## 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.

Why are you talking about weird stuff like 3 in a row, odds changing, shit like that? Who cares about all that? I don't.

Flannel Jesus

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

You've offered me a bet at break even odds for both of us, I've rejected the bet because I'm not interested in break even odds, so... that's the end of that bet. The end of it is, no bet. You keep your money, I keep my money, no other weird shit to talk about because there's no bet.

Flannel Jesus

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Joined: Thu Mar 31, 2011 11:32 pm

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

Flannel Jesus wrote:You've offered me a bet at break even odds for both of us, I've rejected the bet because I'm not interested in break even odds, so... that's the end of that bet. The end of it is, no bet. You keep your money, I keep my money, no other weird shit to talk about because there's no bet.

Fine, that's your choice.

Why, again, are you mentioning 3 prior flips of heads? Why not mention the 17 prior flips outcomes?

The ONLY thing you ever consider is 1 flip, not 4 flips, so stop talking about 4 flip scenarios with 1 flip chances.

We get it, 1 flip has a 50% chance of landing on heads. Duh?

Philosopher

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

Why are you saying duh? You agree with me. That's what I've been saying for pages. Duh.

Flannel Jesus

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Joined: Thu Mar 31, 2011 11:32 pm

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

Flannel Jesus wrote:Why are you saying duh? You agree with me. That's what I've been saying for pages. Duh.

I agree that 1 flip has a 50% chance of landing on heads.

Philosopher

Posts: 1693
Joined: Fri Aug 27, 2021 5:32 pm

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

"Why, again, are you mentioning 3 prior flips of heads? Why not mention the 17 prior flips outcomes?"

Because origami believes that if you've seen a coin flip heads 3 times in a row, the next flip does not have 50-50 odds. So in the case of origamis claim, for origamis position, HE is mentioning 3 prior flips because HE thinks they change the probability that the next flip is heads.

Duh.

Can we please stop with the duh shit? It's annoying and childish, you can do better.

Flannel Jesus

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Joined: Thu Mar 31, 2011 11:32 pm

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

Flannel Jesus wrote:"Why, again, are you mentioning 3 prior flips of heads? Why not mention the 17 prior flips outcomes?"

Because origami believes that if you've seen a coin flip heads 3 times in a row, the next flip does not have 50-50 odds. So in the case of origamis claim, for origamis position, HE is mentioning 3 prior flips because HE thinks they change the probability that the next flip is heads.

Duh.

Can we please stop with the duh shit? It's annoying and childish, you can do better.

But you can not speak about 4 flip scenarios, because you only ever consider 1 flip, which has a 50% chance of landing on heads.

If you want to discuss 4 flip scenarios then you have to start at the beginning of 4 flips, not the beginning of 1 flip.

Philosopher

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Joined: Fri Aug 27, 2021 5:32 pm

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

Anybody can discuss anything they want whenever they want. Who are you to tell me I can't discuss 4 flip scenarios? Who are you to tell origami he can't discuss 4 flip scenarios?

Origami is certainly free to discuss a 4 flip scenario from the point of view of a person who has already seen 3 of the 4 flips. There's no law against that. There's no forum rule against that.

Flannel Jesus

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Joined: Thu Mar 31, 2011 11:32 pm

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

Flannel Jesus wrote:Anybody can discuss anything they want whenever they want. Who are you to tell me I can't discuss 4 flip scenarios? Who are you to tell origami he can't discuss 4 flip scenarios?

Origami is certainly free to discuss a 4 flip scenario from the point of view of a person who has already seen 3 of the 4 flips. There's no law against that. There's no forum rule against that.

You can't discuss 4 flip scenarios because you are limited to your position that every flip is independent and has a 50% chance of landing on heads.

Like I said, according to you, at the start of a 4 flip bet the odds are 15:1, but on the 4th flip you want to claim the odds are only 1:1.

If you agree that the odds of the 4th flip are 15:1, then you must also agree that the chance is 6.25% for that last flip, right? Is it 1:1 50%, or 15:1 6.25% on the 4th of 4 flips??

Philosopher

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Joined: Fri Aug 27, 2021 5:32 pm

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

"You can't discuss 4 flip scenarios because you are limited to your position that every flip is independent and has a 50% chance of landing on heads."

Is this not also your position?

Flannel Jesus

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

Flannel Jesus wrote:"You can't discuss 4 flip scenarios because you are limited to your position that every flip is independent and has a 50% chance of landing on heads."

Is this not also your position?

No.

My position is that the 4th flip of a 4 flip bet has a 6.25% chance and a 15:1 odds, like it is at the start of the bet, prior to the start of flipping.

The bet covers all 4 flips, not 4 independent flips. The 4th flip after 3 heads in a row is covered from the start, 6.25% and 15:1 odds. The 6.25% is of all 4 flips, not 3 flips independent of the last flip.

Philosopher

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Joined: Fri Aug 27, 2021 5:32 pm

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

"every flip is independent and has a 50% chance of landing on heads."

You believe that there are flips that are not independent, that do not have a 50% chance of landing on heads?

Flannel Jesus

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

Motor Daddy wrote:A coin ALWAYS has a 50-50 chance of landing on heads or tails.

On page 38 you said this. This means the same thing.

Flannel Jesus

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

Flannel Jesus wrote:"every flip is independent and has a 50% chance of landing on heads."

You believe that there are flips that are not independent, that do not have a 50% chance of landing on heads?

The chances of 1 flip are not considered when the bet is that 4 flips in a row will land on heads. That is a 6.25% chance of happening. The 4 flips are a set of 4, not 4 individual flips.

There is no single flip of a 4 flip scenario, it is 4 flips of 1 set of flips.

What you are doing is taking the 4 flip bet and giving me 15:1 odds because the chances of a 4 flip set landing on heads is 6.25%. But then after seeing 3 of those flips land on heads you are claiming the 4th flip has a 50% chance.

Who cares what the chances of 1 flip are? If you claim the 4th flip has a 50% chance, then you must also claim the odds are 1:1, right? So you are only paying $2 on a$2 bet because the last flip has 1:1 odds due to a 50% chance of occurring??

That was not the bet. The bet was that 4 flips have a 6.25% chance of occurring, and so the odds are 15:1, so you WILL pay $30 on a$2 bet if the 4th flip lands on heads.

Your position is contradictory. How can you pay $30 on a$2 bet if the 4th flip lands on heads?

Philosopher

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Joined: Fri Aug 27, 2021 5:32 pm

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

I'm not talking about any particular bet right now. You offered me a bet and I said I wouldn't take it, so i don't understand why you keep bringing up a bet I didn't take.

You said I'm not allowed to talk about 4 flip scenarios because I believe that every flip independently has a 50% chance of being heads. Your quotes in the past imply you also believe every flip has an independent 50% chance of landing heads.

Now I don't know where you got this strange rule from that someone with that belief is not allowed to talk about 4 flip scenarios, but it seems to me that that rule, if it does exist, applies to you as much as it does to me. Because you also believe that every flip has 50% odds, just like I do.

Motor Daddy wrote:A coin ALWAYS has a 50-50 chance of landing on heads or tails.

Flannel Jesus

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Joined: Thu Mar 31, 2011 11:32 pm

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

Flannel Jesus wrote:I'm not talking about any particular bet right now. You offered me a bet and I said I wouldn't take it, so i don't understand why you keep bringing up a bet I didn't take.

You said I'm not allowed to talk about 4 flip scenarios because I believe that every flip independently has a 50% chance of being heads. Your quotes in the past imply you also believe every flip has an independent 50% chance of landing heads.

Now I don't know where you got this strange rule from that someone with that belief is not allowed to talk about 4 flip scenarios, but it seems to me that that rule, if it does exist, applies to you as much as it does to me. Because you also believe that every flip has 50% odds, just like I do.

Motor Daddy wrote:A coin ALWAYS has a 50-50 chance of landing on heads or tails.

You can talk about whatever you wish, I couldn't care less.

I am talking about a 4 flip set. If you want to talk about purple cars in Spain you have that right. But you know that has nothing to do with the subject, right? You know that the chances of the 4th flip of 4 still have 15:1 odds, right?

Are you giving 15:1 odds on a single flip that has a 50% chance of occurring?

Philosopher

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Joined: Fri Aug 27, 2021 5:32 pm

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

You're asking me about a bet but you're not wording it carefully enough for my taste. What are the specific terms of the bet? What has to happen for me to win the bet? What has to happen for me to lose the bet? Am I making the bet before any flips?

If you're asking me to make a bet, I can't have any ambiguity about what exactly I'm betting on

Flannel Jesus

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Joined: Thu Mar 31, 2011 11:32 pm

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

Flannel Jesus wrote:What are the specific terms of the bet? What has to happen for me to win the bet? What has to happen for me to lose the bet? Am I making the bet before any flips?

The specific terms of the bet are that a 4th flip must land on heads after 3 previous flips land on heads.

You are giving 15:1 odds, and I place a $2 bet. If the 4th flip lands on heads after the previous 3 flips landed on heads then I win$30. If any of the 4 flips land on tails then I pay you $2. Obviously you are making a bet on 4 flips prior to the 4 flips occurring. Why would you bet on previous flips that have already occurred and you already know the outcome? Motor Daddy Philosopher Posts: 1693 Joined: Fri Aug 27, 2021 5:32 pm ### Re: A fun little probability puzzle for you. So what happens if one of the three prior flips doesn't land on heads? There are possibilities in this bet you haven't covered, the terms are unclear. 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:So what happens if one of the three prior flips doesn't land on heads? There are possibilities in this bet you haven't covered, the terms are unclear. I specifically stated that if any of the 4 flips land on tails I pay you$2. In other words, if any of the 4 flips lands on tails I lose the bet.

Philosopher

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

It sounds like you're just bringing up the same bet I already rejected before. Can't I just reject that bet permanently? You can bring it up as often as you want, I'll reject it every time. If you're asking me to bet on the next 4 flips all being heads, there's no bet, because there's no disagreement.

Flannel Jesus

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

Flannel Jesus wrote:It sounds like you're just bringing up the same bet I already rejected before. Can't I just reject that bet permanently? You can bring it up as often as you want, I'll reject it every time. If you're asking me to bet on the next 4 flips all being heads, there's no bet, because there's no disagreement.

So you aren't willing to consider a bet where there are 4 flips and you have to bet prior to any of the 4 flips occurring. Great.

So your ONLY bet is that of a 1 flip scenario, where you bet on 1 flip. Right?

Philosopher

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

I haven't agreed to any bet with you, ever. You haven't described a betting scenario yet where we actually disagree. So no, not right.

I'm interested in a bet where we disagree. Me and origami disagree, so there's room for a bet there. Me and you both believe that every flip has 50-50 odds, so what bet is there to make? There's no disagreement, there's no bet.

Flannel Jesus

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Joined: Thu Mar 31, 2011 11:32 pm

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

Flannel Jesus wrote:I haven't agreed to any bet with you, ever. You haven't described a betting scenario yet where we actually disagree. So no, not right.

I'm interested in a bet where we disagree. Me and origami disagree, so there's room for a bet there. Me and you both believe that every flip has 50-50 odds, so what bet is there to make? There's no disagreement, there's no bet.

I am speaking hypothetically and you damn well know it, or are you really that stupid? Stop playing dumb!

You are not willing to place a bet on 4 flips, you are only willing to place a bet on 1 flip.

Why not just say that 1 flip has a 50% chance of landing on heads, and you will take a bet with 1:1 odds of that happening?

What, you will only place a bet on 1 flip if the odds are 2:1? 5:1? 25:1??

Philosopher

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Joined: Fri Aug 27, 2021 5:32 pm

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

"You are not willing to place a bet of 4 flips, you are only willing to place a bet on 1 flip."

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

"Why not just say that 1 flip has a 50% chance of landing on heads, and you will take a bet with 1:1 odds of that happening?"

1 flip has a 50% chance of landing on heads - I have said that, multiple times. But you're wrong about the second thing, I'm NOT interested in a 1:1 bet on that.

"What, you will only place a bet on 1 flip if the odds are 2:1? 5:1? 25:1??"

As I've made clear, I am only interested in bets where I have positive expected value. I can show you how to calculate that if you don't already know.

Flannel Jesus

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