ITH Poker Forum

[chillin411]

Zoom In Zoom Out

"I recently tried out that Google Earth thing. In case you don’t know what it is, it’s a piece of software that you can download that lets you look at any place on earth from any height using satellite images. It's actually really impressive and lots of fun. I found it incredible to look at England from space then zooming in bit by bit… I was finally looking at a close up image of my street. It reminded me why I like statistics so much. Perspective. Statistics allows us to zoom in and zoom out on things. I’ll show you what I mean by looking at limit holdem earn rates. "

Discuss Pauli's article here.

[nsidestrate]

This is an excellent article. I am going to refer people to it in discussion of the long run from now on. This does a really good job of translating the figures into real-world examples that make sense to everyone.

[nsidestrate]

Cross-posting:

-- I am not sure if this is the best place for article discussion because the Article Discussion forum, where I assume this belongs, has no replies to the sticky's. Please move if needed. --

I think this is a great article to demonstrate how short-term results are no indication of earn rate. The problem that beginners continue to face, though, is that the only information they have are short-term results.

If I start out playing at, let's say, .25/.50, and after 1000 hands my BB/100 is -1 that does not tell me if I am a losing player or not. After 2000 hands if your BB/100 has improved to +1 it doesn't tell me if I am a winning player or not.

I think it is important to recognize that these 2000 hands provide a margin of error that is too big to allow for conclusive results to made about the long-term earn rate, this is easier to accept if your last 50,000 hands show that have earned 2BB/100.

I think for beginners it may be somewhat useful to provide a Confidence Interval formula to allow them to work out the probability that they are a winning player. I am new to poker so I am guessing that this might be useful for begginers, players who are debating moving up levels, or players looking to determine whether or not they are profitable at the level they just moved up to. This may help players assess the likelihood that they are winning/losing with a given sample size?

I'm interested to hear what some of the more experienced players think about this. Thoughts?

**Edit** I do not want this post to come off as critical. I am simply looking to see if the more experienced poker players think a confidence interval approach may help provide information to those who do not have much. Or, what are some other indicators new players or players moving up limits can use to assess themselves.

[nsidestrate]

Your request is quite timely. I believe that the ITH website will soon provide you a handy calculator for working this out. In the meantime, I will search for the formula.

I don't think this is at all a criticism of the article. In fact, I think that it was a point Pauli intended to make. Note that the losing player was still winning after 2,000 hands 43% of the time. It takes a pretty long time to get any confidence in your true earn rate. You probably never really know it, because by the time you have enough hands to have a confidence in your earn rate, your playing style has probably changed enough that the old hands shouldn't be used in the calculation.

[PauliF]

my intention is to continue with the discussion of the properties of normal distributions in my next article

i am probably going to look at confidence intervals next time.,..
not just the formula but where they come from etc
there is lots of things i always want to say but i am just trying to get through a little of the science each time...

sorry for any frustration

[jeffnc]

"I think for beginners it may be somewhat useful to provide a Confidence Interval formula to allow them to work out the probability that they are a winning player."

But I thought the whole problem here (and I wholeheartedly agree that it's a problem) is that the confidence interval itself will not be useful. Let's say it says there's a 50% chance I'm a winning player. Then what? Or 40%, or 60%. That's the whole point - your sample size is so small that you're going to get an ambiguous number like that.

[fep]

Thanks for the great article Paul. I definately want to improve my knowledge of statistics.

I'm probably going to have tons of questions but let me work through one at a time.

1st, I'd like to know if my excel spreadsheet is calculating the standard deviation correctly. Since you also use excel I thought you could verify this for me.

I keep all my sessions on excel and in one column I have BB earned per session. At the bottom of that column I have this forumula:

=STDEV(K6:K1009) where column K is the BB earned per session column.

I'm assuming that's the correct formula. It comes up with 15.67 (and my BB/100 is 2.06 over 110K hands).

Does this look right?

Okay two questions. I use to record every table as a seperate session. Now I summarize by week by site by limit/type of game. So my "sessions" have become much larger, from averaging 77 hands a while back to 148 hands now. What is the impact of different session lengths on standard deviation?

[taz115]

I agree with jeffnc that a sample size of only 2000 a CI will most likely not be too relevant either. I would have to play around with it to see what kind of a sample size you need to say have an interval of say +/- 0.50BB for a 90% CI. That info would be very useful, but I suspect we would require 20k or 50k hands for that kind of precision.

Anyway this entire topic of earn rates and short-term / long term discussion very interesting having done a ton of statistics over the past few years. I also am finding it particularly relevant because I have about 4500 hands in PT about half at 0.50/1.00 and half at 1/2. Last night I was actually thinking about this subject because my current rates are approx. 6.5BB/100 at 0.50/1.00 and 1.5BB/100 at 1/2. One good/bad session can throw my 1/2 rate up or down by 0.50BB right now so any kind of conclusions are going to have to wait for more hands played.

[taz115]

I guess another reason why new players will find your articles useful is because if they experience some intial success (as I did) they find themselves asking questions like this:

taz115 wrote:
1700 hands at .5/1... I know that I have that level beat.
Would it be totally insane for me to move up to 2/4 after only 1700 hands at .5/1 and 1000 hands at 1/2? I'm thinking it might be.

Zool1 wrote:
woh there! You may well have this level beat, but with 1700 hands you are an absolute MILE away from knowing that, regardless of your current bottom line. Yes it would. I play 1000 hands in a long afternoon, and believe me it's not enough to draw any conclusions one way or another.

LOL!! I am just lucky that I found this site and that the experienced players are willing to spend the time to help out the naive.

Keep up the good-work on the articles because the free content is what draws prospective members to eventually look at the forums, join new sites ect.

[PauliF]

Thanks for the great article Paul. I definately want to improve my knowledge of statistics.

I'm probably going to have tons of questions but let me work through one at a time.

1st, I'd like to know if my excel spreadsheet is calculating the standard deviation correctly. Since you also use excel I thought you could verify this for me.

I keep all my sessions on excel and in one column I have BB earned per session. At the bottom of that column I have this forumula:

=STDEV(K6:K1009) where column K is the BB earned per session column.

I'm assuming that's the correct formula. It comes up with 15.67 (and my BB/100 is 2.06 over 110K hands).

Does this look right?

Okay two questions. I use to record every table as a seperate session. Now I summarize by week by site by limit/type of game. So my "sessions" have become much larger, from averaging 77 hands a while back to 148 hands now. What is the impact of different session lengths on standard deviation?

do you use poker tracker?
poker tracker gives you your standard deviation per hour and per 100 hands.
i prefer to use the per 100 figure and it seems to be the most common.
B&M pros tend to use the hourly rate

the figure you are using above are by session.
now there two problems with this... the first is the main problem (the second somewhat minor)

1) as you suggest there is likely to be some problems with different sessions having different numbers of hands... and this is key... unless all your sessions are for exactly the same length of time (or even better hands) there are going to be some major distortions.... probably severe enough to make any investigations based on this data seriously compromised if not useless

2) the more data you have the better. the law of large numbers etc etc... we can only start using the properties of statistical distributions when we have large sample sizes... obviously this will take longer if your unit of measurement is the session rather than 100 hands

i think you are much better off looking at your statistics for 100 hands (or the hour) and from there think about how your earn rate is distributed over longer periods...

i hope this has helped but please ask again or more questions if it hasn't

[fep]

I'm looking but I can't find Std Dev in PT. Can someone help me?

[taz115]

I don't have it here at work but it's on one of the 'Additional Information' buttons. I think it might the the button on the General Tab.

[fep]

Okay I found it, it's the "More Detail..." button under the "Session Notes" tab.

14.84 for the Std Dev/100 hands. It's just a number out of the blue for me but is lower than both examples in PauliF's article. Don't know if that's good or bad. Makes me think I might be playing too cautiously.

Actually maybe I remember what it means, I really need to read PauliF's previous article.

From the article I gather since my win rate is 2.04 then:

Fepie can expect over the next 100 hands to:

lose 12.84 big bets or more one time in 6
win 16.84 big bets or more one time in 6

Isn't a standard deviation 67%? Which puts about 16% on each tail? Just trying to remember. I'm swimming here...

Edit, progress I'm reading the 1st article and now know

lose 30 big bets or more one time in 64
win 30 big bets or more one time in 34
be in profit only 55% of the time.

Thanks PauliF, I'm making progress

[the_hawk]

But I thought the whole problem here (and I wholeheartedly agree that it's a problem) is that the confidence interval itself will not be useful. Let's say it says there's a 50% chance I'm a winning player. Then what? Or 40%, or 60%. That's the whole point - your sample size is so small that you're going to get an ambiguous number like that.

Isn't the abiguity in itself the very "usefulness" of all of this?

Unless you're producing level-crushing apparent earn rates and/or you have a large sample you simply cannot be reasonably confident (in the ordinary English or in the mathematical sense of the term) that you are a winning player, period.

That in itself would seem to be very useful information.

[taz115]

Good point. The ambiguity certainly drives home the importance of controlled BR management and responsibility in moving between levels.