## A fun little probability puzzle for you.

For discussing anything related to physics, biology, chemistry, mathematics, and their practical applications.

Moderator: Flannel Jesus

### Re: A fun little probability puzzle for you.

Flannel Jesus wrote:
I'm willing to place a bet on ANY set of flips, 1 or 4, that we disagree on.

So we both agree that a coin has a 50% chance of landing on heads, right?

Say I give you 10:1 odds for 1 flip. You can choose either heads or tails. If you are right I will give you 10:1 on your bet. If you bet $10 and win I'll pay you$100.

You wouldn't take that bet because we both agree there is a 50% chance of 1 flip landing on heads??

Philosopher

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### Re: A fun little probability puzzle for you.

There's a mathematical relationship between "we disagree on the probability of this event" and "there's a bet we can make where we both have positive expected value."

What you've offered there is a bet that gives me positive expected value, and you've willingly accepted negative expected value. So, yes, I would agree to that bet, but you're making the bet DESPITE our agreement, despite what you think about the actual probabilities, not because of them.

Obviously if you're making irrational decisions on bets that will benefit me, I'm happy to take the bet.

The "disagreement" requirement is under the assumption that you're also behaving rationally, and you're also only interested in bets that you think have positive expected value.

So you're right, pedantically, that I don't strictly require disagreement - irrational bets on your part can override the mandate that we disagree.

Flannel Jesus

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### Re: A fun little probability puzzle for you.

Would you like to willingly make a bet with me that you have negative expected value on?

Flannel Jesus

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### Re: A fun little probability puzzle for you.

Flannel Jesus wrote:So you're right, pedantically, that I don't strictly require disagreement - irrational bets on your part can override the mandate that we disagree.

You're so full of shit.

Now "disagreement" isn't a requirement of yours to place a bet?

I'm done here. See ya!

Philosopher

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### Re: A fun little probability puzzle for you.

Damn, I thought you were gonna offer me some free money!

Bye.

Flannel Jesus

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### Re: A fun little probability puzzle for you.

_
The end..?
The possibility of anything we can imagine existing is endless and infinite.. ~MagsJ

I haven't got the time to spend the time reading something that is telling me nothing, as I will never be able to get back that time, and I may need it for something important at some point in time.. Huh!? ~MagsJ

You’re suggestions and I just simply don’t mix.. like oil on water, or a very bad DJ ~MagsJ

Examine what is said, not him who speaks ~Arab proverb

aes Sanātana Dharma Pali: the eternal way ~it should not be rigid, but inclusive of the best of all knowledge for the sake of Ṛta.. which is endless.

MagsJ
The Londonist: a chic geek

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### Re: A fun little probability puzzle for you.

Unless someone wants me to prove that HTHT really does occur as often as HHHH! I already wrote the damn software.

Flannel Jesus

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### Re: A fun little probability puzzle for you.

Ichthus77 wrote:
Ichthus77 wrote:You showed above you already know this, but, when it doesn’t have to be one or the other, it goes like this:

H H - possible outcome, collapse redundancy
H T - SIDE … improbable outcome
T H - SIDE … improbable outcome
T T - possible outcome, collapse redundancy

unless a coin can land on its side

No, honey. Three options. That’s why pi

Don’t kick the table. Spin that coin like a top
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Fall semester ends 12/16/22. Apologies if I do not reply immediately.

“In choosing myself, I choose the other.”
- A marriage of Sartre & Levinas

Ichthus77
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### Re: A fun little probability puzzle for you.

You think it's more likely to land on heads twice than to land on heads and then tails?

Flannel Jesus

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### Re: A fun little probability puzzle for you.

I was talking out of turn. Begging your pardon.
Fall semester ends 12/16/22. Apologies if I do not reply immediately.

“In choosing myself, I choose the other.”
- A marriage of Sartre & Levinas

Ichthus77
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### Re: A fun little probability puzzle for you.

I'm just trying to understand matey, no problem at all.

Flannel Jesus

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### Re: A fun little probability puzzle for you.

Just crystalizing & generalizing some structure/pattern from previous convo with Motor Daddy in the thread. Relevant to something else I’m working on.
Fall semester ends 12/16/22. Apologies if I do not reply immediately.

“In choosing myself, I choose the other.”
- A marriage of Sartre & Levinas

Ichthus77
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