Accuracy of short term standard deviation?

[barongreenback]

Let's say I know the standard deviation of my win rate. As I play more hands the SD number may change. This might be due to game conditions or my play changing. However, even if we assume that these variables are consistent my SD should 'settle down' over time, coming closer and closer to the true figure. How do I estimate how close to this 'true figure' my current SD is? In effect what is the SD of my SD?

This is a difficult subject to search for because the search terms are common. If it has been covered before can you provide a link? I do remember a link to a rather deep essay on this a while back but I've lost it. I suspect this could be quite an interesting subject but at the moment I'm mainly looking for a practical answer.

Thanks,
James

[BruceZ]

[ QUOTE ]
Let's say I know the standard deviation of my win rate. As I play more hands the SD number may change. This might be due to game conditions or my play changing. However, even if we assume that these variables are consistent my SD should 'settle down' over time, coming closer and closer to the true figure. How do I estimate how close to this 'true figure' my current SD is? In effect what is the SD of my SD?

This is a difficult subject to search for because the search terms are common. If it has been covered before can you provide a link? I do remember a link to a rather deep essay on this a while back but I've lost it. I suspect this could be quite an interesting subject but at the moment I'm mainly looking for a practical answer.

Thanks,
James

[/ QUOTE ]

Here (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Board=genpok&Number=149814&F orum=genpok&Words=chi-square&Match=Entire%20Phrase&Searchpage=0&Limit=25 &Old=allposts&Main=149588&Search=true#Post14981 4) is an old post that I wrote on that topic. Also search for some advanced posts by Jason1990 from 1-2 years ago. Your standard deviation converges much faster than your win rate.

[ohnonotthat]

Your adjusted SD is determined by taking your hourly SD (or your per 100 hand SD as most online players calculate it) and dividing it by the square root of the number of hours (100 hand units) played.

Example:

You have a SD of $ 1,000 per 100 hands.

You go on to play 10,000 hands over the next month and decide to recalculate your SD.

There are one hundred 100-hand-units in 10,000 [hands].

The square root of 100 is 10.

Your $ 1,000 per-100-hand SD can now be adjusted (lowered) to $ 100 per 100 hands.

The bad news is that you'll need to play 30,000 more hands to cut the new figure in half and 150,000 more hands to cut THAT figure in half.

The good news is that with online play you are able to do in a year what most old-timers were unable to do in a lifetime.

If you play 2 games at once and see 50 hands/hr/game (100 hands/hr) you'll see 1,000 hands in a 10 hour day.

It would take a week for most live players to play 1,000 hands; if you play 4 games at once you can equal 2 of his weeks in a day - or one of his years in a month.

Three years of online poker equals more hands than most live players see in a lifetime; 5 yrs of fulltime online play is more poker than ANY live player ever saw.

The world it is a'changin.

[BruceZ]

[ QUOTE ]
Your adjusted SD is determined by taking your hourly SD (or your per 100 hand SD as most online players calculate it) and dividing it by the square root of the number of hours (100 hand units) played.

Example:

You have a SD of $ 1,000 per 100 hands.

You go on to play 10,000 hands over the next month and decide to recalculate your SD.

There are one hundred 100-hand-units in 10,000 [hands].

The square root of 100 is 10.

Your $ 1,000 per-100-hand SD can now be adjusted (lowered) to $ 100 per 100 hands.

The bad news is that you'll need to play 30,000 more hands to cut the new figure in half and 150,000 more hands to cut THAT figure in half.

The good news is that with online play you are able to do in a year what most old-timers were unable to do in a lifetime.

If you play 2 games at once and see 50 hands/hr/game (100 hands/hr) you'll see 1,000 hands in a 10 hour day.

It would take a week for most live players to play 1,000 hands; if you play 4 games at once you can equal 2 of his weeks in a day - or one of his years in a month.

Three years of online poker equals more hands than most live players see in a lifetime; 5 yrs of fulltime online play is more poker than ANY live player ever saw.

The world it is a'changin.

[/ QUOTE ]

When the OP said:

[ QUOTE ]
Let's say I know the standard deviation of my win rate. As I play more hands the SD number may change. This might be due to game conditions or my play changing. However, even if we assume that these variables are consistent my SD should 'settle down' over time, coming closer and closer to the true figure. How do I estimate how close to this 'true figure' my current SD is? In effect what is the SD of my SD?


[/ QUOTE ]

He was really asking about the accuracy of the computed standard deviation of his winnings for say 100 hands, not the standard deviation of his win rate as he wrote in his first sentence. The standard deviation of the win rate, or standard error of the win rate (SE) is a measure of the accuracy of the computed win rate, and it decreases toward 0 the longer you play as your win rate becomes known more accurately, and it is equal to SD/sqrt(N), where N is the number of hands/100, and SD is the true standard deviation for 100 hands. It is the SE which you are discussing in your post. The true value of the SD doesn't change if we assume that conditions stay the same. Our estimate of the SD becomes more accurate. He wants to know about the accuracy of the SD estimate, which actually introduces another standard error, the SE of the computed standard deviation.

[ohnonotthat]

His wording confused me a bit but it seemed as though he was asking about the confidence level for his [not quoted] win rate.

You are of course correct when you state that the hourly (or per 100/hand) SD will never change - providing, of course, that his skill, both absolute and relative to his opponents, never changes.

Certainly his hourly SD would drop if his skills improved to the point where he knew with 100% certainty the cards his opponents held; it's also true that his SD would plummet if he AND his opponents both posessed this skill.

- It's more or less accepted as fact that the SD for 20-40 holdem typically exists between 300 and 900 per hour depending on a player's style of play - if I played with 9 opponents all of whom played as well but no better nor worse than I play and we changed the rules so as to eliminate the final round of betting (the equivalent of having total knowledge of each other's hole cards) certainly all our SDs would drop - hard to say how much but safe to say not an insignificant amount.

Standard deviation in poker measures volatility and nothing else. Ones SD does not drop as his skills improve unless the improvement is such that it allows for (or in some cases causes) less volatility. Back in school I used to eke out a few extra dollars at 1-2 thru 3-6 games playing in a manner that would in today's world be called "weak-tight"; I had a limited bankroll and modest needs - I was fiercely protective of the former while wanting very much to meet the latter, ergo weak-tight was just the ticket. (The truth is I didn't know much what I now know but I may well have stayed the course even if I had - utility theory).

When gambler's ruin ceased to be an issue I played faster; when I learned more I played faster still. As one would expect my faster play and increased knowledge/skills led to a higher win rate but it also led to a huge increase in SD - though to be candid I seldom bothered to calculate it back then and I'm not a big fan of crunching numbers now for any other than curiosity. The important point however is that the faster play would have caused a big jump in SD even if it had been BAD play.

Think about the craps shooter who plays only pass/don't pass as opposed to the player is constantly firing chips all over the layout. While both will lose in the long run the former will undoubtedly lose less. Nonetheless it is the latter who posesses the only realistic chance of "breaking the joint" in an hour.

I now see that as per usual I have held to the motto, "never use 50 words to make a point if there's a way to use 100" so I'll sum it up in this way:

Playing 10 hours a day for a year will likely lead to a lower hourly SD but it's quite possible the change will be minimal; you'll improve you're reading skills (SD plummets) but you'll also learn when to make razor thin value bets (SD soars).

Similarly, you're win rate is also apt to see only minor improvements over the course of the year assuming you were competent to begin with.

You're confidence level, however, will soar over the course of these 12 months.

You may be an X dollar/hour winner at the start with an SD of 20X only to find these figures mostly unchanged when the year is over but whereas they were virtually theoretical figures when you began they are now facts - hardly the most reliable facts you'll ever posess but facts nonetheless.

[barongreenback]

Thanks for the replies. I was worried I'd mess up the terminology somewhere and cause some confusion and I now see the problem with my first sentence. Luckily, just as I can usually understand my cat, BruceZ seems to know what I'm talking about. The link is just what I'm after. Also, it was Jason1990's posts I remembered.

Was my use of 'SD of my SD' also incorrect?

I'm going to need several lifetimes to do all the study that I want to do.<sigh>

Thanks again,
James