On average how many trials will it take to lose 2 in a row on a 50/50 game of chance?

Quote: JyBrd0403

I guess what I'm saying is the normal question people ask is "What is the chance of winning 2 in a row". My answer would be 33%.

"What is the chance of winning 2 in a row"
This is an incomplete statement.
Why do you not see that?
"What is the chance of winning 2 in a row in 2 flips?" is what most people want to know and then they will follow that with OK how about in 10 flips? Because the chance or probability is dependent upon the number of trials.

OK

"What is the chance" is about a probability; a percentage, a ratio and that is directly related to the number of trials.
I ask you, "What is the chance of 2 in a row in 1 flip?"

"What is the chance of 2 in a row in 1000 flips?"
The answers will be a probability between 0 and 1.

"On average" how many trials will it take to lose 2 in a row on a 50/50 game of chance?

Now this talks about an average not a probability and it comes from the sum-product of all possible outcomes.
average (or mean) is a number, not a probability, and the average could be between 0 and infinity depending on the sample size.

(It looks to me that Sally was just trying to show that there are many ways to "see" 2 in a row.
Does one mean HH only
HHT
THHT
HHHT
They are all 2 in a row.)

Quote: JyBrd0403

If I had said, on average you win 2 in a row 25% of the time, everyone would have said that's absolutely correct. Right?

No. You are mixing probability with averages. They are totally 2 different things.
ME already showed you why this can never be done.

"on average you win 2 in a row" every 6 flips
"25% of the time" you will see 2 heads (or 2 tails) in a row in exactly 2 flips.

One needs to make sure they understand the difference between a "probability" and an "average" You seem to mix the two up all the time and that is where the confusion comes from.

Hey, start flipping a coin for 2 flips and tabulate the data.
The more 2 flip sequences you do, the closer you will see that 2 heads (or 2 tails) in a row occurs about 25% of the time, not 33%.

Good Luck and
Enjoy!

Here we go again. LOL

Just answer this simple, very common question. What is the chance of winning 2 in a row? Is it 25% or 33%, or what you keep telling me, that you have no way of knowing the answer to this question without more details. Is that what your response is when someone asks you that very simple question, that you don't know? LOL

The question means, on average. And, it's 2 out of 6, 2/6, 1/3, 33%. It's not 1 out of 6, 1/6, 16.67%. That's incorrect.

So, what's you're answer 25%, 33%, or you don't know?

Quote: guido111

Hey, start flipping a coin for 2 flips and tabulate the data.
The more 2 flip sequences you do, the closer you will see that 2 heads (or 2 tails) in a row occurs about 25% of the time, not 33%.

Good Luck and
Enjoy!

I thought you just got done telling me you couldn't state this in percentage terms. LOL Now, you're saying it's 25%. Interesting.

As far as flipping a coin in 2 flip sequences, you're right it would be close to 25% of the time, I've done this before. However, if you flip the coin continuosly, it's 33% of the time. I've also done this.

You see, the only way you can say it's on average 25% of the time, is if you do exactly what you're suggesting and flip the coin in 2 flip sequences. That's the only time you will get an average of winning 2 in a row 25% of the time. Otherwise, if you continually flip the coin, the average would be 33%. There's a reason for this. Do you know what it is?

Quote: JyBrd0403

Here we go again. LOL

Just answer this simple, very common question. What is the chance of winning 2 in a row?

You can't answer that question unless you specify the total number of plays you're making.

In one play, the chance of winning 2 in a row is 0%.
In two plays, the chance of winning 2 in a row is 25%.
&c.

Quote: MathExtremist

You can't answer that question unless you specify the total number of plays you're making.

In one play, the chance of winning 2 in a row is 0%.
In two plays, the chance of winning 2 in a row is 25%.
&c.

LOL So, you're answer is you don't know? LOL

Hey, they're offering a 50/50 game of chance at this casino, what are the chances of me winning 2 in a row?

I have no idea. LOL

Quote: JyBrd0403

However, if you flip the coin continuosly, it's 33% of the time.

33% of WHAT time? Time has a value. The number of flips.
2 flips?
4 flips?
100 flips? These will give you a X% a percentage

if you flip the coin continuously, and add up all the flips until you see 2 in a row (known as the "wait time") and divide that by the total number of times you did the experiment, you will have an average, NOT a percentage.

Man, I want what you are drinking!

Quote: guido111

33% of WHAT time? Time has a value. The number of flips.
2 flips?
4 flips?
100 flips? These will give you a X% a percentage

if you flip the coin continuously, and add up all the flips until you see 2 in a row (known as the "wait time") and divide that by the total number of times you did the experiment, you will have an average, NOT a percentage.

Man, I want what you are drinking!

I'm a Bud man, and a Cub fan! LOL

Okay, but you can also represent this as a fraction, and then take the fraction and state it in percentage terms. Which is a very common thing to do. For example 2 out of 8 trials, 1/4, 25%. Which, is what you did to come up with 25% of the time you would win 2 in a row, if you continuously flip a coin in 2 flip sequences.

Quote: JyBrd0403

I'm a Bud man, and a Cub fan! LOL

Okay, but you can also represent this as a fraction, and then take the fraction and state it in percentage terms. Which is a very common thing to do. For example 2 out of 8 trials, 1/4, 25%. Which, is what you did to come up with 25% of the time you would win 2 in a row, if you continuously flip a coin in 2 flip sequences.

Sure, but what you're doing there is saying "one out of every four 2-flip trials will be 2 wins in a row, 1/4 = 25%". That's very different than saying "6 trials is the average wait time for 2 wins in a row". You can't meaningfully state "6" in percentage terms here. What you seem to be doing is saying "2/6 = 33%", which doesn't even make any sense when you look at what the 6 actually represents. It's not that something happens every 2 out of 6 games on average, which would be a probability -- it's that out of all possible number of games, the average number of games played to see 2 wins in a row is 6 games.

Quote: JyBrd0403

I'm a Bud man, and a Cub fan! LOL

Okay, but you can also represent this as a fraction, and then take the fraction and state it in percentage terms. Which is a very common thing to do. For example 2 out of 8 trials, 1/4, 25%. Which, is what you did to come up with 25% of the time you would win 2 in a row, if you continuously flip a coin in 2 flip sequences.

Me too! I even went to Kentucky!

You are right.

probability formula: number of total successes / total possible outcomes

is a fraction. And fractions represent probabilities, but in a decimal form it is a percentage of the total possible outcomes, not a number, that will always be between 0 and 1.

Probability of at least 2 in a row in 2 flips is exactly 1/4 = 0.25 or 25%
Probability of at least 2 in a row in 1 flip is exactly 0/4

Probability of at least 2 in a row in 6 flips is exactly 43/64
There is a possibility that one sequence will have 2 - 2 in a rows like THHTHH
But when counting successes for a probability we only count 1 for the frequency of a run of 2 for that sequence. This is done in the math formulas.

But for averages, the formula is: add up all the numbers or occurrences every time they happened, then divide by how many total numbers there are
an average is still a fraction but of how many numbers there are, or trials, outcomes etc.
The value in decimal form, say .75 is not a percentage but a number. It could be 2.75, not 275%

Time to walk the dog!

added:
summary
probability (value of p) is expressed as a percentage between 0 and 1, not a number
average (the mean) is expressed as a number and not a percentage.

Quote: MathExtremist

it's that out of all possible number of games, the average number of games played to see 2 wins in a row is 6 games.

Yes, so the average number of games played to see 2 wins in a row is 2/6=33%. I don't know why that doesn't make sense to you. See, you would also take this as 2 flip sequences, reason being, we're looking for 2 wins in a row, you couldn't do it for 1 flip sequences or 3 flip sequences, because we're looking for 2 wins in a row, not 1 win in a row or 3 wins in a row. So it's, 2/6, 1/3, 33%. Again, this is common place. I think the problem is you're not breaking the average 6 trials down into 2 flip sequences. You can break the 6 trials down into 2 flip sequences, because we're looking for 2 wins in a row. So, it's 2/6, 1/3, 33%. Where as for Guido111's game it would be on average 8 trials to see 2 wins in a row. 2/8, 1/4, 25%. These are 2 different games. Guido111 starts his game over after 2 flips. I don't.

So, I'm stating it exactly like guido111 stated for the 2 flip trials. He stated that a 2 in a row would occur 25% of the time. That's on average 25% of the time you would win 2 in a row. Nobody, including me, is arguing with that. At least I don't think anyone is.

I'm stating that on continuous coin flips a 2 in a row would occur 33% of the time. Same wording, different game! This game is continuous flips of the coin. Guido's game is 2 flips and then start all over.

So, yes if you flip the coin 2 times and start all over it would average 2 wins in a row 25% of the time. This is, again, the only time you would be able to state that it is 25% of the time. If you play exactly this way.

If you continuously flip the coin, without starting over, you would average 2 wins in a row 33% of the time. There's a reason for this.

Quote: guido111

But for averages, the formula is: add up all the numbers or occurrences every time they happened, then divide by how many total numbers there are
an average is still a fraction but of how many numbers there are, or trials, outcomes etc.

Infinite trials. As a matter of fact, after probably 1000 continuous trials or so, the average will be close to 33%. In a million trials it will be 33%. In a trillion trials it will be 33%. The average stated as a decimal for this is .33 stated in percentage terms is 33%.

Probability of at least 2 in a row in 2 flips is exactly 1/4 = 0.25 or 25%

It's not exactly 25% on actual trials. If you actually flip the coin, you would have to take the average number of times you get 2 in a row. If you just flipped the coin 2 times and then stop you might get 0%. That's what I mean by "average".

Quote: JyBrd0403

Yes, so the average number of games played to see 2 wins in a row is 2/6=33%. I don't know why that doesn't make sense to you.

Because it's not 2/6, it's 6. Think about what you're saying. How do you win 2 games if you only play 2/6 of a game?

Sorry, you're right, I worded that incorrectly. On average, 2 wins in a row occurs 33% of the time, would be the correct wording.

Quote: JyBrd0403

Sorry, you're right, I worded that incorrectly. On average, 2 wins in a row occurs 33% of the time, would be the correct wording.

It might be how you meant to word it, but it's still incorrect. 2 wins in a row occurs with varying percentages depending on how long you play. The average number of games before observing 2 wins in a row is 6. It is improper to attempt to conflate these two concepts and suggest that 2 wins in a row occurs a fixed percentage of the time regardless of how long you play. If I play 1000 games, I am almost certain to observe 2 wins in a row.

Edit: 7craps posted a chart of the probability of seeing 2 wins in a row over N flips. Look at the middle column in this post. Note that the probability of 2 heads in 2 flips is 25%, in 4 flips is 50%, in 6 flips is 67.187%, and in 20 flips is 98.310947%.

You seem to be saying that the chances of seeing 2 heads in a row over 20 flips is the same as over 2 flips. Go ahead and do 10 sets of 20 flips and for each set, write down yes/no for whether you observed 2 in a row. The do 10 sets of 2 flips and write down yes/no for the same question. You will have many more "yes" answers for the 20 flip trials.

"It's 33%"

"NO! It's 25%!!!"

12 pages of threads later, I have summarized the entirety of this thread.

MathExtremist, I applaud you for your countless attempts at explanation, but I'm getting the impression that you could say the sky is blue and get an equally futile retort from JyBrd.

Kudos for the efforts though.

Quote: duckmankilla

Kudos for the efforts though.

The OP just likes to mix up probabilities with averages.
He will find more that agree with him over at Yahoo Answers.
So be it.

It is done. Stick a fork in it.

Quote: duckmankilla

"It's 33%"

"NO! It's 25%!!!"

12 pages of threads later, I have summarized the entirety of this thread.

MathExtremist, I applaud you for your countless attempts at explanation, but I'm getting the impression that you could say the sky is blue and get an equally futile retort from JyBrd.

Kudos for the efforts though.

Thanks for the appreciative comments. It's in my nature to explain things -- I just have to learn not to do it for free so often.

And I don't know what you mean by "the sky is blue". Where I come from, the sky is gray. And wet. :)

Quote: MathExtremist

And I don't know what you mean by "the sky is blue". Where I come from, the sky is gray. And wet. :)

You are standing too low.
Were you born and raised in WA state?
I have lived there. You have to look above the clouds. The sky really is a most beautiful blue where you come from.

(plug. Also in Berlin, New Hampshire)

FWIW, you would make an excellent educator with that kind of mentality. Many teachers are one-dimensional in their approach on providing instruction in a certain topic. Constantly explaining it in new and different terms is what allows students to understand and all you can do is hope that one of your many explanations gets through to them (coming from a future educator... at least I hope). Unfortunately, when dealing with the adult population, some skulls are just too thick to penetrate no matter how sound your reasoning may be.

Sorry for the derail, just thought ME deserved some credit for his endless attempts at explanations.

Quote: 7craps

You are standing too low.
Were you born and raised in WA state?
I have lived there. You have to look above the clouds. The sky really is a most beautiful blue where you come from.

I was, and yes, I agree. But shhh, don't tell anyone. Emmett Watson's legacy lives on. And apparently, if you look in the right place, the KBO torch is being carried by none other than the former Vegas Rex. It's a small world.

Quote: MathExtremist

I was, and yes, I agree. But shhh, don't tell anyone. Emmett Watson's legacy lives on. And apparently, if you look in the right place, the KBO torch is being carried by none other than the former Vegas Rex. It's a small world.

Then can I properly assume you are a card carrying member of KBO* ??




* KEEP THE BASTARDS OUT

Quote: buzzpaff

Then can I properly assume you are a card carrying member of KBO* ??

I'm one of the advanced scouts on the southern front.

Quote: MathExtremist

I'm one of the advanced scouts on the southern front.

Really. I thought you were on duty at the Oyster Bar. LOL

Quote: buzzpaff

Really. I thought you were on duty at the Oyster Bar. LOL

If I'm going to be on duty, it will either be at the Spud on Alki or Dick's on Broadway. But now we're off-topic, and now I'm starving.

Quote: JyBrd0403

As far as flipping a coin in 2 flip sequences, you're right it would be close to 25% of the time, I've done this before. However, if you flip the coin continuosly, it's 33% of the time. I've also done this.

The theoretical probability, not the average, is exactly 1/4 or 25% or 1 in 4.
1 in 4 is a statement showing that there is only one possible success in 4 possible outcomes.

Quote: JyBrd0403

You see, the only way you can say it's on average 25% of the time,

Wrong. I said the "probability" is 25% NOT the "average"

Quote: JyBrd0403

is if you do exactly what you're suggesting and flip the coin in 2 flip sequences. That's the only time you will get an average of winning 2 in a row 25% of the time.

There is your mistake again.

I say "probability is 25% or a 1 in 4 chance" and you say the average is 25%.

You will get a failing grade every time you say that.

The probability is expressed as a percentage, 25%, you just changed the probability to an average.
That is not allowed.

They are not the same thing, but you use them as they are.
This is math 101.
I think you need to learn the absolute differences between "probability of an event" and "average of an event"

It is very obvious to me that no one here so far is able to help you "turn on the light"

Probability
1: being probable
2: something that is probable
3: a ratio expressing the chances that a certain event will occur (1/4 or 1 chance in 4 or 0.25 or 25%)
The result will be expressed as a percentage between 0 and 1.

Average
1: The result obtained by adding several quantities together and then dividing this total by the number of quantities.
The result will always be in the same unit value as the sample data.
a)The average value from one six-sided die
1+2+3+4+5+6 = 21
The average will be 21/6 or 3.5
not 3.5%

b) 3.2% + 3.5% + 3.8% = 10.5%
10.5% / 3 =
3.5% not 3.5

My dog wants to go for a walk.
Wish I could train him to fetch me a Bud!

Quote: guido111

I think you need to learn the absolute differences between "probability of an event" and "average of an event".

More specifically, it's the difference between "probability of an event" and "average (e.g. mean) of a distribution of events".

A single event has a probability but not an average. A distribution of events has an average but not a meaningful probability (it's 100% that you pick something from the distribution).

Contrast:
a) I roll a die. What's the probability? Well I rolled it, so 100%. What's the average outcome? 3.5, just like you said.
b) I roll a 6 with a die. What's the probability? 1 in 6 or 16.67%. What's the average outcome? I only had one outcome, so you could say 6, but that's not saying much.

Averages usually refer to the whole distribution, while probabilities usually refer to specific events within the distribution. This thread stands as a testament to how messy things get when those distinct concepts are conflated.

You know, you people have really lost it. Let me try to put this together, you're saying the probability of winning 2 in a row is 25%, and that in actual trials you will win 2 in a row once every 6 trials. Correct?

You do know you're not the end all on math. I just google the damn question to get the answer, hell I can look on the wizards site. There's question after question of people asking the simple question "what are the chances of winning 2 in a row, 3 in a row etc.". The Wiz, the google websites, any math teacher on the planet, nobody needs to know any more information then what the p of winning is to answer the freaking question. MathE, already is so gone he can't answer the question at all LOL

So, what's all the B.S. about. Simply state the incorrect answer and say it's 25%. You're really making jackasses out of yourselves with this nobody could answer the question stuff.

By the way, probable outcomes don't mean a damn thing. The only thing that matters is the actual trials, because when you tell me I have a 25% of winning 2 in a row and I flip the coin and I get 2 in a row once every 6 trials, your probabilities and your actual trials aren't matching up, and that means what?

In other words your hypothesis is differing from your actual results. And that means what? Oh, I know, I know this one, reality is a fraud. LOL

Repost. Stupid computer.

Quote: mustangsally

For at least 2 in a row in 6 trials the exact answer is 67.1875%

And there could be more than 1 streak of length 2.
This is even more advanced math but easy in Excel.
(my Dad likes the colors)


Sally

Sally,

does the column "Prob x runs occuring" refer to the probability of consecutive occurence? In other words, "at least 2 runs of length 2 or more" refers to 2 consecutive runs of length 2 or more? No shorter streak then at least 2 in between?

Thanks for an explanation.