "Mickey" <mickeycrimm@...> wrote:

The dead guy, whoever he was, was found the morning before the night I arrived to that spot. I was random coming into that spot. No one in Spokane could have known I was coming. The killing was probably random tramp shit. Killing a guy for his little money or food stamps...by a hard core FTRA.

#34

The name of the movie was Emporer of the North. "Stay the hell off my road, kid! I better not catch you on my road, kid! Stay the hell off my road, kid!"

···

--- In vpFREE@yahoogroups.com, "bobbartop" <bobbartop@...> wrote:

--- In vpFREE@yahoogroups.com, "Mickey" <mickeycrimm@> wrote:
>

> The dead guy, whoever he was, was found the morning before the night I arrived to that spot. I was random coming into that spot. No one in Spokane could have known I was coming. The killing was probably random tramp shit. Killing a guy for his little money or food stamps...by a hard core FTRA.
>

I cannot imagine riding a freight train and sleeping in homeless camps without being armed. As I mentioned, I always wanted to ride one but never got the courage. And, of course, I've never been homeless either. But how can one put oneself in that situation without having a gun in his pocket?

Hey Mickey, what were the railroad police like? What was their job detail, and how did they deal with people riding the trains?

That reminds me of an old movie I saw many years ago. It was with Ernest Borgnine, and I think Lee Marvin. Do you know the movie I'm talking about? Borgnine was the railroad cop, and he was a mean son of a bitch. lol

#35

That reminds me of an old movie I saw many years ago. It was with Ernest
orgnine, and I think Lee Marvin. Do you know the movie I'm talking about?
orgnine was the railroad cop, and he was a mean son of a bitch. lol

he movie was called "Emperor Of The North Pole".

[Non-text portions of this message have been removed]

#36

I never carried a gun. It's best to travel with someone you trust. My policy was I didn't meet anyone out on the rails. In the towns fine. But not on the rails. I didn't sleep in the hobo jungles. I didn't trust any strangers. I found my own spots to crash. I thought that spot in Spokane was a good one. Turns out it wasn't.

The job of the Railroad Police (better known as bulls) is to protect the cargo. The only thing keeping anyone out of those stackers you see going thru Vegas is an easily broken federal seal. The Vegas yard got real hot one time because some of the cargo was being thrown off the hot shots by thieves up in the desert north of LV. Those idiots give freight tramps a bad name. I've been given warning tickets. Arrested one time.

Backpack Phil and me got in a little jam onetime north of LV. The hotshot stopped. We were in the back of a 48. We both got up. He watched his side of the tracks. I watched mine. Here come three toughs up the tracks. When they got up to our car one of them headed for the ladder up the side of the 48. "Be glad to meer you guys up in SLC. We don't meet anyone on the rails." The guy starts coming up the ladder. I jumped up on the deck. Phil grabbed his ball peen hammer. I was waiting for the guy;s head to pop up above the deck. I was gonna kick a field goal with my steel toed boots. It took that idiot all the way until his head was about 2 inches below the deck to figure out what was gonna happen to him. I can still see the look his eyes. He went back down the ladder and they went on up the tracks. We had to watch out for those idiots all the way to SLC.

···

--- In vpFREE@yahoogroups.com, "bobbartop" <bobbartop@...> wrote:

I cannot imagine riding a freight train and sleeping in homeless >camps without being armed. As I mentioned, I always wanted to ride >one but never got the courage. And, of course, I've never been >homeless either. But how can one put oneself in that situation >without having a gun in his pocket? Hey Mickey, what were the >railroad police like? What was their job >detail, and how did they >deal with people riding the trains?

#37

I think that won an award last week at the AVN Awards!

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From: vpFREE@yahoogroups.com [mailto:vpF…@…com] On Behalf Of
Cardfather@Aol.com
Sent: January-10-11 2:21 PM
To: vpFREE@yahoogroups.com
Subject: [vpFREE] Re: Best Randomness Analogy Contest

That reminds me of an old movie I saw many years ago. It was with Ernest
orgnine, and I think Lee Marvin. Do you know the movie I'm talking about?
orgnine was the railroad cop, and he was a mean son of a bitch. lol

he movie was called "Emperor Of The North Pole".

[Non-text portions of this message have been removed]

[Non-text portions of this message have been removed]

#38

cardfather, it is so nice to hear from you again. Hope all is well. Annie

···

On Jan 10, 2011, at 2:21 PM, Cardfather@Aol.com wrote:

That reminds me of an old movie I saw many years ago. It was with Ernest
orgnine, and I think Lee Marvin. Do you know the movie I'm talking about?
orgnine was the railroad cop, and he was a mean son of a bitch. lol

he movie was called "Emperor Of The North Pole".

#39

YES, that was it! Now, here's something really scary. I'm thinking of where I was when I saw it, and that puts me at about 20 years old. I'm over 50 now. OMG! I can't believe I am reminiscing about something 30 freaking years ago. I think I'm going to cry, and then go eat some oatmeal.

···

--- In vpFREE@yahoogroups.com, "Mickey" <mickeycrimm@...> wrote:

The name of the movie was Emporer of the North.

#40

No, you are not! You are not going to cry about a man's situation. A man puts himself into the situations's he gets himnslf into. A man lives and dies with the situations he put himself into.

···

--- In vpFREE@yahoogroups.com, "bobbartop" <bobbartop@...> wrote:

YES, that was it! Now, here's something really scary. I'm thinking of where I was when I saw it, and that puts me at about 20 years old. I'm over 50 now. OMG! I can't believe I am reminiscing about something 30 freaking years ago. I think I'm going to cry, and then go eat some oatmeal.