Something I've been thinking about

[Check_The_Nuts]

Ring,

Your extremely insulting. "read the thread". [censored] off. Go talk down to an 8 year old something.

Rain,

I see the difference now. You made the assumption that in every example there is either a yes/no response. Either a win or a loss. My problem with this reasoning is the following data set:

0 0 0 0 0 0 1

From your logic, it seems like the standard deviation is 0.25. Your logic also seems to point that the mean would be 0.5. Either you win or you don't. When clearly this is not the case. I guess you reasoned that because they have the same means, they have the same standard deviations. This isn't the case though. Two data sets can have two completely different standard deviations but similar means.

[Rainclouds]

[ QUOTE ]
Rain,

I see what your saying now. We make the same amount of money on all of the situations because our equity is 50%.


[/ QUOTE ]Yes

[ QUOTE ]
So really in the long run it doesn't matter which sample we choose. We make the same amount of cash on each situation.


[/ QUOTE ]Yes, but the short or long run is irrelevant for my point

[ QUOTE ]
However, in the short run you'd prefer one that is right skewed, because there is a better chance of catching one of the higher equities as opposed to the lower.


[/ QUOTE ]This does not matter. Also in the short run (take 1 hand), you should not prefer any situation if you are interested in the outcome of the hand.

[ QUOTE ]
For example, the first sample you have a 50/50 shot of making it or not.

[/ QUOTE ]Yes

[ QUOTE ]
In the next, 2/3 of the time you have a good chance, 1/3 of the time you have a bad.

[/ QUOTE ]Which combined make it also exactly a 50/50 shot of making it or not.

I feel like I'm starting to be a broken record now.

[Ratamahatta]

[ QUOTE ]
rata has obviously been corrected on the variances not being the same. They clearly have different variances, different standard deviations. Your really just averaging numbers (even tho their equity).

The distributions of the sample are different. They aren't the same at all.

Two samples:

0 1
.75 .75 0

They have the same mean, 0.50, they have different standard deviations/variances and distributions. If you plotted the 3 on a bar graph the two graphs would not be the same.



[/ QUOTE ]

You are talking about stochastic variables (Y={0,1}, Z={0,.75}) which we are not interested in at all! When dbitel said: "although all these plays are 0 EV" he was clearly talking about the stoch. var. X={-1,1} (X={-a,a} in general w/e) which is a transformation of those you mentioned and which describes how much and how often we win/lose. This stoch. var. can be applyed to each example which means that they all have the same distribution and clearly same mean and variance.

[Rainclouds]

[ QUOTE ]
Ring,

Your extremely insulting. "read the thread". [censored] off. Go talk down to an 8 year old something.


[/ QUOTE ]
Dismissing a solid reasoning as a trick without being able to tell what's wrong is quite insulting as well.

[ QUOTE ]
Rain,

I see the difference now. You made the assumption that in every example there is either a yes/no response. Either a win or a loss. My problem with this reasoning is the following data set:

0 0 0 0 0 0 1

From your logic, it seems like the standard deviation is 0.25.

[/ QUOTE ] The standard deviation is not 0.25. It's 0.5. The variance is 0.25.

[ QUOTE ]
Your logic also seems to point that the mean would be 0.5. Either you win or you don't. When clearly this is not the case.

[/ QUOTE ] Tell me how this is not the case. Please tell me. Prop bet on it?

[ QUOTE ]
I guess you reasoned that because they have the same means, they have the same standard deviations. This isn't the case though. Two data sets can have two completely different standard deviations but similar means.

[/ QUOTE ]
I believe you still don't get it that the variance on the distribution of the equities of villains hand is irrelevant and that the variance of the outcome of the hand is the only relevant thing.

[Ringmaster]

[ QUOTE ]
Ring,

Your extremely insulting. "read the thread". [censored] off. Go talk down to an 8 year old something.

[/ QUOTE ]

Whoa. Take it easy. I wasn't trying to be condescending at all, I was just implying that I had written a more detailed explanation (several times) earlier in the thread, and didn't feel like typing out yet another one. So have many other posters.

Why do people always take things in the worst possible context online?

[ QUOTE ]
I feel like I'm starting to be a broken record now.

[/ QUOTE ]

QFMFT

[ReptileHouse]

[ QUOTE ]
We want to know about the distribution of wins and loses when we talk about variance in poker.

[/ QUOTE ]

This is correct. The other questions may be mathematically interesting, but they're not going to tell us how much we should expect our bankroll to vary.

Many of you are overcomplicating this significantly. In each of the suggested situations, the outcome of the hand is that we win 1/2 of the time and we lose 1/2 of the time. That's all we need to know. Everything else is just a distraction.

[Check_The_Nuts]

Ok guys,

so if these equities all averaged out to 60%, would you get a similar answer? Or would your assumptions be invalid then.

[Check_The_Nuts]

[ QUOTE ]
[ QUOTE ]
Ring,

Your extremely insulting. "read the thread". [censored] off. Go talk down to an 8 year old something.

[/ QUOTE ]

Whoa. Take it easy. I wasn't trying to be condescending at all, I was just implying that I had written a more detailed explanation (several times) earlier in the thread, and didn't feel like typing out yet another one. So have many other posters.

Why do people always take things in the worst possible context online?

[ QUOTE ]
I feel like I'm starting to be a broken record now.

[/ QUOTE ]

QFMFT

[/ QUOTE ]

Ring,

Just don't attack me when your discussing something. There's no reason to say I didn't read the thread. Your post count is low (so what?).

All of my explanations are pretty detailed, thought out, and long. Its OK to have discussion, I'm allowed to disagree.

Its hard to point out which step is wrong because the string of yes's in that post are very hard to contridict. That's why I asked him to rephrase his point. I just wanted to know what the assumptions he made were, so that I could figure out where (or if) he went wrong.

[Ringmaster]

[ QUOTE ]
Ok guys,

so if these equities all averaged out to 60%, would you get a similar answer? Or would your assumptions be invalid then.

[/ QUOTE ]

From an earlier post in this thread:

[ QUOTE ]
We either win the pot or lose the pot each time the villain calls. Our equity versus his range tells us the likelihood of each of these events happening, and hence the distribution of outcomes. In other words, the distribution of wins and loses depends solely on our equity.


[/ QUOTE ]

This means that the variance will be the same as long as the equity vs his range is the same.

[Check_The_Nuts]

Rain,

Just to be clear, you want to prop bet on the mean of this data set:

0 0 0 0 0 0 0 0 0 1

Is 0.5. Ok sure, my friends a mathematician...actually several of them are. I'm certain the mean of this data set is not 0.5. I can send this to a few of them to verify if you want, on facebook. Wouldn't take long. Let me know.

A good number for me is $1200. Be good to escrow with someone.