Re: Something I\'ve been thinking about
 

a seperate thought, for those where you have narrowed his range down to 2 or 3 hands, you're more likely to see if you were right. if his range is 10 hands, its less likely that he will have a hand that is in his range that you didn't think was in his range.

Re: Something I\'ve been thinking about
 

Since the distribution is the same and the overall equity is the same, my first impression is that the variance will actually be the same for all of these situations. That is, a coin flip is a coin flip, no matter how complicated the "coin" is. In all cases, we have a sample size of a single hand, which we will win or lose, where we have 50% equity. There is no difference.

What am I missing?

Re: Something I\'ve been thinking about
 

To those more mathematically inclined than me-

Am i right in thinking that Example 4 has the least variance?

Also, in terms of variance, 2=3, and 1=5 right?

Re: Something I\'ve been thinking about
 

[ QUOTE ]
Since the distribution is the same and the overall equity is the same, my first impression is that the variance will actually be the same for all of these situations. That is, a coin flip is a coin flip, no matter how complicated the "coin" is. In all cases, we have a sample size of a single hand, which we will win or lose, where we have 50% equity. There is no difference.

What am I missing?

[/ QUOTE ]


There is no lottery-style variance with 100% equity and 0% equity.

Re: Something I\'ve been thinking about
 

[ QUOTE ]
Since the distribution is the same...

[/ QUOTE ]
What do you mean by that? Distributions of those 5 examples are not the same...

Re: Something I\'ve been thinking about
 

[ QUOTE ]
There is no lottery-style variance with 100% equity and 0% equity.

[/ QUOTE ]

This is not true. 50% of the time we'll have 100% equity, and 50% of the time we'll have 0% equity. This is the same as having 50% equity 100% of the time.

Re: Something I\'ve been thinking about
 

[ QUOTE ]
[ QUOTE ]
Since the distribution is the same...

[/ QUOTE ]
What do you mean by that? Distributions of those 5 examples are not the same...

[/ QUOTE ]

Hero has 50% equity against villain's stated range in all 5 examples.

When we know the villain's range with 100% certainty, the only thing that matters is our equity against that range. The composition of that range is irrelevant.

The composition of villain's range generally DOES matter, because we aren't 100% confident in that range. We need to analyze, even if only by gut feel, how sensitive our equity is to small changes in the range.

Re: Something I\'ve been thinking about
 

[ QUOTE ]
[ QUOTE ]
There is no lottery-style variance with 100% equity and 0% equity.

[/ QUOTE ]

This is not true. 50% of the time we'll have 100% equity, and 50% of the time we'll have 0% equity. This is the same as having 50% equity 100% of the time.

[/ QUOTE ]


WHAT?!?!

[ QUOTE ]
Example 1: Villain has 2 hands in his range, One you have 0% equity against, the other, you have 100% equity against.


[/ QUOTE ]


This means that the lottery-variance of cards that have yet to come have 0 influence on the outcome.

Re: Something I\'ve been thinking about
 

[ QUOTE ]
This means that the lottery-variance of cards that have yet to come have 0 influence on the outcome.

[/ QUOTE ]

No. I'm talking about equity, not outcome.

Re: Something I\'ve been thinking about
 

in a vaccuum i don't care, but in reality it depends on the villain