Terger

It's "streger", I think. I saw it tattooed somewhere once.

Any Mathematicians in the house? My understanding of how probability works is being contradicted by my first hand observations...

Say I want to "Get X", and in an attempt to do that, I "do the thing". Each time I do the thing there's an 80% chance of A happening, and a 20% chance of B happening. If A happens then there is a 0% chance that I will get X. If B happens then there is a 10% chance that I will get X. What are the chances of me getting X when I do the thing?

My maths is that one-in-five multiplied by one-in-ten equals one-in-50, or 2% chance. So if I do the thing 50 times then I should get X. But I've done the thing over 100 times and still haven't gotten X... So am i just unlucky? Or am I completely forgetting how the maths works?

Side-note: Z behaves the same as X, except that there is a 30% chance of getting Z if B happens. So I'm three times as likely to get a Z as I am an X right? Cause I've gotten eight+ Zs and haven't gotten a single X.

...

...asking for a friend...

Say I want to "Get X", and in an attempt to do that, I "do the thing". Each time I do the thing there's an 80% chance of A happening, and a 20% chance of B happening. If A happens then there is a 0% chance that I will get X. If B happens then there is a 10% chance that I will get X. What are the chances of me getting X when I do the thing?

My maths is that one-in-five multiplied by one-in-ten equals one-in-50, or 2% chance. So if I do the thing 50 times then I should get X. But I've done the thing over 100 times and still haven't gotten X... So am i just unlucky? Or am I completely forgetting how the maths works?

Your calculations are correct; you're just unlucky. Not even all that unlucky: if the probability of success on one try is 2%, the probability of not getting any successes in 100 tries is 13.26%, or about 1 in 7.5. Nothing too surprising about that.

Any Mathematicians in the house? My understanding of how probability works is being contradicted by my first hand observations...

Say I want to "Get X", and in an attempt to do that, I "do the thing". Each time I do the thing there's an 80% chance of A happening, and a 20% chance of B happening. If A happens then there is a 0% chance that I will get X. If B happens then there is a 10% chance that I will get X. What are the chances of me getting X when I do the thing?

My maths is that one-in-five multiplied by one-in-ten equals one-in-50, or 2% chance. So if I do the thing 50 times then I should get X. But I've done the thing over 100 times and still haven't gotten X... So am i just unlucky? Or am I completely forgetting how the maths works?

Side-note: Z behaves the same as X, except that there is a 30% chance of getting Z if B happens. So I'm three times as likely to get a Z as I am an X right? Cause I've gotten eight+ Zs and haven't gotten a single X.

...

...asking for a friend...

It might help to think of it as the probability of losing 100 times in a row. So, (49/50)^100 = 13% chance of 100 losses at a 98% probability. So, yeah, pretty unlucky. It's easy to fall into the gambler's fallacy where you might feel every loss means a greater chance of success later on, or that there must be a success after a large number of losses, but assuming your system is truly random, you could go the rest of your life without a win.

My maths is that one-in-five multiplied by one-in-ten equals one-in-50, or 2% chance.

Correct!

So if I do the thing 50 times then I should get X.

Incorrect!

Delbin mentioned the gambler's fallacy, and that's exactly what you're falling into here. Assuming that each time you attempt to do the thing you have the same chances as the last time you did it, your odds will never improve.

Think of it like a deck of cards. You're going to shuffle a deck of cards and draw the top card. If you draw the Ace of Spades, you win!

But what happens if you lose? If you take the card you drew that wasn't the Ace of Spades and set it aside, and then shuffle the deck and draw the top card, then your odds of drawing the Ace of Spades as the top card go up each time. One in 52, then one in 51, then one in 50, etc. Eventually, over the course of at most 52 attempts, you will draw the Ace of Spades.

But! What if you *don't* discard the losing card? Your odds of drawing the Ace of Spades as the top card of the deck will *always* be one in 52. Period. Forever. 52 attempts; 520 attempts; 52,000 attempts; your odds never go up, and they never go down. It's possible (but unlikely) that you'll never, ever draw the Ace of Spades as the top card.

So keep that in mind as you're Doing The Thing. If your odds are fixed at 2% with no mechanism for removing bum attempts from the equation, then it could take many more than 100 attempts to get what you're after.

(This is also why you can miss five shots in a row in XCOM even if you have an 80% chance to hit and it doesn't mean that the game's random-number generation is busted. If there's no mercy rule in place to up your odds with each shot, you could keep right on missing forever, even if you think you have a good chance to hit.)

Ok, I can just about follow all of that. I guess I underestimated the likelihood of never getting X, no matter how many times I do the thing.

It's also throwing me off that I keep getting so many Z...but I'm just thinking about it wrong.

Thanks for the help everyone!

Update: **I GOT X!!!**

But more importantly, I learned important life lessons and made some new friends along the way.

Ok, I can just about follow all of that. I guess I underestimated the likelihood of never getting X, no matter how many times I do the thing.

It's also throwing me off that I keep getting so many Z...but I'm just thinking about it wrong.

Thanks for the help everyone!

Update:

I GOT X!!!But more importantly, I learned important life lessons and made some new friends along the way. :)

Excellent!

Now you're ready for the Monty Hall Problem.

That one still gets me. I’ve read the logic behind it but my brain just won’t accept that “switch” is a better answer.

That one still gets me. I’ve read the logic behind it but my brain just won’t accept that “switch” is a better answer.

You're basically turning a 1/3 choice into a 1/2 choice. You can only lock in the better odds by switching.

(This is also why you can miss five shots in a row in XCOM even if you have an 80% chance to hit and it doesn't mean that the game's random-number generation is busted. If there's no mercy rule in place to up your odds with each shot, you could keep right on missing forever, even if you think you have a good chance to hit.)

Yeah now tell me about the 100% chance shots missing. XCOM is a dirty dirty liar.

Excellent!

Now you're ready for the Monty Hall Problem. ;-)

I've had a couple of people go through that one with me and it still seems counterintuitive...

I know you should swap doors, but is it:

A) You swap because when you pick "1" there's a 66% chance you're wrong, so by swapping to "2" after "3" has been ruled out, there's a 66% chance you're right...

Or, B) You swap because when you picked "1" there was a 33% chance you were right, but if you swap to "2" after "3" has been ruled out then there's a 50% chance you're right?

I guess the important thing is that I know to swap, even if I don't understand why.

Side note: I don't know why, but I find it quite disheartening that when trying to Get X, I was far more likely to fail 100 times than succeed on my first attempt...

I know you should swap doors, but is it:

A) You swap because when you pick "1" there's a 66% chance you're wrong, so by swapping to "2" after "3" has been ruled out, there's a 66% chance you're right...

Or, B) You swap because when you picked "1" there was a 33% chance you were right, but if you swap to "2" after "3" has been ruled out then there's a 50% chance you're right?

A. There's a 66% chance swapping is right.

Three possible scenarios:

1. You picked door 1. It is door 1. Swapping to whichever door isn't removed is wrong.

2. You picked door 1. It is door 2. Door 3 is removed. Swap = win.

3. You picked door 1. It is door 3. Door 2 is removed. Swap = win.

The only reason odds improve is because the door removal is *not* random. It is informed by what's behind the door - the correct door is never removed.

If door removal was random, as in the correct door could possibly be removed, then your odds would not improve any by swapping. Each door would still only have its original 1/3 probability. It's the fact that, in the 2-out-of-3 scenarios where your first choice was wrong, the other wrong door is ALWAYS removed, leaving the correct door behind, which shifts the odds.

If I want to try to get into a Civilization game which should I start with? I have Civ 4 with all expansions, and I have the base game of Civ 6.

There was a mobile one I really liked. It was very simplified but still fun. Since you have the complete 4 you should play that.

Stevintendo wrote:I know you should swap doors, but is it:

A) You swap because when you pick "1" there's a 66% chance you're wrong, so by swapping to "2" after "3" has been ruled out, there's a 66% chance you're right...

Or, B) You swap because when you picked "1" there was a 33% chance you were right, but if you swap to "2" after "3" has been ruled out then there's a 50% chance you're right?

A. There's a 66% chance swapping is right.

Three possible scenarios:

1. You picked door 1. It is door 1. Swapping to whichever door isn't removed is wrong.

2. You picked door 1. It is door 2. Door 3 is removed. Swap = win.

3. You picked door 1. It is door 3. Door 2 is removed. Swap = win.

The only reason odds improve is because the door removal is

notrandom. It is informed by what's behind the door - the correct door is never removed.If door removal was random, as in the correct door could possibly be removed, then your odds would not improve any by swapping. Each door would still only have its original 1/3 probability. It's the fact that, in the 2-out-of-3 scenarios where your first choice was wrong, the other wrong door is ALWAYS removed, leaving the correct door behind, which shifts the odds.

See, that makes sense.

Will I remember that for the next time this comes up? Probably not...

Boudreaux wrote:Is there a word in English, or perhaps another language, that means the opposite of regret?

Regret as in the verb ("I regret doing that") or as in the noun ("I have regrets", "he was filled with regret")?

Shoot, I forgot I asked this question. I was thinking more in the verb sense.

I was talking to my son after picking him up from a particularly rainy and muddy Boy Scout campout last weekend. He was talking about how it sucked and made everything twice as difficult. He's going on a high adventure trip this summer, so I told him "You're really going to (opposite of regret) going on campouts like this when you have to deal with tougher stuff this summer." At least, that was the sentence I tried to say but I couldn't think of the verb I wanted. Maybe 'appreciate' is the word I wanted, but that didn't quite seem right.

Stevintendo wrote:Ok, I can just about follow all of that. I guess I underestimated the likelihood of never getting X, no matter how many times I do the thing.

It's also throwing me off that I keep getting so many Z...but I'm just thinking about it wrong.

Thanks for the help everyone!

Update:

I GOT X!!!But more importantly, I learned important life lessons and made some new friends along the way. :)

Excellent!

Now you're ready for the Monty Hall Problem. ;-)

How does the monty hall problem work if what I really want is a new goat?

ClockworkHouse wrote:Boudreaux wrote:Is there a word in English, or perhaps another language, that means the opposite of regret?

Regret as in the verb ("I regret doing that") or as in the noun ("I have regrets", "he was filled with regret")?

Shoot, I forgot I asked this question. I was thinking more in the verb sense.

I was talking to my son after picking him up from a particularly rainy and muddy Boy Scout campout last weekend. He was talking about how it sucked and made everything twice as difficult. He's going on a high adventure trip this summer, so I told him "You're really going to (opposite of regret) going on campouts like this when you have to deal with tougher stuff this summer." At least, that was the sentence I tried to say but I couldn't think of the verb I wanted. Maybe 'appreciate' is the word I wanted, but that didn't quite seem right.

“Train hard, work easy.”

ClockworkHouse wrote:Boudreaux wrote:Is there a word in English, or perhaps another language, that means the opposite of regret?

Regret as in the verb ("I regret doing that") or as in the noun ("I have regrets", "he was filled with regret")?

Shoot, I forgot I asked this question. I was thinking more in the verb sense.

I was talking to my son after picking him up from a particularly rainy and muddy Boy Scout campout last weekend. He was talking about how it sucked and made everything twice as difficult. He's going on a high adventure trip this summer, so I told him "You're really going to (opposite of regret) going on campouts like this when you have to deal with tougher stuff this summer." At least, that was the sentence I tried to say but I couldn't think of the verb I wanted. Maybe 'appreciate' is the word I wanted, but that didn't quite seem right.

Relish

ClockworkHouse wrote:Boudreaux wrote:Is there a word in English, or perhaps another language, that means the opposite of regret?

Shoot, I forgot I asked this question. I was thinking more in the verb sense.

In Ireland we'd say "be glad" in that context. E.g.: "*You'll be glad you went on campouts like this when you have to deal with tougher stuff this summer. Ya feckin' eejit.*"

How does the monty hall problem work if what I really want is a new goat?

The goat is always behind door number two.

The secret to remembering why the Monty Hall problem works, and other some other non intuitive problems, is extrapolate. Imagine the same setup with 100 doors instead of 3.

1 pot of gold and 99 nothings.

Contestant picks a door.

Host opens 98 doors with nothing.

Contestant may swap.

'Be glad' is also the term that would've been used in the Alabama dialect my mother spoke when I was younger. I like 'relish' better though personally.

LeapingGnome wrote:If I want to try to get into a Civilization game which should I start with? I have Civ 4 with all expansions, and I have the base game of Civ 6.

There was a mobile one I really liked. It was very simplified but still fun. Since you have the complete 4 you should play that.

Civ with expansions generally has too many subsystems and is probably too overwhelming for a complete newbie.

If you're completely new I would probably recommend Civ5 vanilla to just start learning the basic concepts of food, production, science and culture, combat, diplomacy and simple governments. Because thats pretty much what Civ5 vanilla was.

In your case I would probably just go with vanilla CIV6 since it would be a bit silly to invest in a third Civ game without playing the others.

There's nothing wrong with Civ4. Civ4 and 6 are just very different games. They might share a name and have numbers close to each other but they are very different game concepts.

So if you think that Civ7 is something you want to get into in the future then Civ6 is your best bet as 7 will play a lot more like 6 than 4.

Side note: I don't know why, but I find it quite disheartening that when trying to Get X, I was far more likely to fail 100 times than succeed on my first attempt...

Nope. You were just as likely to succeed the first time as you were the hundredth. Your odds never changed.

If your XCOM CTH percentage is too low, the solution is usually a grenade.

If your XCOM CTH percentage is too low, the solution is usually a grenade.

This is good advice in many walks of life.

See, that makes sense.

Will I remember that for the next time this comes up? Probably not...

I think the reason it confuses people is that we're not used to *conditional* probability. The key insight is that the odds for the second decision depend on the outcome of the first.

That is, in essence the Monty Hall thing is just like your loot drop question. There you had: "initially a 20% chance of B happening, and if B happens then 10% chance of The Thing", giving an overall 2%, right? With Monty Hall that just becomes: "initially a 2/3 chance of guessing wrong, and if that happens then 100% chance that swapping will win". And you get the overall odds by multiplying through, just as before.

My wife lost the extra fob for her 2018 Hyundai Elantra. The dealership is quoting us nearly $500 to replace it. Is there a cheaper alternative?

Not really. It's like that on purpose.

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