Estimating the age of the Universe, and getting it all wrong

[Jon]

I don't disagree with you regarding the odds being in the casinos favour. But let's break down the "guess" thing.

1. A calculated risk does not mean you can be sure of being correct. True or false?

2. A guess does not mean you are sure of being correct. True or false?

3. A calculated risk is an estimate of an outcome where you cannot be sure. True or false?

4. A guess is an estimate of an outcome where you cannot be sure. True or false?

I think you have imbued the term guess with a modifier: "random" guess. But no one has said it has to be random. It can be a calculated guess. And of course that is what casinos do.

When you take a calculated risk, you are guessing because you cannot be sure.

Edit: I am using the term "guess" to be consistent with the words used by the author of the following post:

Estimating the age of the Universe, and getting it all wrong

Now Monty opens a door and shows a zonk. The probabilities MUST still add up to 1 because there IS a car back there somewhere, so the higher math types say that all of the probability that vanished from the revealed door must have gone to the other doors. It is here that mathematicians do it...

www.access-programmers.co.uk

They then guess at what the likely lifespan of this universe will be based on how old it currently is and some other principles (like the probability that we are living toward the beginning or end of its lifespan specifically vs somewhere in the middle of its lifespan).

Their context is using the word "guess" when talking about a calculated estimate.

 

[Minty]

I think your use of the word guess is misleading.
From a bigger dictionary - to give an answer to a particular question when you do not have all the facts and so cannot be certain if you are correct.

A Casino does know all the facts, and is operating based on those. The fact(sic) that they occasionally lose money has nothing to do with them guessing, it's just the maths working out. They know in advance it will happen occasionally, but not the majority of the time.

Like I said - semantics.

 

[Jon]

Not sure if you missed my edit for why I used the term "guess". I was speaking in the term the other poster was using.

A Casino does know all the facts, and is operating based on those.

The casino does not know all the facts. They do not know the opponents cards, for a start. Is that not true?

Let us consider your new definition from the bigger dictionary.

to give an answer to a particular question when you do not have all the facts and so cannot be certain if you are correct.

See if you can answer the following questions:

1. When the casino follows its rules of how to play a particular Blackjack hand, are they CERTAIN it was the correct move, or just most probable?

2. When the casino is playing that Blackjack hand, do they have ALL the facts, including what cards the opponent has, or what cards will appear if they twist?

3. Do you agree that in Q1 they are not certain, and in Q2 they do not have ALL the facts?

4. Given that your new definition of "guess" states that conditions in Q2 and Q3 have to be fulfilled, can you now see why guess indeed is an accurate term to use?

 

[Minty]

In short no.

They are certain that they are playing the hand by the best rules to ensure they will win overall. They aren't guessing what to do.

They don't pay any attention to what you have in your hand. They only apply the rules to their cards.
And they have all the facts about their hand. Below 17 they twist, 17 or above they stick and payout if required. No guessing involved.

 

[Jon]

And they have all the facts about their hand

So you agree they do not have all the facts about the other hands, and that what those other hands are influences the outcome?

They are certain that they are playing the hand by the best rules to ensure they will win overall.

So you agree they are not certain that they are correct on any one hand, or even a series of hands?

 

[Minty]

So you agree they do not have all the facts about the other hands, and that what those other hands are influences the outcome?

No - they pay zero attention to the other hands. It has no bearing on how they play their own hand. None, nada, Zero influence.
They play by a fixed set of rules.

So you agree they are not certain that they are correct on any one hand, or even a series of hands?

No - they are absolutely certain on how they play each hand, regardless of any external influence or chance.

I'll give you two examples -
Play A) 5 players all sitting with 20 or 21.
The dealer turns over a 10 and 4. He twists because that is the rule, he gets another 4. He sticks on 18 even though all the hands are beating him, and pays up. Every time.
Play B) 4 out of 5 players have all stuck on 15, one has stuck on 18 because they can see a 6 as the dealers face card.
The Dealer turns over a face card (now scoring 16), and despite beating 4 out of 5 players with his 16 he still twists, regardless of the fact he would be up by beating the other 4. He would then stick even if he turned up an ace still losing the 5th hand despite the previous risk of losing the other 4 hands.

This is not guessing, it's playing to a fixed system. Zero guessing involved.

 

[Jon]

No - they pay zero attention to the other hands. It has no bearing on how they play their own hand. None, nada, Zero influence.
They play by a fixed set of rules.

Forgive me for pointing this out, but you answered a different question to the one I asked. I asked if they had all the facts about the other hands, not whether or not they paid attention to them. So, do they have all the facts about the other hands?

No - they are absolutely certain on how they play each hand, regardless of any external influence or chance.

Forgive me again, but similarly, you are answering a different question to the one I asked. There is a difference between thinking your strategy and rules are the best ones verses being certain you are correct on any one hand. To be certain you are correct on any one hand, you need to know what the other persons cards are, do you not?

When you say "regardless of any external influence or chance", are you saying that if in a dealer verses one player scenario they got to see the other persons cards (Player 1 was on 19), the dealer was on 18, it would not benefit the dealer to take this additional information into consideration, and therefore should twist?

Essentially you are saying this:

1. A guess means you cannot be certain you are correct because you do not have all the facts.

2. The casino is involved in a game where the other persons cards are unknown. But these unknown cards do not represent part of the facts of this game.

3. The casino is certain they will win.

Parts 2 and 3 are incorrect.

Firstly, the definition of fact is:

a thing that is known or proved to be true.

If the dealer knows what the other persons cards are, they can say what they are as a fact since they are "a thing that is known." But they are unknown. Therefore, the dealer does not have all the facts. Not having all the facts is a requirement for something being a guess, using your own preferred definition. It doesn't matter if they have a set of rules for making their best guess or not, it is still a guess. They are missing facts in the game that prove certainty.

Secondly, the casino can never be certain they will win, since they work on probabilities and not certainties. I take it for granted that you know the difference between something being highly probable and being certain. They are not the same thing. So again, using your own preferred definition of a guess, the requirement for something to be a guess is that you cannot be certain.

This is not guessing, it's playing to a fixed system. Zero guessing involved.

Why is playing to a fixed system not guessing? When you don't have certainty of the answer, it has to be guessing. For your statement above to be correct, you need to be certain, which you can never be.

I think the sticking point is you are assuming a guess is something random, and that you cannot have a system for guessing something. But you can have a system for guessing something. It is still a guess, because you are not certain if you have the right answer or not.

 

[conception_native_0123]

The problem is that most people think too much.

and I'm talking to one of those people, right? =) I always thought the problem was choice.

 

[The_Doc_Man]

Jon, the "house" knows EXACTLY what cards are in your hand - in the aggregate. Your cards will have 1 of 13 ranks, for which the median rank is 8.5 so two of those cards taken in aggregate over several hands will on the average total 17. The dealer's cards will be the same way. The thing that makes the house win long-term is greed and the "stand on 18" rule. Long-term, all the players will average 17 - but the question will be whether they STAND on 17. (Many won't.) The dealer, holding at 18 or above, will win by one point on the average. A few lucky players will sometimes get above 17. But that is merely a fluctuation of short-term probabilities, a tremor in the force, or something like that.

Your problem is that you see each hand individually, but this is a forest vs trees scenario. The trees are single games. The forest is all about how much you play that evening, and how badly you lose your shirt. And over the long game, the dealer has 8 and the field has 17 - if they don't bust.

 

[Minty]

The only real "Guess" the casino is ever making is how many punters are coming through the door, it's the one thing they don't have a very good idea about.
Everything else in their business model is at worst case a very "Educated Guess"

I think I understand what a fact is.

 

[Jon]

and I'm talking to one of those people, right? =) I always thought the problem was choice.

There is a book called The Paradox of Choice. Its hypothesis is that too much choice reduces happiness.

 

[Jon]

The only real "Guess" the casino is ever making is how many punters are coming through the door, it's the one thing they don't have a very good idea about.

But you just said earlier that you don't need to know the answer to something unknown (the opponents hand), you just need a system for making decisions on how to respond, and that makes it not a guess. So how is this different? You don't know how many punters will come through the door, you just need a system for how to respond. So now you are saying these similar scenarios are both a guess and not a guess, using your own definitions and criteria. You can't have it both ways.

I think I understand what a fact is.

I think I understand what a guess is. But we won't solve world peace squabbling over the term.

 

[Jon]

Jon, the "house" knows EXACTLY what cards are in your hand - in the aggregate. Your cards will have 1 of 13 ranks, for which the median rank is 8.5 so two of those cards taken in aggregate over several hands will on the average total 17. The dealer's cards will be the same way. The thing that makes the house win long-term is greed and the "stand on 18" rule. Long-term, all the players will average 17 - but the question will be whether they STAND on 17. (Many won't.) The dealer, holding at 18 or above, will win by one point on the average. A few lucky players will sometimes get above 17. But that is merely a fluctuation of short-term probabilities, a tremor in the force, or something like that.

Your problem is that you see each hand individually, but this is a forest vs trees scenario. The trees are single games. The forest is all about how much you play that evening, and how badly you lose your shirt. And over the long game, the dealer has 8 and the field has 17 - if they don't bust.

Actually Doc, I know exactly how it works and the difference between a single event and an accumulation of events. I also know the mathematical formulas for working out these probabilities. I see both the forest, the trees and the implications of different sized forests, or numbers of events, if you like.

Jon, the "house" knows EXACTLY what cards are in your hand - in the aggregate

The implication from what you are saying is that they know exactly what is in your hand in the aggregate, but not on each individual hand, right? Given this, each individual hand is a guess, since not being certain and not having all the facts is the very definition of "guess".

Regarding the house knowing exactly what cards are in your hand...well, they actually don't! They can never know for sure. This is why they are guessing. If you know the answer, it is not a guess. As you are aware, the casino plays on probabilities (not certainties) and the odds are stacked in the casinos favour. To an extent, it resembles investing in the stock market. In the short term (single hands), there is great volatility in the outcomes. You can come out ahead or behind. In the longer term (over many games over a longer period of time), you are likely (but not guaranteed, and this is key) to come out ahead.

In the aggregate, the higher the number of hands played, the closer they will get to guesstimating what your average hand will be. But they never get to 100% certainty. The only way this can happen is if they played an infinite number of hands. Considering some seem to think that the Universe has a finite length, a casino can never play an infinite number of hands.

Ask yourself this question: Are they CERTAIN to come out ahead? And we all know the answer to that one. They can never be certain. They can only be highly likely.

Example: https://en.wikipedia.org/wiki/Breaking_the_bank

Since they can never be CERTAIN, it is a guess. I've never argued it isn't a calculated guess that is likely to maximise their potential revenue. Just that the lack of certainty defines it as a guess.

 

[JonXL]

And what if their hypothesis is statistically impossible? If the Universe does not have an end in time, then the midway point is infinity. Consequently, the probability of these scientists being correct by stating the Universe is 13.8 billion years old is infinitely small. i.e. zero chance.

The Universe not having an end doesn't preclude it from having had a beginning and, thus, a current age.

You are correct to state that using your approach to get the age of a universe with an infinite lifespan would prevent getting its age since we can't get a midway point and so could never figure its age (using the methodology you're employing to figure age).

But that's only a problem if we use your approach. Alternatively (whether the Universe has an infinite lifespan or not), we could figure its current age the same way we figure age for everything else - by developing some scientific means to measure how much time has passed since the beginning point. We do this already in every other scientific field that might concern assessing age whether that is counting rings on a tree, measuring closure of skull bones, or measuring red-shift in the distant Universe. The Universe is not special in this regard to other physical things. It is a physical thing about which we can ask questions and attempt to develop answers through physical investigative methodologies.

How can you start with "how old is the Universe" by observation if by logic it is statistically impossible? An interesting thought experiment, me thinks.

Why impossible? If the Universe had a beginning in the past then it has an age in the present (regardless of whether it will have an end in the future). Now determining that age may be practically impossible (certainly it would have been so several hundred years ago or longer back when scientific tools were more limited) but that doesn't make doing so "statistically impossible" and as we develop better methodologies to measure and chart the physical world, we doubtless improve upon our practical - empirical - abilities to measure the age of the Universe thereby overcoming some of those practical impossibilities and enhancing the figures our methods arrive us at.

I am not aware of any scientific method for determining the age of something that tries to start with an assumption of its longevity and then picks the midpoint. Are you?

 

[conception_native_0123]

too much choice reduces happiness.

didnt know that Jon, but that wasn't the point of my statement. it was....problem is choice = the matrix movie line

 

[Jon]

didnt know that Jon, but that wasn't the point of my statement. it was....problem is choice = the matrix movie line

Red Pill, Blue Pill. Got you!

 

[Jon]

The Universe not having an end doesn't preclude it from having had a beginning and, thus, a current age.

I agree. But it also doesn't mean it had a beginning either, right? I will tackle the current age bit shortly. But for the sake of your argument, let us assume that it did have a beginning but had an infinite lifespan. The maths is still the same: choose the midpoint, which is infinity.

You are correct to state that using your approach to get the age of a universe with an infinite lifespan would prevent getting its age since we can't get a midway point and so could never figure its age (using the methodology you're employing to figure age).

There must be a misunderstanding because I never said it would pevent getting its age. Firstly, getting the midway point isn't to be precise about its age. It is just to find an age that is statistically likely to be closest to the real age. Secondly, the midway point of a Universe that has an infinite lifespan is infinity. That isn't preventing getting its age, because its statistically most likely age is infinity.

Since the most likely halfway point is infinity, any guess of a finite number (e.g. 13.8 billion years) is likely to be infinitely far from the most likely age, the midpoint. Therefore, it is infinitely wrong. i.e. 100% wrong.

But that's only a problem if we use your approach.

And consequently, because of your misunderstanding, that isn't a problem in using that approach.

Alternatively (whether the Universe has an infinite lifespan or not), we could figure its current age the same way we figure age for everything else - by developing some scientific means to measure how much time has passed since the beginning point. We do this already in every other scientific field that might concern assessing age whether that is counting rings on a tree, measuring closure of skull bones, or measuring red-shift in the distant Universe. The Universe is not special in this regard to other physical things. It is a physical thing about which we can ask questions and attempt to develop answers through physical investigative methodologies.

"Scientific means" includes probability, statistics and maths too, right? It isn't just using a ruler or stopwatch. And since probability, statistics and maths is used to estimate the age of things, by your own reasoning it should also be reasonable to use in estimating the universe. As you say, the Universe is not special in this regard to physical things.

Disagree? Then why are they using Bayesian probability in estimating fossil ages?

Bayesian phylogenetic estimation of fossil ages - PMC

Recent advances have allowed for both morphological fossil evidence and molecular sequences to be integrated into a single combined inference of divergence dates under the rule of Bayesian probability. In particular, the fossilized birth–death tree ...

www.ncbi.nlm.nih.gov

The scientific method is riddled with maths, probability and statistics.

we doubtless improve upon our practical - empirical - abilities to measure the age of the Universe

The Big Bang is littered with speculative and theoretical physics, not just observation. That is not empirical. They cannot observe what happened in the very early stages of the Big Bang, or before the Big Bang.

I am not aware of any scientific method for determining the age of something that tries to start with an assumption of its longevity and then picks the midpoint. Are you?

Are you aware of anything that has an infinite longevity apart from the Universe? Besides, lack of awareness does not beat logic.

As a side point to all of this, large numbers of physicists state that the Big Bang didn't arise out of nothing. Instead, they state that there was already something there, just very small. So perhaps talk of the beginning of time is a mute point because the beginning of the Universe may not have been the start of anything, except the Universe.

 

[Jon]

@The_Doc_Man I had a look recently at your pdf for the Monty paradox. It took me quite a while to understand what you did there, but I got there in the end. I've also identified where the error would be, according to Marilyn vos Savant.

I understand you will disagree regarding my explanation, but in any case you can see the specific point of contention.

In your analysis, you have worked out the number of different permutations based on the games rules. The Win Lose columns count those permutations and consequently form the opinion that the probabilities are equal. Now for what I have identified as the crux of it.

In the Win or Lose column, you should be allocating probabilities, and not counts. Counts do not equal probabilities, even if on first appearance they seem to. You should be allocating 2/3 rds probability if you switch, and 1/3 rd if you don't. Instead you are allocating 1's and 0's, disregarding if they are a switch or not.

The reason is, because you now have more information about that group, namely door 2 and 3. If you switch after you initially picked door 1, you know the group of doors 2 & 3 had a 2/3 rds probability in aggregate of containing the car. But since a goat was revealed in one of them, it must follow that the other door holds a 2/3 rds probability. It doesn't get shared with door 1 because there is no additional information revealed about door 1. Door 1 was not part of the group 2 & 3.

So I think the point of contention is that while you initially agree that door 1 only has a 1/3 rd probability of containing the car, there is no additionally information available that alters that probability, because the door revealing in group 2 is independent of the probability of door 1.

 

[The_Doc_Man]

I will work up a slightly different presentation and get back with you. I still do not agree with the asymmetric reassignment of probability after the reveal, because what I learned applies equally to the picked and unpicked doors. (I learned where the car WASN'T but not where it was.)

 

[Cronk]

In a similar manner to the tenth toss of a coin where the previous 9 have been heads, the odds for the tenth toss is 50/50. After one of three doors has been opened, there are now 2 doors and it is a 50/50 probability that the car is behind either.