Puzzle time: the baseball fan

[Axtremus]

:::

No. There is nothing to be happy about.
Your team is already down 2 to 1.
The opposing team still expects to win 2.4 of the remaining 4 games, more than enough to wind the World Series.

:::

[jon-nyc]

I should be more specific. Did the news make you more or less optimistic than you were before hearing it?

[bachophile]

I should be more specific

Link to video

[Klaus]

Randomness has no memory. The events are independent. Hence you should be happy.

[jon-nyc]

@klaus

Your reasoning doesn’t make any sense. What if his team was down 0-1 games when he left and 0-3 games upon his return? Surely the odds of his team winning the series would have dropped considerably, even though all the games are independent.

[Klaus]

Well, you didn't specify what "Should you be happy?" means.

If I were a stoic, for instance, all that would matter to make me happy was whether the team played as well as they could, and it wouldn't matter whether they won or lost.

I figured that "one game each" is better than what is to be expected at the given odds, hence one should be happy.

But you seem to mean something else.

[jon-nyc]

I thought I clarified in my second post.

[Klaus]

Doesn't really clarify it. Do you mean: Does the news improve the odds that your team will win at least 4 out of the 7 games?

[jon-nyc]

Yes.

[Klaus]

The odds that the news improves the odds is less than 60%, Bayesianistically speaking.

[jon-nyc]

I think the odds that you’re odd are even higher.

[Klaus]

That's odd.

[Klaus]

Isn't this just yet another comparison of two "probability of >=k heads in n throws of a biased coin p"?

[jon-nyc]

You know what's funny?

My kid's old math circle mailed this question out Sunday. I have nobody to ask any clarifying questions of, they send out hints Tuesday and Thursday and an answer Saturday. But somehow I managed.

I think there's a skill called 'questionology' that I'm apparently better at than you and Ax.

[taiwan_girl]

You guys should become a comedy troupe!!!

[Klaus]

@jon-nyc said in Puzzle time: the baseball fan:

I think there's a skill called 'questionology' that I'm apparently better at than you and Ax.

The difference is that you know you have nobody to ask for clarification, whereas for us its a small investment to ask a clarifying question compared to investing valuable brain time for questionology. You are not better; you are just in a situation with less options

[Klaus]

He shouldn't be happy. Probability of winning goes down from 0.29 to 0.179.

[jon-nyc]

You’re comparing the time before the first game to the time after,

Should be the time before the camping trip to the time after.

[Horace]

It mostly depends on whether Tom Brady is the pitcher.

[Klaus]

@jon-nyc said in Puzzle time: the baseball fan:

You’re comparing the time before the first game to the time after,

Should be the time before the camping trip to the time after.

Oh, you are right.

Looks like the probabilities are identical, then: both are 0.1792.