Puzzle time: the baseball fan

[jon-nyc]

You are a rabid baseball fan and, miraculously, your team has won the pennant — thus, it gets to play in the World Series.

Unfortunately, the opposition is a superior team whose probability of winning any given game against your team is 60%.

Sure enough, your team loses the first game in the best-of-seven series.

You leave for a camping trip and, upon your return, you run out into the street and grab the first passerby.  "What happened in games 2 and 3 of the World Series?"

"They were split," he says.  "One game each."

Should you be happy?

[bachophile]

Thought this was going to be about the 69 Mets who lost their first game. But then they swept past the Orioles.

FTW

[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.