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Date: 04 Jan 2009 19:41:15
From: Porsche_Dan
Subject: Understanding the Mathematical Concept of Variance

Very enlightening!

http://www.pocketfives.com/poker-articles/Understanding-the-Mathematical-Concept-of-Variance-2423479

Let us begin with a hypothetical situation. Say you have played
100,000 45-man turbo SNGs over the course of a few years, and your
investment has yielded a 24% ROI. What would you guess the percent
chance would be of playing 1,000 more SNGs and recording a 40% ROI
over that sample, even though you played identically as you had in the
first 100,000? What about the chance of recording an 8% ROI over that
1,000 SNG sample? By the end of this article, you will know that the
chance of both of these events occurring is roughly the same (though
unlikely, it is important to know that it is quite plausible). What
underscores this notion is that one simply cannot make an accurate
statistical analysis of their expectation with a one thousand SNG
sample.

Instead of presenting you with a jargon filled definition of variance
(if you are interested, there is one available at http://en.wikipedia.org/wiki/Variance),
here is an illustration that can be more easily translated to poker:

Using a standard pair of six-sided dice, say you were trying to roll
"snake eyes" (rolling a 1 on each die). There is precisely a 1 in 36
chance of that happening on any given roll of the dice (1/6 * 1/6 =
1/36). So mathematical expectation says you should be averaging one
roll of snake eyes per 36 rolls. If you actually try this, you'll
notice that it does not always take exactly 36 tries to roll snake
eyes.

Sometimes you'll do it on your very first try. Sometimes you'll go 17
rolls in a row before rolling it. And when you are really 'running
bad,' you might go 84 rolls in a row without snake eyes. In short: it
varies. In a small sample (such as a few hundred rolls), there will be
wild swings between the results and what is mathematically expected in
the long run.

So what does this have to do with poker?

You have probably heard your fellow poker players mention "variance,"
particularly when those players were in the midst of a gruesome
downswing. What this really means is that their short term results
have deviated from their perceived mathematical expectation. They may
have lost a large number of times as a 4:1 favorite or been on the
losing end of multiple coin flips in a row. The psychological pain of
these losses increases dramatically when combined with a foggy notion
of variance.

As one begins to understand (and ultimately embrace) the wild swings
they will face in any form of poker, they will be better protected
from the irrational poison that is tilt. Carefully rendered reason is
one cure for this complex and perilous emotional state. We should also
remember that variance is also a factor in all of our positive
results: winning more coin flips than not is often the difference that
helps you cash in a SNG or go deep in a tournament. When one fails to
recognize that their positive results are often dependent on running
better than average, their experience of a downswing will have a much
harsher emotional effect.

Another way to protect against variance-related tilt is to always be
playing with a comfortable bankroll. You will be less affected by
variance if you lose a smaller portion of your bankroll when you
experience a downswing. This makes it easier to escape from a
downswing; your mental mood will be on a more even keel, less clouded
by loss and more focused on making good decisions. When you play over
your head, the effects of variance will be exacerbated. The ups and
downs are that much harder to handle, and this can lead to a poker
player's tunnel vision: an analysis of their short term results will
dominate perception, leading one to make severely incorrect judgments
about their game. Remember that poor short term results do not
necessarily equate to poor play.

If you are mentally prepared for a downswing, you will be better
protected from the desire to unnecessarily overhaul your game. You
might simply be experiencing a nasty but mathematically reasonable
downswing, which you simply need to play yourself out of. If you find
yourself unable to make speculative but long-run profitable moves (and
are constantly questioning these moves when they don't work), you are
probably misunderstanding the ever present role of variance.

In large field MTT poker where most of our profit comes from making
the top 3 spots, we have to be especially prepared for large
downswings. Even the very best MTTers will finish in those top few
spots only a small percentage of the time. And just like in the dice
example, anytime a desired result occurs only a small percentage of
the time, a statistically reasonable downswing can get pretty massive
and extreme. For example, a standard U.S. quarter has 1 chance in
1,024 of coming up heads 10 times in a row. One chance in a thousand
isn't very likely, but if there are approximately 10 million online
poker players, and all 10 million tried flipping a coin 10 times in a
row, then about 10,000 of the players would have a result of 10
heads.

Similarily, this means that if you viewed an MTT in terms of big
scores, with a big score occuring let's say 1 out of every 100 mtts on
average, then this means there would be 1 chance in 1,024 of going for
1,000 straight MTTs without a single big score. Or if a big score
came on average only once every 200 mtts, then there would be 1 chance
in 1,024 of going 2,000 straight MTTs without a single big score. The
crazy thing is that this could happen to even a very good MTT player
if most of their tourneys have 1,000-2,000 entrants, even if they have
a solid 70% ROI. This example wouldn't be all that odd, statistically.

Below is a video on how to use an ROI simulator that calculates any
number of sample sizes and expected distributions of variance.

http://www.youtube.com/watch?v=sELOkX9Ra2g

It can be downloaded from this link:

http://www.rvgsoftware.com/roisimulator.zip


Hopefully this article will help people gain a more solid grasp of the
kind of variance that is normal for poker players, so they can temper
their expectations accordingly.




 
Date: 05 Jan 2009 18:39:40
From: JB
Subject: Re: Understanding the Mathematical Concept of Variance
Great post Dan. Played B&M poker in NV for over 30 years, and had my fair
share of "running bad" LOL. Not tilting is a very hard lesson to learn. And
very costly too.

"Porsche_Dan" <Porsche.Dan@gmail.com > wrote in message
news:5b31109d-5a5b-4f2a-a1fd-6502ebf95125@w1g2000prk.googlegroups.com...
>
> Very enlightening!
>
> http://www.pocketfives.com/poker-articles/Understanding-the-Mathematical-Concept-of-Variance-2423479
>
> Let us begin with a hypothetical situation. Say you have played
> 100,000 45-man turbo SNGs over the course of a few years, and your
> investment has yielded a 24% ROI. What would you guess the percent
> chance would be of playing 1,000 more SNGs and recording a 40% ROI
> over that sample, even though you played identically as you had in the
> first 100,000? What about the chance of recording an 8% ROI over that
> 1,000 SNG sample? By the end of this article, you will know that the
> chance of both of these events occurring is roughly the same (though
> unlikely, it is important to know that it is quite plausible). What
> underscores this notion is that one simply cannot make an accurate
> statistical analysis of their expectation with a one thousand SNG
> sample.
>
> Instead of presenting you with a jargon filled definition of variance
> (if you are interested, there is one available at
> http://en.wikipedia.org/wiki/Variance),
> here is an illustration that can be more easily translated to poker:
>
> Using a standard pair of six-sided dice, say you were trying to roll
> "snake eyes" (rolling a 1 on each die). There is precisely a 1 in 36
> chance of that happening on any given roll of the dice (1/6 * 1/6 =
> 1/36). So mathematical expectation says you should be averaging one
> roll of snake eyes per 36 rolls. If you actually try this, you'll
> notice that it does not always take exactly 36 tries to roll snake
> eyes.
>
> Sometimes you'll do it on your very first try. Sometimes you'll go 17
> rolls in a row before rolling it. And when you are really 'running
> bad,' you might go 84 rolls in a row without snake eyes. In short: it
> varies. In a small sample (such as a few hundred rolls), there will be
> wild swings between the results and what is mathematically expected in
> the long run.
>
> So what does this have to do with poker?
>
> You have probably heard your fellow poker players mention "variance,"
> particularly when those players were in the midst of a gruesome
> downswing. What this really means is that their short term results
> have deviated from their perceived mathematical expectation. They may
> have lost a large number of times as a 4:1 favorite or been on the
> losing end of multiple coin flips in a row. The psychological pain of
> these losses increases dramatically when combined with a foggy notion
> of variance.
>
> As one begins to understand (and ultimately embrace) the wild swings
> they will face in any form of poker, they will be better protected
> from the irrational poison that is tilt. Carefully rendered reason is
> one cure for this complex and perilous emotional state. We should also
> remember that variance is also a factor in all of our positive
> results: winning more coin flips than not is often the difference that
> helps you cash in a SNG or go deep in a tournament. When one fails to
> recognize that their positive results are often dependent on running
> better than average, their experience of a downswing will have a much
> harsher emotional effect.
>
> Another way to protect against variance-related tilt is to always be
> playing with a comfortable bankroll. You will be less affected by
> variance if you lose a smaller portion of your bankroll when you
> experience a downswing. This makes it easier to escape from a
> downswing; your mental mood will be on a more even keel, less clouded
> by loss and more focused on making good decisions. When you play over
> your head, the effects of variance will be exacerbated. The ups and
> downs are that much harder to handle, and this can lead to a poker
> player's tunnel vision: an analysis of their short term results will
> dominate perception, leading one to make severely incorrect judgments
> about their game. Remember that poor short term results do not
> necessarily equate to poor play.
>
> If you are mentally prepared for a downswing, you will be better
> protected from the desire to unnecessarily overhaul your game. You
> might simply be experiencing a nasty but mathematically reasonable
> downswing, which you simply need to play yourself out of. If you find
> yourself unable to make speculative but long-run profitable moves (and
> are constantly questioning these moves when they don't work), you are
> probably misunderstanding the ever present role of variance.
>
> In large field MTT poker where most of our profit comes from making
> the top 3 spots, we have to be especially prepared for large
> downswings. Even the very best MTTers will finish in those top few
> spots only a small percentage of the time. And just like in the dice
> example, anytime a desired result occurs only a small percentage of
> the time, a statistically reasonable downswing can get pretty massive
> and extreme. For example, a standard U.S. quarter has 1 chance in
> 1,024 of coming up heads 10 times in a row. One chance in a thousand
> isn't very likely, but if there are approximately 10 million online
> poker players, and all 10 million tried flipping a coin 10 times in a
> row, then about 10,000 of the players would have a result of 10
> heads.
>
> Similarily, this means that if you viewed an MTT in terms of big
> scores, with a big score occuring let's say 1 out of every 100 mtts on
> average, then this means there would be 1 chance in 1,024 of going for
> 1,000 straight MTTs without a single big score. Or if a big score
> came on average only once every 200 mtts, then there would be 1 chance
> in 1,024 of going 2,000 straight MTTs without a single big score. The
> crazy thing is that this could happen to even a very good MTT player
> if most of their tourneys have 1,000-2,000 entrants, even if they have
> a solid 70% ROI. This example wouldn't be all that odd, statistically.
>
> Below is a video on how to use an ROI simulator that calculates any
> number of sample sizes and expected distributions of variance.
>
> http://www.youtube.com/watch?v=sELOkX9Ra2g
>
> It can be downloaded from this link:
>
> http://www.rvgsoftware.com/roisimulator.zip
>
>
> Hopefully this article will help people gain a more solid grasp of the
> kind of variance that is normal for poker players, so they can temper
> their expectations accordingly.




 
Date: 04 Jan 2009 22:25:18
From: joeturn
Subject: Re: Understanding the Mathematical Concept of Variance
Mathmatical variences have nothing to do with online poker cheats!!