No, your calculations with Kolmogorov's definition give an answer that contradicts mine. They do not directly address or disprove that 75/225=1/3. — BlueBanana
Basically the thing I question on them is the usage of the term "heads" and claiming its odds to be 1/2. Do you mean the odds of throwing heads or the odds of them having been thrown when the question is asked? The former leads to what I described above; right answer to the wrong question. The latter is circular reasoning. — BlueBanana
The wagering argument confirms that this is the proper degree of belief — Srap Tasmaner
With the common sense, how does that sound rational to you? Heads and tails being thrown are each as likely, so how does the knowledge that it's Monday change that? — BlueBanana
There are two wins with every tails — Michael
I suppose I could ask you the same question. Heads and tails being throw are each as likely, so how does knowing that you'll wake up twice if it's tails change that? — Michael
You get to guess more when tails are thrown, so if you're guessing it's likelier tails were thrown. — BlueBanana
The above reasoning only works if --- — Michael
My calculation is that expecting that profit is the same as if there were a single $1 bet at even odds that the result of a coin toss will be tails and the coin had a 3/4 probability of coming up tails. To see this, note that in that case the expected profit is
$1 x 3/4 + (-$1) x 1/4 = $0.50 — andrewk
By betting tails, I get to double what I risk only when my profit is guaranteed to double. — Srap Tasmaner
Bet H T Toss H 1 -1 T -1 1
Bet H T Toss H .25 -.25 T -.75 .75
Bet H T Toss H 1 -1 T -1 2
Bet H T Toss H .5 -.5 T -.5 1
It explains why guessing tails is profitable. — BlueBanana
So if guessing tails doesn't win more times, why is it profitable? — BlueBanana
We flip a coin. If it's heads then the result stands. If it's tails then we flip again and the new result stands.
What is the probability that it's heads? 2/3, because two of the three outcomes are heads? Or 3/4 because the probability is 0.5 + (0.5 * 0.5)?
This seems to be the crux of the disagreement. — Michael
Completely different situation. There's no "eliminated" outcome. — BlueBanana
Heads and Tuesday. — BlueBanana
That's irrelevant and doesn't have anything to do with the probability. We can change the scenario slightly to:
If it's heads then we wake her once. If it's tails then we wake her twice.
What's her credence that it's heads? — Michael
there are two guesses for each flip of a tails
— Michael
Because of which each guess is more likely to have been caused by tails. — BlueBanana
Then it's likelier the waking up was caused by flipping tails. — BlueBanana
and can ignore your "there's no 'eliminated" outcome" objection — Michael
We flip a coin. If it's heads then the result stands. If it's tails then we flip again and the new result stands.
What is the probability that it's heads? 2/3, because two of the three outcomes are heads? Or 3/4 because the probability is 0.5 + (0.5 * 0.5)? — Michael
I toss a coin and ask you what I got, but if it's heads I toss it again and if it's tails that round isn't played. What are you guessing when I ask you what I got? — BlueBanana
No, we can't. Eliminating that possibility diminishes the chances of heads being the correct guess. — BlueBanana
Not from there. That's where you get when you first take the trivial case where she's woken twice either way. — BlueBanana
We flip a coin. If it's heads then the result stands. If it's tails then we flip again and the new result stands.
What is the probability that it's heads? 2/3, because two of the three outcomes are heads? Or 3/4 because the probability is 0.5 + (0.5 * 0.5)? — Michael
3/4 — BlueBanana
We can assume without loss of generality that she decides before the experiment begins what she is going to guess when awoken.Nevertheless, if it's Tuesday only tails will save her. — Benkei
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.