Major Problem with Bill Chin's Article on Variance [Archive]

brianmarc

08-09-2005, 09:51 AM

I believe there is a major, possibly even fatal flaw with all the work currently done on gambling variance - the use of standard deviation as the measure of the variance being measured. SD assumes the distribution of observations is symmetrical around the mean; i.e., that the normal distribution is the correct statistical model to use. However, this is often not the case: a successful player will have a significantly positively skewed distribution of returns, and vice versa for the consistent loser. This means that even if the better player has a high SD, much of it will be "good" variance. Again, vice versa for the loser. The conclusion is that a better measure of this variance is the 2nd degree lower-partial moment (LPM2). LPM2 essentially captures just the variances below the mean and, since it is distribution-free it avoids the fatal flaw of SD in an asymmetric world. In the financial investment world where this measure has replaced SD, LPM2 is known as "Downside Risk", and has now become the risk measure of choice for the non-normal investment distributions that are typical for derivative and hedge fund strategies. For addition material on this concept see my website www.investmenttechnologies.com. (http://www.investmenttechnologies.com.)

RedManPlus

08-09-2005, 01:06 PM

I agree with this.

Finally a lone voice of reason...
In repsonse to the chorus that...
"You gotta play 5,000,000 SNGs before your results mean anything".

Your point in analogous to using the Sharpe Ratio...
To quantify risk/reward for a hedge fund...
Which is ridiculous...
Because the Sharpe Ratio penalizes upward/downward variance equally.

I manage a small hedge fund (about $1 million)...
And if I'm averaging a 25% return...
But have a big year and do 50%...
The Sharpe Ratio penalizes me for "variance".

Simply analyzing your drawdowns...
To quantify the most important thing - "downside risk"...
And is far more meaningful then misapplied stats.

You are very perceptive to have a gut feeling...
That the way the "geniuses" around here...
Apply off-the-shelf freshman stats...
To very exotic games such as SNGs...
Is equally ridiculous.

The dogma they push...
Would result in the conclusion...
That winning the WSOP is not "statistically significant"...
Becuase you only play about (a guess) 2000-3000 hands to win.

I suspect that smart, good players...
Have far less variance...
Than what is "conventional wisdom" around here.

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fyodor

08-09-2005, 05:26 PM

For a statistical ingnoramus how would one go about calculating downside risk (LPM2) with PokerTracker numbers?

AaronBrown

08-09-2005, 06:36 PM

Without disputing your argument, the rationale for standard deviation is generally based on the Central Limit Theorem rather than the symmetry of the underlying distribution. If you add up enough independent observations, whether Poker hand outcomes or daily portfolio returns, only the mean and variance matter. The shape of the distribution washes out.

Say your successful player with the positively skewed distribution loses $10 on nine hands in ten and wins $200 on the tenth hand. The unsuccessful one has the opposite pattern, making $10 on nine hands in ten and losing $200 on the tenth hand. All hands are independent. The successful one makes $10 per hand, the unsuccessful loses $10, but both have the same $63 standard deviation.

After 1,000 hands, the distribution of total profit and loss is almost indistinguishable from Normal in both cases. Average profit per hand will be plus or minus $11 with a standard deviation of $2. The probability that the successful player is between $9 and $11 is 34.7%, versus a Normal approximation of 34.1%. The probability that the unsuccessful player is one standard deviation below his mean (-$13 to -$11) is 33.6%. The probability that the successful player is between $7 and $9 is 14.1%, versus 13.6% in a Normal, and also 13.6% for the unsuccessful player being two standard deviations below his mean ($15 to -$13). So knowing the standard deviation per hand, and the mean, tells you almost all you need to know about the long term distribution of outcome.

I think the more important issue is independence. Poker hands are not independent, neither are hedge fund returns. Even small deviations can skew these calculations.

AliasMrJones

08-09-2005, 06:49 PM

[ QUOTE ]
I suspect that smart, good players...
Have far less variance...
Than what is "conventional wisdom" around here.

[/ QUOTE ]

And...
I suppose...
The fact that smart, good players...
with significant gains...
over a large sample of hands...
have had the significant downswings...
predicted by the "freshman statistics"...
and, in fact, are usually the ones warning about variance...
means nothing.

StellarWind

08-09-2005, 07:21 PM

Well I see that your post is still here.

Maybe I was mistaken in thinking this was just a clever off-topic plug for your investment business website /images/graemlins/confused.gif?

[ QUOTE ]
I believe there is a major, possibly even fatal flaw with all the work currently done on gambling variance - the use of standard deviation as the measure of the variance being measured. SD assumes the distribution of observations is symmetrical around the mean; i.e., that the normal distribution is the correct statistical model to use. However, this is often not the case:

[/ QUOTE ]
I'm very surprised to hear that the normal distribution is not a good approximation for ring-game poker, blackjack, and similar gambling activities. Do you have any evidence or explanation for this?

[ QUOTE ]
a successful player will have a significantly positively skewed distribution of returns, and vice versa for the consistent loser. This means that even if the better player has a high SD, much of it will be "good" variance. Again, vice versa for the loser.

[/ QUOTE ]
This is just a restatement of the obvious fact that the distribution of a winning player's results will be centered on a positive mean (his win rate). It in no way shows that the distribution is not normal.

[ QUOTE ]
This means that even if the better player has a high SD, much of it will be "good" variance.

[/ QUOTE ]
Again, why would I expect favorable and unfavorable variance events to be anything other than equal (on average)? Surely you are not going to define "bad" variance to mean losing? A month where you only win half as much as your average rate is certainly an example of unfavorable variance.

All the research I've read on bankroll requirements fully integrates a player's win rate as an important parameter. Everyone knows that a winning player's results are "positively skewed". Unless you can back up your assertion that results are not approximately normally distributed, you have added nothing.

BillC

08-09-2005, 09:00 PM

The use of the normal distribution arises from the belief that bets (or an hour of play, or sets of 100 hands) are approximately independent. The net result of independent bets converges (with increasing number of trials) to a normal random variable. If you think the independence of bets or sets of bets does not approximately hold, it might be interesting to hear why.

The beauty of simple games of chance such as poker and blackjack, as opposed to say financial instruments, is that our assertion of approximate normality is much easier to justify (because of the ramdomness of the shuffle. please do not take this as bait).

That being said, it would be interesting to see data to suggest that (say for sets of 100 hands) results are or are not approximately normal or symmetric, i.e. that they are skewed. Anyone have data on this? I would be surprised to see any sinifigant skewing.

The normal/Brownian motion model is a continuous approximation of a discrete reality, and the speed of convergence to the idealized model can be hampered by skewing. In the case of skew, larger samples are needed for accurate predictions.

The poster above may be confusing positive EV with skewing in the sense that the distribution of results is asymmetric about the mean.

AaronBrown

08-09-2005, 09:50 PM

[ QUOTE ]
If you think the independence of bets or sets of bets does not approximately hold, it might be interesting to hear why.

[/ QUOTE ]
Players will change their play as they win and lose. One common pattern is to loosen up when you win, but fail to tighten up when you lose. The gambler's ruin theorem means you will almost always be a big loser with this rule, even if you have positive expectation per hand. This violates independence and, with a player like this, I would base my long-term prediction of his wealth on his poor strategy rather than the mean and standard deviation of individual hands.

Another dependence is bluffing. If a player is caught in a bluff, he will be played differently on future hands. That's the point of bluffing.

AliasMrJones

08-09-2005, 10:10 PM

[ QUOTE ]
[ QUOTE ]
If you think the independence of bets or sets of bets does not approximately hold, it might be interesting to hear why.

[/ QUOTE ]
Players will change their play as they win and lose. One common pattern is to loosen up when you win, but fail to tighten up when you lose. The gambler's ruin theorem means you will almost always be a big loser with this rule, even if you have positive expectation per hand. This violates independence and, with a player like this, I would base my long-term prediction of his wealth on his poor strategy rather than the mean and standard deviation of individual hands.

Another dependence is bluffing. If a player is caught in a bluff, he will be played differently on future hands. That's the point of bluffing.

[/ QUOTE ]

The statements above are complete claptrap. A player with a losing strategy CANNOT have long term positive expectation and a player with a winning strategy CANNOT have negative long term expectation. This is by definition. Therefore, someone who employs the strategy you outline above (loosen up when winning, but fail to tighten up when losing) will not have a winning strategy and WILL NOT have positive per hand expectation. Do you see why?

Just because a player is caught in a bluff one hand and players may play him differently on the next hand does not mean his long-term winrate and SD will change. In fact, a good player will mix bluffs into a well-rounded strategy and will be caught sometimes. This will already have been factored into the players long-term winrate and SD, assuming the sample size is large enough.

Your problem is you seem to be focused on small samples (i.e. per hand vs. long term strategy in the first part and how 1 caught bluff will affect a small number of subsequent hands.)

As I said before, the predicted results of winrate and SD with the regularly discussed formulas have been proven out through observed results of real players with sufficiently large sample sizes and posted about on this forum.

uuDevil

08-10-2005, 01:01 AM

[ QUOTE ]
SD assumes the distribution of observations is symmetrical around the mean; i.e., that the normal distribution is the correct statistical model to use.

[/ QUOTE ]
Whether or not the assumption of normality is justified, calculating the standard deviation requires no knowledge of the shape of the distribution. It would be a valid statistic, whatever the distribution. Or am I crazy?

StellarWind

08-10-2005, 02:13 AM

[ QUOTE ]
Whether or not the assumption of normality is justified, calculating the standard deviation requires no knowledge of the shape of the distribution. It would be a valid statistic, whatever the distribution. Or am I crazy?

[/ QUOTE ]
You're not crazy. The SD computation is valid regardless of the distribution.

However poker players often use the resulting SD value in ways that might not be valid for distributions that aren't approximately normal. Such as computing the probability that a 2 BB/100 player with SD = 15 BB/100 will experience a loss over a given set of 2000 hands.

BillC

08-10-2005, 04:59 PM

I am not sure how useful a statistic like semivariance (or downward deviation really is. It would seem to depend on the type of distribution one has. I have not seen any mathematical development of it. All there seems to be is a bunch of financial types throwing around sample numbers. The virtue of standard deviation as a measure of disperion about he mean is that you can actually prove theorems about its use, e.g. Chebyshev's theorem, Central Limit Theorem. There doesn't seem to be any theory for downward deviation, which seems to be more of seat-of the-pants sort of measure. But hey most poker discussion is pretty much wild-ass speculation, so maybe that's OK...

Btw, One can bet (fractional) Kelly and practice risk-management with skewed distributions. This is done usefully in video poker (for determining bankroll and bet size) and it is what I do in my article for evaluation long-shot bets. But for highly nonnormal situations, you may not be able to just use one or two parameters, such as mean variance (or semivariance!) -- anyone that tells you so is selling snake oil.

An example of a really skewed bet: Sklansky's Zillion-to-one bet that the proof of Fermat's last Theorem is wrong.

AaronBrown

08-10-2005, 07:42 PM

[ QUOTE ]
The statements above are complete claptrap. A player with a losing strategy CANNOT have long term positive expectation and a player with a winning strategy CANNOT have negative long term expectation. This is by definition. Therefore, someone who employs the strategy you outline above (loosen up when winning, but fail to tighten up when losing) will not have a winning strategy and WILL NOT have positive per hand expectation. Do you see why?

[/ QUOTE ]
It's not that simple. It is entirely possible to have a positive per hand expectation, and be 100% certain of losing all your money. For an example, suppose I bet you at even odds that the Ace of spades will be dealt first from a well shuffled deck. You clearly have a positive expectation. But if you play me double or nothing at this game until you lose, you will certainly lose eventually. The only question is how long it will take.

The same thing is true of a gambler who has a positive expectation on each bet, but increases his bets when he wins and doesn't reduce them when he loses. Say you're flipping coins with me and I pay you 2:1 each time you win. Again, you have a positive expectation on each bet.

You start with $10 and bet $1. You always bet 10% of your stack or your last bet, whichever is greater. Sooner or later you will lose ten flips in a row and lose all your money. This is the gambler's ruin theorem. Positive expected value on each bet does you no good if you have a pathological strategy. Ever wonder why casinos keep increasing the denomination of your chips if you win?

Kelly is an attempt to exploit this insight for gain rather than loss.

[ QUOTE ]
Just because a player is caught in a bluff one hand and players may play him differently on the next hand does not mean his long-term winrate and SD will change.

[/ QUOTE ]
His long-term winrate and standard deviation do not have to change, that's the point. As long as the hand results are not independent, the long-term distribution of outcomes may not resemble a Normal distribution. And the long-term standard deviation may not be the per hand standard deviation times the square root of the number of hands.

StellarWind

08-10-2005, 08:52 PM

[ QUOTE ]
You start with $10 and bet $1. You always bet 10% of your stack or your last bet, whichever is greater. Sooner or later you will lose ten flips in a row and lose all your money. This is the gambler's ruin theorem. Ever wonder why casinos keep increasing the denomination of your chips if you win?

[/ QUOTE ]
I assume the casino would do this because they have an edge and they hope you'll increase the amount of action you give them.

It's ironic that you would give this practice as an example because it's the opposite. Your own theorem shows that if the casino carried coloring up customers and taking ever-larger bets to its ultimate extreme the casino would eventually go bankrupt. Gambler's ruin is a problem for the side that is +EV.

RedManPlus

08-10-2005, 08:56 PM

Dude...
This an internet forum filled with sociopaths...
As are 100% of internet forums.

There is constant gamesmanship going on around here...
With the veterans abusing the newbies.

Misusing statistics to invalidate other people's results...
Is part of that gamesmanship.

This place gets better every day...
Because I now have about 50 nut bars on ignore.

Your assumption that a "good player's" downturn...
Is automatically due to expected variance...
Is ridiculous.

It's equally likely that the player in question...
Is bored...
Has a drinking/drug problem...
Is suffering from erectile dysfunction...
Has emotional problems or personal crises...
Needs to have his medication adjusted...
Is watching porn while he 4 tables...
Or all of the above.

The variance in SNG play is not very high...
Maybe a 20 buy-in downswing every few months...
On the backdrop of a 15-20% ROI...
With no significant capital investment.

It's hard to imagine a better business model.

I trade about $2,000,000 in stock every day...
And have been dealing with risk and variance...
In a ** real world way ** for 10 years...
So I have a better gut feeling...
About what is statistically bogus...
Than some egomaniacal grad student.

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AngryCola

08-10-2005, 09:33 PM

[ QUOTE ]
gut feeling

[/ QUOTE ]

Gut feelings are meaningless in statistics.

Use facts or actual theories to back up your arguments. I saw neither in your post. All you did was insult everyone who actually posted facts and/or theories without providing any reasonable alternatives of your own.

I'm inclined to listen to people who will actually discuss issues more than those who throw around insults consisting of vague assertions and a murky claim of expertise.

RedManPlus

08-10-2005, 10:06 PM

[ QUOTE ]
[ QUOTE ]
gut feeling

[/ QUOTE ]

Gut feelings are meaningless in statistics.

Use facts or actual theories to back up your arguments. I saw none of that in your post. All you did was insult everyone who actually posted facts and/or theories without providing any reasonable theories and/or facts of your own.

I'm inclined to listen to people who will actually discuss issues more than those who throw around insults with nothing behind it besides vague assertions and a murky claim of expertise.

[/ QUOTE ]

Sir, it is those exact "gut feelings"...
That separate a Poker Champion...
For the also rans.

I have a degree in Computer Science...
With a heavy emphasis on stats/mathematics...
From the University of Toronto.

I have made over 200,000 trades on the NYSE...
Over the last 10 years...
And make a very good living...
Using very sophisticated quantitative analysis.

The stock market world is overrun...
With completely bogus statistical fallacies...
That are packaged and marketed as "financial products"...
Designed to fleece the average investor.

The vast majority of "truth" out there is nonsense.
So the ability to dismiss such nonsense...
In 5 minutes...
Without resorting to complex, time consuming analysis...
Is the ** essence of business/life experience **...
Which would obviously be lacking...
In a student who has never had a serious job...
Or never run a successful business.

Angry Cola,

Why would you take the time...
To send me a bizarre email yesterday...
Criticizing my writing style?

Shall I post your email?

Mr. Sklansky has made this forum a bastion of free speech...
And you don't like it.

There can be a fine line between being a mod...
And being an ** angry stalker **.

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AngryCola

08-10-2005, 10:09 PM

[ QUOTE ]
And you don't like it.

[/ QUOTE ]

No, I simply brought up a few issues which you have still failed to really answer.
But that's fine.

Also, I was only responding to your attack on members of these forums. Do not act like your post wasn't an attack on people who post here.

[ QUOTE ]

Why would you take the time...
To send me a bizarre email yesterday...
Criticizing my writing style?

[/ QUOTE ]

Actually, I just asked why you chose to write the way you do. I then explained that your points would be taken more seriously if you used regular paragraph breaks. I had no idea you would take it so personally.

[ QUOTE ]

There can be a fine line between being a mod...
And being an ** angry stalker **.

[/ QUOTE ]

So, sending you one PM, answering your replies, and replying to your attack on posters in this forum equates to stalking?
I think not.

[ QUOTE ]

Mr. Sklansky has made this forum a bastion of free speech...

[/ QUOTE ]

This is not true, but your sentiment is appreciated.

RedManPlus

08-10-2005, 10:24 PM

I re-read my post...
And I don't see any specific "attack" on anyone.

I just made some general statements...
About the reality of internet forums...
Most of which are a pretty hard place.

And some examples of how people sabotage their poker EV...
By boredom, drinking, etc.
And then blame it on "variance".

Half the post was a big joke.

You need to lighten up...
This is just an internet forum about poker.

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AliasMrJones

08-10-2005, 11:19 PM

[ QUOTE ]
The variance in SNG play is not very high...
Maybe a 20 buy-in downswing every few months...
On the backdrop of a 15-20% ROI...
With no significant capital investment.

[/ QUOTE ]

Again you're making statements without knowing what the [censored] you're talking about. Have you spent much time in the STT forum? The simulations using SD and ROI (the STT equivilent of winrate) show larger than 20 buy-in drops. And guess what. VERY GOOD STT PLAYERS HAVE SHOWN THOSE SAME LARGER DROPS. Have you seen posts by IrieGuy? ZeeJustin?

Here's a snippet from ZeeJustin's report about his 1,000 SnG in a month quest:

------
My goal was to make 30k in this quest, so things were going very well, until they took a turn for the worse. After that, I went on the biggest downswing I have ever had at the $200+15 level, and lost $8,500.
------

That's a 39 buy-in downswing. And this is from a guy who made almost $30,000 playing those 1,000 $215 SnG's in a month.

I'm sorry to burst your bubble with real-world results. I agree that SnG's are a great deal. I play them myself. But, I don't care what you think about your "gut feeling" for this stats stuff. Real world results agree with the "freshman statistics" and disagree with your "gut".

RedManPlus

08-11-2005, 12:11 AM

So I said 20 buy-in drawdown...
And you found one that was 39...
At a completely different level.

How does that invalidate my point...
That low end SNGs are a very low risk business proposition?

And exactly why is a 20-30 buy-in downswing a disaster?
Seems pretty normal to me.

I've read several articles on ZeeJustin's web site...
And he is definitely not playing Party 22s.

The higher you go...
The lower your ROI...
The higher your variance...
The greater your potential downswings.

It also matters if you play a very aggressive push game...
As opposed to using more finesse.

I have a database of about 2000 SNGs...
Mostly Party 22s and 33s from June-Aug ...
And then I label all the Party Leaderboard guys.

When I set the minimum to 10 tourneys played...
I'm left with 33 players.

Of these 33...
10 are June or July Top 100 Leaderboard players...
With tournies played ranging from 10 to 50.

Of these 10...
7 are way up, 2 break even...
And only one is on a 10 game downturn.

As a group these 10 people (9 guys and 1 lady)...
With a sample size of about 200 tournies...
Are just ** totally cleaning up **...
Just crushing the weak opposition.

My personal biggest downswing so far is 5-6 buy-ins...
Which is virtually erased by 1st place finish.

This is risk?
I need fancy stats for what?

I just don't see it...
Unless you are a homeless man with $200 in your shoe.

At the low end Party SNGs...
The Leaderboard players TOTALLY OUTCLASS their opposition...
Play 30-40 per day...
And just leave variance in the dust.

The only people sweating variance...
Are the marginal, undercapitalized subsistence players.

You know...
The ones that shouldn't be trying to play poker for a living.

Are you one of those guys?

Don't be.

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AaronBrown

08-11-2005, 09:04 AM

[ QUOTE ]
It's ironic that you would give this practice as an example because it's the opposite. Your own theorem shows that if the casino carried coloring up customers and taking ever-larger bets to its ultimate extreme the casino would eventually go bankrupt. Gambler's ruin is a problem for the side that is +EV.

[/ QUOTE ]
I think you're crediting me with a bigger point than I'm trying to make. The original post said that standard deviation was not useful when the underlying distribution was not symmetric. I replied that if you have enough independent outcomes, the shape of the underlying per-bet distribution doesn't matter much, and standard deviation is useful for long-term risk analysis. But if you don't have independence, standard deviation of individual bets can be an unreliable guide to long-term risk.

The Poker and casino examples were answers to the question of why someone might think individual bets were not independent. I'm not claiming that these effects are enough to invalidate standard deviation in Poker or casinos. It's all theory.

You're entirely correct that a casino that chipped up forever would eventually go broke. However large their customer base, someone would win 20 in a row betting black on roulette, or take every hand in six decks of blackjack, or have a similar streak at the craps tables. That's why casinos also have maximum bet limits. It's surprising to a lot of people how low those limits are relative to the available capital and daily profits of the casino, given how big the house edge is. But even a huge casino would face a significant probability of bankruptcy if it followed a gambler's ruin strategy.

The real point of chipping up, as you say, is to maximize profit, since the casino makes more money from a large bet than a small one. But it also has the desirable effect (from the casino's point of view) of increasing the standard deviation of customer outcome. A casino with a 40% average drop doesn't want every customer to walk out with 60% of their initial stake. Too much money walks out the door to other casinos, and people would stop coming back. It's much better if lots of people lose all their money, but a few walk away with big wins. That's good advertising, since people always exaggerate the amount and frequency of these events. Plus, those winners will take their money home, and return to lose it later, rather than stopping into the casino next door. Chipping up helps most winners go broke, but a few winners become spectacular winners. Whenever you see those pictures of big winners with giant checks, think "chipped up," just as bulging muscles these days make you think "steroids."

In Poker, one hand influences the next. It may well be true that these effects average out over a hour or two of play, or don't exist at all with good players. But certainly with bad and average players, if a guy is caught in a bluff, he's more likely to get called the next time he bets big; while if he wins with a strong hand, he's less likely to be called. Also, big losers often become looser, or even move to a higher stakes table to try to recoup their losses.

BillC

08-11-2005, 01:29 PM

[ QUOTE ]

.

My personal biggest downswing so far is 5-6 buy-ins...
Which is virtually erased by 1st place finish.

This is risk?
I need fancy stats for what?

I just don't see it...
Unless you are a homeless man with $200 in your shoe.

At the low end Party SNGs...
The Leaderboard players TOTALLY OUTCLASS their opposition...
Play 30-40 per day...
And just leave variance in the dust.

The only people sweating variance...
Are the marginal, undercapitalized subsistence players.

You know...
The ones that shouldn't be trying to play poker for a living.

Are you one of those guys?

Don't be.

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[/ QUOTE ]

If you aren't paying attention to variance at all, then maybe you are playing stakes that are too small for yur bankroll. Or maybe your skill level doesn't allow you to play higher.

I agree that SNGs are statistically superior to a lot of other poker endeavors at low stakes. The problem is that they get a lot tougher as you go up. I can crush the 20$ SNGs, but it is pretty small potatoes; its like working for minimum wage.

AliasMrJones

08-11-2005, 01:30 PM

[ QUOTE ]
At the low end Party SNGs...
The Leaderboard players TOTALLY OUTCLASS their opposition...
Play 30-40 per day...
And just leave variance in the dust.

[/ QUOTE ]

This just plain old isn't true. You have implied in your previous postings that the variance is small, that is not as large as the "freshman statistics" say it will be for good players. I have provided real-world evidence to the contrary. Now you change your story to only be referring to low buy-in STT's. Guess what. Even very, very good STT players who "totally outclass" the competition do not "leave variance in the dust." They experience variance as well, however they 1) know to expect it and are sufficiently bankrolled to absorb the variance and 2) play so many per day/week that the variance is a bump in the road that they are past relatively quickly. That is not to say they don't feel it at all -- reference the ZeeJustin 39 buy-in drop blog entry. And his is not the only mention of drops like this. Other good players have posted about drops like this at every level in the STT forum.

RE: your database. Wow -- 200 whole tourneys on these guys, huh? That's some ginormous sample size you have there. It's basically meaningless. There are guys who post in the STT forum about how great they are. They can crush the STT's. They have sample sizes around that range. Guess what -- it doesn't last. 200 tournies is NOTHING. You can get someone's ROI to within +/- 22 percentage points with that sample size. At that point, you're just beginning to be able to say your a better than break even player, let alone how much better than break even you are.

Are STT's a nice money-maker? Yes. Is variance smaller than limit ring game play? Unquestionably. Is variance and are downswings larger than you are saying? Absolutely yes. The statistics predict it and real-world results (with sufficient sample sizes) from very good players confirm it.

RedManPlus

08-11-2005, 05:23 PM

[ QUOTE ]

If you aren't paying attention to variance at all, then maybe you are playing stakes that are too small for yur bankroll. Or maybe your skill level doesn't allow you to play higher.

[/ QUOTE ]

Right on both counts...

But I haven't started for real...
Because I'm reworking my trading infrastructure...
To allow me to manage high volume SNG play...
In the same way that my software allows me to make 100 trades/day on the NYSE.

"too small for your bankroll"

I idea is not to "optimize" earnings by magnifying risk...
(This is for gamblers)...
But to grind out profits with ZERO medium to long term risk.
I'll explain later.

[ QUOTE ]

I agree that SNGs are statistically superior to a lot of other poker endeavors at low stakes. The problem is that they get a lot tougher as you go up. I can crush the 20$ SNGs, but it is pretty small potatoes; its like working for minimum wage.

[/ QUOTE ]

You are underestimating...
The amount of money Leaderboard Players make on SNGs.

Because the Party Leaderboard formula is non-linear...
And skewed to the low end games...
Roughly 50% of the Leaderboard guys are playing $22 and $33.

It's trivial to reverse engineer the Leaderboard...
And ** estimate ** how much people are making.

This is a correction...
To the numbers I posted a few days ago:

#1 $12,000/month
#50 $4,500/month
#100 $3,500/month
#200 $2,500/month (probably high)
#300 $2,000/month (probably high)

The 200-300 range is probably high...
Because you can make zero money and place this high...
Just on sheer volume played.

If I can be #50-#100 in 6 months and skim $3,000/month off SNGs...
Then it's worth my while as a sideline...
But ONLY because I have a 6 figure income trading stock.
(And poker is just so damn interesting mathematically).

In conclusion:

Real world Pros... whether it's stock trading or poker...
Are expert at risk management that eliminates serious damage.

If you have a big 20% edge in the Game...
Your losing streaks consist of breaking even for a while...
And your winning streaks consist of doing 30-40% for a while.

Repeat...
Your "losing streaks" consist of breaking even for a few weeks.

Gambler's ruin does not even come into play...
For properly capitalized players with a Big Edge.

Two examples of "properly capitalized players with a Big Edge" are...
Most of the Leaderboard SNG players...
About 10% of hedge fund managers.

For example...
I have a Big Edge in the stock market...
Significantly bigger than a comparable 20% SNG ROI edge...
And over 5 years my hedge fund Units have tripled in value (up 200%)...
While my biggest drawdown in 5 years has been about 4%.

I might be concerned about variance 20% of the time...
But mostly it's been 90% arbitraged out.

Hard to believe?

Well... Edwin Thorpe...
The father of blackjack counting...
Still runs a similar, but much larger, operation...
Makes 3000 trades/day and has results similar to mine.
(Google Thorpe and learn a lot).

I read the article by Chin...
And it's stuff I knew when I was 18.

If someone doesn't have the sense...
Or the means to put together $10,000 for a 500 buy-in $22 SNG bankroll...
Why in the world should I take that person seriously?

If someone needs Chin to tell them very basic stuff...
It's extremely unlikely that person is going places.

When I start doing 30-40 SNGs/day...
A $10,000 bankroll which is 5% of my net worth...
Will leave me with no worries about variance...
And risk/reward ratio of $10,000 invested...
With expectation of $2,000-$3,000/month in profit.

In conclusion:

As a general rule...
The losers and marginal players around here...
Give themselves away with their obsession with variance.

And a marginal player is the Mother of all Fish...
Because that person has sacrificed everything...
To make a dreary, subsistence level "living" at poker.

Reading posts by losers is a waste of time.
But yours was nice, Professor.

Regards,

rm+

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AliasMrJones

08-11-2005, 06:09 PM

[ QUOTE ]

If you have a big 20% edge in the Game...
Your losing streaks consist of breaking even for a while...
And your winning streaks consist of doing 30-40% for a while.

[/ QUOTE ]

Please defing "big 10% edge". You're spouting a bunch of flim-flam and pseudo-mathematics without any real supporting proofs or real-world observed results. Your 200 sample results and "reverse engineered" assumptions don't count. Average $ won per month has nothing whatsoever to do with variance.

For a good player, with 95% confidence, about 200 SnG's is enough to ensure breakeven. If a very good player plays 200 SnG's in a week, then for any weeklong span that player has a 95% chance to come out breakeven or better. During that week, however, they could be down 20, 30, or more buy-ins. And then there's the 5% chance that they end up worse than breakeven...

RedManPlus

08-12-2005, 11:39 AM

Most academic types...
Have been notoriously unsuccessful in the financial markets.

One reason for this...
Is that they believe that using overly complex mathematical approaches...
Can somehow defeat their true opponents...
Who are the sophisticated market pros...
Like a CBOT floor trader or NYSE market maker...
A top Wall Street firm or a top Hedge Fund Manager.

I've been doing this for 20 years...
And you cannot use complex math...
To take money away from Market Pros...
(Or World Class Poker players for that matter).

Market pros develop shortcuts...
That closely approximate high level math...
(As do World Class Poker players).

Also...
Market pros will have a significant advantage...
Using ** real world ** risk management techiques...
Which incorporate knowledge and analysis...
Which is not easily quantified by high level mathematics.

They will crush the academic type in the long run.
(As will a World Class Poker player).

What works best is a simple rational concept...
In a very well defined market niche...
And extemely disciplined implementation with low transaction costs.

Generally...
When I read about some academics starting a hedge fund...
Using some complex mathematical approach to the markets...
I laugh...
Because they are out of their depth...
And the stock market pros will eat them for lunch.

Regards,

rm+

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chezlaw

08-12-2005, 12:27 PM

[ QUOTE ]
Market pros will have a significant advantage...
Using ** real world ** risk management techiques...
Which incorporate knowledge and analysis...
Which is not easily quantified by high level mathematics.

[/ QUOTE ]

How do you know these '** real world ** risk management techiques' work ?

chez

BillC

08-12-2005, 01:10 PM

[ QUOTE ]

Market pros develop shortcuts...
That closely approximate high level math...
(As do World Class Poker players)..
...
What works best is a simple rational concept...
/images/graemlins/cool.gif /images/graemlins/cool.gif /images/graemlins/cool.gif

[/ QUOTE ]

You want it both ways...
You want to approximate high-level math...
by using shortcuts...
But where do you get the shortcuts...?

And...
the simple rational concept will always lead to...
mathematical analysis...

Ellipsis ad infinitum...
ad nauseum.

RedManPlus

08-12-2005, 01:16 PM

I would define a "market pro"...
As someone with at least 10 years of experience...
Managing, say, $1 million or more...
And trading very actively (> 50 trades/day)...
So this is a pro who has made >100,000 trades...
** Over an entire bull/bear market cycle **.

I would especially totally eliminate anyone...

That has a good 1-2 year track record and nothing more...
Because that person is likely a "lucky coin flipper".

Now I will give you a simple stock hedge...
A typical "risk arbitrage" position for a market pro...
For example,
Hedging GM (common stock)...
Versus GXM (convertible debenture unit trading on the NYSE).

Now what are the 10 things that can go wrong with that position?
What are the various risks?
Convertible specific risks?
NYSE specific risks?
Short sale specific risks?
Liquidity risks?
Market risks?
Industry risks?
Company performance and credit risks?

Is something goes wrong... exactly what do you do?

Well...
Mathematics cannot give you the answer to those questions.

Only through experience (taking losses and learning)...
Will you know all of the (mostly rare) things that can do wrong...
And whether to avoid that position entirely...
Or how to manage it and limit risk...
Or when to get out.

For example...
I would avoid that position entirely...
For at least 3 good reasons.

But there are no books...
Or academic papers that can teach you this...
Only 10 years and 100,000 trades.

It's very much an art form learned through experience...
Just like World Class level poker play.

rm+

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AliasMrJones

08-12-2005, 01:45 PM

[ QUOTE ]
It's very much an art form learned through experience...
Just like World Class level poker play.

[/ QUOTE ]

More flim-flam. More pseudo-science.

You're confusing playing poker with measuring variance and predicting the peaks and valleys of a bankroll. These are two very different things. There is "feel" in playing NLHE. There is no "feel" to measuring and predicting variance.

There is a degree of luck involved in poker over the "short term." This degree of luck cannot be overcome by expert play, nor by "feel", nor by experience. It is constant. Experience can give one an edge over a less experienced opponent, but not over a random event like which of 47 remaining cards will fall next. This means there is a hard limit to the edge a player, even a world class player, can have over the "short term." Witness the poor play that is often rewarded on TV poker.

With as much text as you're written in this thread, you still have yet to provide any theoretical proof or real-word evidence (with more than a sample size of 200) for any of your claims about variance in Poker.

08-14-2005, 04:05 PM

This is not correct. The stdev is a measurment of distrubution about the mean; it is not a measuremeant of distribution about 0 (breaking even). The fact that a winning player will have larger positive swings than negative swings means that the player will have a positive mean, but that doesn't imply anything about the distrubution about the mean.

2ndGoat

08-19-2005, 07:49 AM

[ QUOTE ]
Dude...
This an internet forum filled with sociopaths...
As are 100% of internet forums.

There is constant gamesmanship going on around here...
With the veterans abusing the newbies.

Misusing statistics to invalidate other people's results...
Is part of that gamesmanship.

This place gets better every day...
Because I now have about 50 nut bars on ignore.

Your assumption that a "good player's" downturn...
Is automatically due to expected variance...
Is ridiculous.

It's equally likely that the player in question...
Is bored...
Has a drinking/drug problem...
Is suffering from erectile dysfunction...
Has emotional problems or personal crises...
Needs to have his medication adjusted...
Is watching porn while he 4 tables...
Or all of the above.

The variance in SNG play is not very high...
Maybe a 20 buy-in downswing every few months...
On the backdrop of a 15-20% ROI...
With no significant capital investment.

It's hard to imagine a better business model.

I trade about $2,000,000 in stock every day...
And have been dealing with risk and variance...
In a ** real world way ** for 10 years...
So I have a better gut feeling...
About what is statistically bogus...
Than some egomaniacal grad student.

rm+

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[/ QUOTE ]

Do you guys know that kid on Malcolm in the Middle? The one that has some kind of lung disorder so he can only say a few words at a time before gasping for more air? I kind of got the feeling that kid was talking to me just now.

2nd

benfranklin

08-19-2005, 12:28 PM

[ QUOTE ]
Actually, I just asked why you chose to write the way you do. I then explained that your points would be taken more seriously if you used regular paragraph breaks.

[/ QUOTE ]

To take his points seriously, you would have to read his posts. I am not able to, and quickly gave up on his posts. It's like listening to a little kid talking in a sing-song voice:

La de dah...
La de dah...
La de dah de dah.

It quickly turns into meaningless syllables.

Proper spelling, punctuation, and sentence structure have a purpose. They put ideas into a standard format, so we can concentrate on the ideas without being distracted by the format. People who use non-standard formats for anything other than poetry are pretentious and annoying. But then, poets are pretentious and annoying too.