Need expert advice on how to handle a seemingly legitimate objection

[Speakpigeon]

That's a God's view of probabilities. But probabilities are based on what we think we know. Given what she thinks she knows, Anna is correct to say there a 50% chance it's "head". Our best scientists would do the same. Bod however knows it's "tail" so he would be wrong to maintain the same claim as Anna.

I think that if you switch to absolute probabilities based on what is the case rather than on what we know or think we know then you have to ditch all inductive arguments because they will be always wrong.
EB

What I would like to see is the wording of a true conclusion such that it's identical for both Anna and Bob.

That's precisely what I say shouldn't happen. Bod knows whereas Anna doesn't that the coin landed on "tail". Why should they say the same thing?

What it's on needs to go out the window.

It not the fact that it's on "tail" that matters but the fact that Bod knows it is while Anna doesn't.

Bob needs to be more concerned about future throws and not let his knowledge of the first throw lead him to think that knowledge of what happened somehow has an effect on probabilities.

In the case we are discussing, as you specified it, Bod and Anna aren't making claims about future throws but about the last one. Anna does not know the result but Bod does. That's why they will make different predictions, as everybody else with half a brain would. How could that be wrong?
EB

 

[fast]

What I would like to see is the wording of a true conclusion such that it's identical for both Anna and Bob.

That's precisely what I say shouldn't happen. Bod knows whereas Anna doesn't that the coin landed on "tail". Why should they say the same thing?

What it's on needs to go out the window.

It not the fact that it's on "tail" that matters but the fact that Bod knows it is while Anna doesn't.

Bob needs to be more concerned about future throws and not let his knowledge of the first throw lead him to think that knowledge of what happened somehow has an effect on probabilities.

In the case we are discussing, as you specified it, Bod and Anna aren't making claims about future throws but about the last one. Anna does not know the result but Bod does. That's why they will make different predictions, as everybody else with half a brain would. How could that be wrong?
EB

the point is that the probability of any given throw is independent of any knowledge or lack thereof. The chance of landing on heads is 50%. This is true both before and after the throw. This is true both with or without knowledge of any given throw. I wish I had some names to reflect the distinctions being made. Clearly, there is no chance that it's heads if it's tails, but that is true whether anyone knows. Think of a lottery ticket; there may be odds of winning, but my odds (in that sense) hasn't changed just because you just so happen to know whether I have the winning lottery ticket. Yes, in one sense, I am the winner (if I have the winning number), but the odds of others winning (although zero in one sense) are a function of that lack of knowledge.

 

[Speakpigeon]

We can assume first that the odds for a particular draw don't depend on the results of draws already made. But this is not quite the problem here. Probabilities are time-stamped and knowledge-based. Before the throw, since you can't know the result, you have to say "The probability of the coin landing on "head" is 50%". After the throw, referring to it, you would have to say "The probability of the coin landing on "head" was 50%". If you repeat "The probability of the coin landing on "head" is 50%" you are making, and understood to be making, a new prediction, about the next throw, not about the one already done.

After the throw, Bob, knowing the result, can still say without contradiction that "The probability of the coin landing on "head" was 50% but/and the coin landed on 'tail'".

Anna, since she doesn't know the result of the throw, can say "The probability of the coin having landed on "head" was 50% and is still 50%." Yet, like Bob, if she gets to know it's "tail", she would have to drop the last part of the sentence since the probability of the coin having landed on "head" would no longer be 50% in this case.
EB

 

[steve_bnk]

I believe the idea that knowledge of the numerical probabilities can affect your odds used to be called

Chronic craps players at casinos tend to be subjectivists. They think they see patterns that can predict the future results.

Back when I did analysis on large numerical data sets with a hand calculator it was easy to think you see patterns.

Take a coin and toss 1000 times. Write down the sequences. You might get 10 heads followed by 10 tails, but the running average will be close to 50%.

A subjectivist might look at 10 heads followed by 10 tails and think he'll bet the next toss will be head thinking a pattern. 50% of the time he will be right.

One can think after watching a craps table for hours a certain sequence will lead to a higher probability of betting correctly.

House odds are stable month to month

in the 60s I had an uncle who made some money at the tracks in NYC. As he put he spent time hanging around getting to know the horses and pokeys. Not personally but injuries and health and the like. He managed to hedge his bets so he came out on the plus side.

One day at a track being a pot smoker at the time the name Dealer jumped out at me and I bet to win. The horse won and it pissed off my uncle.


Mathematical probability is a number.

Most A are B. George is A therefore George is probably B as well is a subjective assertion.

90% of A is also B. George is A, therefore there is a 9 in 10 chance George is B. Objective statement.

 

[fast]

Ok