So i started using *************.com about 2 months ago and i'm really glad i did.. It really shows how profitable i've been and allows me to see what games i'm most profitable at. I really recommend it to any Serious Poker Player.

That being said, the only thing i didn't understand was a stat at the bottom called, "Standard Deviation"

So i googled standard deviation and found that it basically means the "swinginess" of your game, how big your swings and varience are.

What I still do not understand, is that my stat means

It says i have a Standard Deviation of $77 -- What does that mean exactly ? The answer i'm looking for is not, "your tight , your too loose or you have high varience" i want to know exactly what the $77 means? Like does it mean all of my wins are on average $77 apart ? Please help me understand this and help me understand how i can use it to benefit my game?

One way of looking at this statistic: 95% of all your results will occur within a distribution of 2 SDs above the mean down to 2 SDS below the mean.

Thinking about a measure of central tendency will make you realize the boundaries of variance.

If you look up Bollinger Bands, you will see a stock market method that says when you get 2 SDs above your moving average, it is time to sell. And buy at 2 SDs below that moving average. etc.

^^ I have no idea what you're talking about, or how it relates to my question...

95% of your results will occur between -$154 and +$154 of the mean.

When you googled sd, what did you then go to? The Wikipedia explantion is pretty good.

if I'm a sportsbettor with 10% ROI with a sample of 1000 bets or whatever and my SD is 2.5% this means:

there is a 95% probability that my TRUE ROI is somewhere between 5% to 15%.

95% confidencde interval = mean +- 2xSD

Higher confidence interval -> bigger interval. For example 90% confidence interval would have a more narrow range but on the other hand there is bigger risk that my true ROI is outside that interval.

so confused..

He's right. It's hard to describe standard deviation but it basically measures ur variance. So the higher the number, the bigger ur swings will be

In order to tell you exactly, we need to know what your average win or loss is.

Then if we know what your average win or loss is, we add $77 and subtract $77. And that gives us a range where we should expect about 68% of your future results to fall, assuming you and your opponents will play as relatively well in the future as you have played thus far.

For example, if your average win is $200, and if you and your opponents keep playing at the same level, then we expect 68% of your future results to fall between winning $133 and winning $277.

There's more. We expect 95% of your future wins to be within two standard deviations of the mean (average). For example, if your average win is $200, and if you and your opponents keep playing at the same skill level, then we expect about 95% of your future wins to range from $46 to $354.

And almost all (99.7% or something like that) of your future wins should fall within three standard deviations.

There's a bit more to it, but I think that's the general idea. I think if you go to the probability forum (under general gambling) you'll get a better idea.

Buzz

The standard deviation tells you something about how far the individual results are from the average. In the case of poker, this average is your winrate, and thus the mean distance from the winrate gives you a measure of swinginess.

So once we know the average we could do the following: For each hand we compute the difference between the winrate and the actual result, and compute the average of this quantity over all hands. The problem is that this difference may be positive or negative, so the various hands will cancel each other out, and what we compute will always be 0.

This could be circumvented by taking absolute values. However for various reasons, another approach is more convenient. We compute the difference for each hand, square it, and then take the average. This gives us a good measure on how far the results are spread out. Since squares are never negative we will have no cancellation anymore. This average of the squared differences is what Mathematicians call the variance.

The only problem with variance in this sense is that it is measured in funny units. What we do is take a dollar amount (the difference from the mean) and square it, so its units are basically square dollars (or square dollars per hand). This is not very intuitive, and leads to problems when converting from dollars to cents or big blinds or so. Thus we take this quantity and consider its square root. This is now measured in dollars, so we can compare it nicely to our expected winnings over a given sample. And this square root of the variance is exactly the definition of the standard deviation.

So to answer your question, having a standard deviation of $77 per 100 hands means that the average of the squared distances from the actual results of 100 hand samples to the expected results (as per the winrate) are ($77)^2.

One caveat of this definition is that the standard deviation doesn't grow linearly with the sample size. So if you have a standard deviation of $77 for 100 hands, your standard deviation for 10k hands will be just $770 (instead of $7700 as one might expect). It is therefore slightly inaccurate to state the stddev as dollars per 100 hands.

Let's just put it really simply; Standard Deviation is equal to the square root of variance. Or you can write it as Standard Deviation^2 = Variance

Both are measures of volatility. A higher standard deviation means a higher volatility snd vice versa. An aggressive player will have a huge standard deviation (think Isildur1) whereas a tight aggressive player's standard deviation will be lower.

A high or low volatility doesn't necessarily reflect how profitable you are over time, but with a high volatility you are more likely to bust your bankroll.

Hi Pulazki:

This is a short chapter from my book Gambling Theory and Other Topics. See if it helps you.

Best wishes,
Mason

Fluctuations


Suppose you are an expert gambler. Perhaps you are a poker player, perhaps you are a blackjack card counter, or perhaps you are highly skilled at some other game. It really doesn’t matter where your expertise lies, but let’s assume that you are good enough to win at a rate of $50 per hour in some hypothetical game. The problem is that you won’t win $50 every hour you play. Sometimes you will do better, and sometimes you will do worse (and perhaps even lose). It so happens that there is another measure besides the expected win rate that should be important to you, the winning gambler. This measure is the (statistical) standard deviation.

The standard deviation is a statistical measure of dispersion, and most statisticians agree that for all practical purposes, the total population of possible results is contained within three standard deviations of the mean. For example, suppose your $50 an hour win rate is accompanied by a $500 per hour standard deviation. In this case, a $1,500 swing — either up or down — in an hour is not to be unexpected in your hypothetical game. No wonder some people seem incredibly lucky while others complain that they have been “running bad.”

Let’s now suppose that you, the expert, play your favorite game for 100 hours. Your expectation after this length of time should be $5,000.

5,000 = (50)(100)

However, as just seen, there is a good chance that you won’t win exactly $5,000. You might do better or you might do worse. It turns out that the standard deviation of a sample mean is inversely proportional to the square root of the sample size. That is, after 100 hours, we divide the per-hour standard deviation by 10 (the square root of 100) to get 50.

50 = 500/10

This means that you could be losing as much as $100 per hour or winning as much as $200 per hour.

-100 = 50 - (3)(50)

200 = 50 + (3)(50)

Imagine you, the expert, playing for 100 hours and being down $10,000. Well, it definitely can happen.

Here’s another example for the same hypothetical game. Suppose you have two break-even players, each of whom is experiencing this $500 per hour standard deviation. After 100 hours, it is actually possible for one of these players to be ahead $15,000 and for the other person to be behind by the very same amount.

Even though a $500 per hour standard deviation coupled with a $50 per hour win rate may appear high, these sorts of results are typical for expert gamblers who follow aggressive non-self-weighting strategies available to them and who expect to do well in the long run. It’s just a fact of life. If you correctly gamble for profit — and it doesn’t matter whether your game is poker, blackjack, sports betting, real estate, stocks, commodities, backgammon, progressive slot machines, or something else — there will be times when your bankroll will jump up and down, and there isn’t much you can do about it. In fact, we shall see that what is extremely important is the relationship between your expectation and the standard deviation that you are experiencing. Knowing one parameter without knowing the other often will lead to disastrous decisions, especially if just the expectation is known.

However, before addressing this, let’s analyze one stream of thought that occupies much of the gambling literature dealing with this area. This concept is known as money management, but I prefer to call it “the extremely silly subject of money management.” It is discussed in the next chapter.

Knowing your hourly is most important if youre confident in your ability.

Sent from my piece of **** Samsung using 2+2 Forums

Possibly a stupid question, but with the third standard deviation away from the mean being a confidence interval of roughly 95% meaning that 95% of your result will fall within the third standard deviation... Is the 5% that lies outside the third standard deviation your Risk of Ruin?

grunching....

one big thing is the denominator of your $77 Stdev i.e. $77 std per what? i'd assume 100 hands.

standard deviation is measure of variability as you mention... i think 67% of your results are within 1 stdev, 95% within 2 stdev and i can't remember the exact number but 98 or 99% within 3 stdev...

and the mean would be your win rate NOT zero. although your win rate will be close to zero relative to the $77 stdev so using zero for win rate would probably be fine

Buy Mason's book. He provides an excellent presentation on this topic. BruceZ posts too btw.

I tells you how far your results spread from each other.

Let me show you a arbitrary example.

(5;10;25;-20;-5;3) are you results over 5 hands.
then your mean is 3 per hand and your StDev is 15.

Mean is the Sum over amount of results. mean = Sum(value)/amount
Standard deviation is Square-root(Sum((Result-Value)^2)/Amount)
Basically something like the mean of the distances of the values to their mean.

High standard deviation means a high spread.
Low standard deviation means a low spread.

With given probabilities you can calculate how "likely" your values are going to have a certain spread.
For example if you have a normal distribution there is 95 % Chance to land in a range of two standard deviation,
therefore if the sample is representative 95 % of the values should be in that range.

Looking to get Mason's book here. Sounds he got most things covered.

hello i am new here

Purchase Mason's book. He gives a brilliant introduction on this subject. BruceZ posts too btw.