## A fun little probability puzzle for you.

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

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

Ichthus77 wrote:You run me the probability of a coin toss actually landing on its side, given the structure of a coin, and I’ll answer your question.

What are you trying to say, that the 3 possibilities of a coin toss are 48% heads, 48% tails, and 4% side?

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

No. I done flipped the table over & the coin flew off into the couch cushions. So.
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Ichthus77
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### Re: A fun little probability puzzle for you.

Ichthus77 wrote:No. I done flipped the table over & the coin flew off into the couch cushions. So.

So go find where it landed and see which it landed on, heads, tails, or side. Take a pic and post it if you need clarification on exactly what the call is.

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

Duplicate
Last edited by Motor Daddy on Tue Jul 26, 2022 5:52 pm, edited 1 time in total.

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

I’ma save it for a rainy day.
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.

Ichthus77 wrote:I’ma save it for a rainy day.

So when it rains you'll go look?

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

I dunno. 50-50.
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.

Ichthus77 wrote:I dunno. 50-50.

So two options, what are they?

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

My homework. k bye
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.

Ichthus77 wrote:My homework. k bye

Study up!

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

https://youtu.be/JHFXG3r_0B8

“It is impossible to complete one’s education.”

or

“Education is not something one ever completes.”

Can’t remember who said it.
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.

Motor, I think I've found a potential way for you to understand what my position is in this debate about coin flipping I've had with Origami. I think that way is betting.

I'm not going to ask you to actually bet me anything, but I'm going to describe my betting scenario with you and I want you to tell me what you think a break-even bet would be.

First, let me once again post the original quote from origami: "If you flip a coin 3 times and get all heads, the odds of it being heads the 4th time are not 50-50."

So here's the betting scenario. Me, you, and origami are sitting around drinking beers. Origami is flipping a coin, and me and you are watching. He flips it a bunch of times, but eventually we see the following sequence: Origami flips tails. Origami flips heads. Origami flips heads again. Origami flips heads again.

We've all seen this - we've seen that the coin is on a streak of 3 heads, and the next flip will either end the streak if it's tails, or continue the streak if it's heads.

So now, after seeing these flips, origami says "Anybody want to make a bet on if the next flip is heads or tails?"

In your opinion, what are break even odds on betting that the upcoming flip is heads? Is a break even bet 50-50? Is it 1-15? Something else entirely?

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

Flannel Jesus wrote:In your opinion, what are break even odds on betting that the upcoming flip is heads? Is a break even bet 50-50? Is it 1-15? Something else entirely?

The previous flips have already occurred and we have seen the outcomes so that is not what is being bet on. What is being bet on is 1 flip and 1 flip alone. There is no bet of "4 flips" because we have already seen the results of the previous 3 flips.

So, the odds of 1 coin landing on heads or tails is 50%, and a 50% chance of something happening should have 1:1 odds.

In other words we bet $1. If it is heads you win my$1 and if it is tails I win your $1. That is 1:1 odds on a 50% chance of something occurring. If you want to bet on previous flips then I'll bet you$10 that the last flip was heads. Since you claim every flip has a 50% chance of occurring, that is 1:1 odds.

So if the last flip was heads you owe me $10. If the last flip was tails I owe you$10. that is 1:1 odds of a 50% chance of occurring, which you claim every flip has, right?

If you want to make a bet on THE NEXT 4 flips being all heads, that has a 6.25% chance of occurring, of which the odds are 15:1, then I'll bet on heads 4 times in a row and if it occurs then you pay me $15 and if it doesn't then I'll give you my$1.
Last edited by Motor Daddy on Fri Jul 29, 2022 11:37 am, edited 1 time in total.

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

Flannel Jesus wrote:In your opinion, what are break even odds on betting that the upcoming flip is heads? Is a break even bet 50-50? Is it 1-15? Something else entirely?

The previous flips have already occurred and we have seen the outcomes so that is not what is being bet on. What is being bet on is 1 flip and 1 flip alone. There is no bet of "4 flips" because we have already seen the results of the previous 3 flips.

So, the odds of 1 coin landing on heads or tails is 50%, and a 50% chance of something happening should have 1:1 odds.

Then you agree with me, and you have agreed with me on this issue the whole time.

This is not origamis position, but this is my position.

Flannel Jesus

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

Flannel Jesus wrote:Then you agree with me, and you have agreed with me on this issue the whole time.

This is not origamis position, but this is my position.

No I do not.

Once again, there is no "4 flips in a row" because the previous 3 flips have already occurred and we already know the outcome.

According to you 4 flips in a row landing on heads has a 6.25% chance of occurring, AND every flip has a 50% chance of occurring.

So prior to any flip I bet you that the NEXT 4 flips in a row will be heads. I claim that has a 6.25% chance of happening and you agree and give me 15:1 odds. I bet $2, so if I win you owe me$30. If I lose I owe you $2. We flip and the first flip lands on heads. You then claim the next 3 flips have a 12.5% chance of occurring and the next flip a 50% chance of occurring. I roll my eyes and tell you to flip the next flip. The next (2nd) flip lands on heads. You then claim the next 2 flips have a 25% chance of landing on heads and the next flip has a 50% chance of occurring. Once again I roll my eyes and tell you to flip the next flip. The next (3rd) flip lands on heads. You then claim the next flip has a 50% chance of occurring. I claim that the bet was that 4 flips in a row would land on heads, and just because you've seen the last 3 flips land on heads does not give you the right to change the odds to 1:1 and claim you have a right to do that because the chances have increased to 50% chance. If the next flip (4th flip) lands on heads you owe me$30 because there was a 6.25% chance of that last flip (and previous 3 flips) landing on heads, and the chance of that happening is 6.25%, and the odds are 15:1, which is the bet we made at the start. NO RENEGING!
Last edited by Motor Daddy on Fri Jul 29, 2022 12:07 pm, edited 1 time in total.

Philosopher

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

If you need evidence that Origami meant his statement the way I'm interpreting it, all you need to do is go and read the conversation I had with Origami. It started back on page 13 or 15 or somewhere around there. My disagreement with origami is, and has always been, about one flip, a flip that we call "the 4th flip".

I'm not going to debate you about it any longer, because the irony of you agreeing with me, while vehemently arguing against me, is too strong. Just read the conversation. If you really try to see, I think you will. If you don't want to read the conversation, then we should just stop talking about it.

Flannel Jesus

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

Flannel Jesus wrote:If you need evidence that Origami meant his statement the way I'm interpreting it, all you need to do is go and read the conversation I had with Origami. It started back on page 13 or 15 or somewhere around there. My disagreement with origami is, and has always been, about one flip, a flip that we call "the 4th flip".

I'm not going to debate you about it any longer, because the irony of you agreeing with me, while vehemently arguing against me, is too strong. Just read the conversation. If you really try to see, I think you will. If you don't want to read the conversation, then we should just stop talking about it.

Bottom line is that the last 3 flips landed on heads and if the next flip lands on heads you owe me $30 on a$2 bet!

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

You don't want to look into any evidence that you've possibly misinterpreted origamis statement, so that's the end of it. There's nothing more to be said.

Flannel Jesus

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

Flannel Jesus wrote:You don't want to look into any evidence that you've possibly misinterpreted origamis statement, so that's the end of it. There's nothing more to be said.

I am pointing out that I do not agree with YOU.

According to you the odds are 1:1 on a 50% chance of a coin landing on heads after seeing 3 heads in a row.

But I already bet you $2 that the 4th flip after 3 heads in a row would land on heads, and you gave me 15:1 odds because the chance of that happening is 6.25%. That is NOT your position. Motor Daddy Philosopher Posts: 1692 Joined: Fri Aug 27, 2021 5:32 pm ### Re: A fun little probability puzzle for you. You are making no effort to understand my position (in fact, you are apparently making effort to deliberately misunderstand it, as far as I can tell), and you're making no effort to even consider the possibility that you've misinterpreted origamis statement. I'm not sure what you hope to gain from this level of engagement. Flannel Jesus For Your Health Posts: 6293 Joined: Thu Mar 31, 2011 11:32 pm ### Re: A fun little probability puzzle for you. Flannel Jesus wrote:You are making no effort to understand my position (in fact, you are apparently making effort to deliberately misunderstand it, as far as I can tell), and you're making no effort to even consider the possibility that you've misinterpreted origamis statement. I'm not sure what you hope to gain from this level of engagement. One more time, I am not talking about origami's position, I am talking about your position, which you claim I agree with. I DO NOT agree with your position. As a matter of fact, if the 4th flip after 3 heads in a row lands on heads you owe me$30 on a $2 bet! Motor Daddy Philosopher Posts: 1692 Joined: Fri Aug 27, 2021 5:32 pm ### Re: A fun little probability puzzle for you. Why would I make a bet with someone who agrees with me? The pretense of the hypothetical bet with origami is that we place different likelihoods on the same event - I can bet origami on coin flips because I disagree with him on the probability of coin flips. I don't disagree with you on the probability of any coin flips, so there's nothing to bet on. You haven't presented me with a bet that I disagree with you on. You've told me I disagree with you, you've insisted I disagree with you, but you haven't yet shown a specific scenario where we actually disagree. Flannel Jesus For Your Health Posts: 6293 Joined: Thu Mar 31, 2011 11:32 pm ### Re: A fun little probability puzzle for you. Flannel Jesus wrote:Why would I make a bet with someone who agrees with me? The pretense of the hypothetical bet with origami is that we place different likelihoods on the same event - I can bet origami on coin flips because I disagree with him on the probability of coin flips. I don't disagree with you on the probability of any coin flips, so there's nothing to bet on. You haven't presented me with a bet that I disagree with you on. You've told me I disagree with you, you've insisted I disagree with you, but you haven't yet shown a specific scenario where we actually disagree. We both agree that 4 heads in a row occurring has a 6.25% chance. I am betting that it will happen, you are betting that it won't happen. According to your logic of "Why would I make a bet with someone who agrees with me?", the reason that we would both bet on opposite sides is because the chances are only 6.25% in my favor of winning, and 93.75% in your favor of winning. You are GAMBLING on the 93.75% chance of being right and winning$2 or losing $30. I am GAMBLING on the 6.25% chance of being right and winning$30 or losing $2. We BOTH agree that 4 heads in a row has a 6.25% chance of happening, but you are betting that it doesn't happen, and I am betting it does happen. Why would I bet$2 on something that only has a 6.25% chance of happening? Because IF I lose I only lose $2, but if I win I win$30.

That's why!
Last edited by Motor Daddy on Fri Jul 29, 2022 12:50 pm, edited 1 time in total.

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

So we both agree that there's a 1/16 chance of it happening. So what bet is there to make? I don't want to make that bet.

Flannel Jesus

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

Flannel Jesus wrote:So we both agree that there's a 1/16 chance of it happening. So what bet is there to make? I don't want to make that bet.

So you aren't willing to take a 6.25% chance of winning $30 or losing$2. That's your choice.

But if we do bet, and 3 heads in a row occur, then you still owe me \$30 if the 4th flip in a row lands on heads.

The odds didn't change the entire bet throughout the flips, they stayed 15:1, because the bet covers all 4 flips, not just the last of 4 flips. The last of 4 flips has the same chance of happening as the first of 4 flips, 6.25% and the odds stay at 15:1 for all 4 flips. The odds do not change to 1:1 just because you witnessed the previous 3 flips landing on heads.

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