A Guide To Variance

[aim786 0]

INSPIRATION:(Note: For those of you who wish to skip this part and get to the meat of the article, goto the next section of this post.)Ugh, another 150 BB downswing. Wait…I’m gaining some momentum….****, my top set just lost to quads for a 33 BB pot (true story)!!!!!!!!!!!!!!10 Days Earlier:4 exams in 4 days (and electrical engineering is no joke), 2 all nighters and closing on a 36 hour no sleep stretch, it finally hits me: school’s out! Time to party it up and finally play some poker. But wait, I took a break from poker before exams because I had to study but also because I was coming off an 80k stretch of being a -0.2BB/100 player. Ugh, time to study again, but this time it’s poker.Just yesterday, a book I had high expectations for arrives in my mailbox only a few days after it’s been released to public. It’s called Winning in Tough Hold’em Games, and I’m really hoping it turns my game around. SSHE, which once was the bible of LHE, is being replaced by the new testament, WTHEG. But wait, no time to savor the moment right now, I got 2 finals tomorrow!I awake a few days later, exams are over, partying is over, and it’s time to get to business. I take the book, my laptop, and my school bag and head to the library. For the next 3 days, I’m immersed in the book: taking extensive notes (like I should have for my university courses), challenging the author’s idea’s, proving to myself why what they suggest is correct, posting on FCP, and most importantly of all making sure I understand the assumptions under which the authors advice is true.Finally, after carefully laying out all my papers on my desk at home, I fire up my laptop ready to put in a session. The next few days, I play and I play, only 1 or 2 tables at a time, take notes on each player, really think about what I’m doing before I do it (lol I killed a few time banks 1 tabling), and then it hits me: I’m losing money like a mother ******. A 150 BB downswing in 1500 hands, and I’m on major tilt (there’s nothing like seeing your hard work get destroyed by some donks chasing 3 outers).I know, I know, everybody must be thinking: well obviously, you made some bad adjustments to your game. Well, I’m quite confident now that that is not the case, even though I have no data to prove my point. I’ve been around the block, and I know the ups and downs of the game, and I know that in the short run there is a lot of luck, especially when you lose 2 25 BB+ pots in 1500 hands when holding the virtual nuts.So, after feeling sorry for myself (WHY ME?!), a friend of mine (who post’s a lot on here ) start’s talking to me and we discuss things like winrate and variance and such. All of a sudden, I feel the need to really understand variance so that I don’t tilt everytime I drop 100 BBs. I read part of Mathematics of Poker again, and create spreadsheets for things such as confidence intervals, risk of ruin, Kelly criterion, and RoRU (which I still haven’t quite figured out). In searching for more explanations of these concepts, I stumble across some old 2+2 articles that I had read early on in my poker career and never fully took the time to understand.After reading one post in particular, combined with everything I looked at before, things really fell into perspective. For one thing, it’s nice to know that what’s happening to me is much more “normal” than I thought it was. At the same time, it’s a bit disappointing since I realize I’m probably not as good as I thought I was. Nevertheless, I strongly feel that in these last 2 weeks I’ve jumped another level in this game we call poker.Now, for what you’ve all been waiting for.A GUIDE TO VARIANCE:Let’s start by looking at some graphs:These are 3 independent samples of 10k hands each. If I asked you to rate these player’s in terms of ability, I bet most of you would say the first player is a winner, the second one is a loser, and the third one is a break even player. Some of the more experienced player’s would say, it’s variance and w/o more information about the player’s we can’t tell who is the best.However, even the experienced players would be shocked to learn that all 3 of these samples are from 3 identical players who are long term winners of 2 BB/100, with a 15 BB/100 standard deviation. Well, they are not quite 3 identical players, more like 3 simulated results for a player with those stats.Most of you must be somewhat confused and/or shocked about all this stuff I’m talking about. Perhaps the easiest way for everybody to understand variance is to actually see it, after all seeing is believing (not!!!!!!!! ). To do that, you’ll have to create your own spreadsheet:(Note: I have attached my own spreadsheet in this post. If you decide to use my spreadsheet, I recommend still reading thru the steps so you have an idea of what is going on.) Variance.xls1. Open up Microsoft Excel. Note: this can probably be done with other spreadsheet programs, but I do not know how use them.2. In cell A1, enter “=RAND()”. This basically generates a random number between 0 and 1. Copy paste cell A1 into cells A2-A1000.3. In cell E1, enter “BB/100”. In E2, enter “SD/100”. These value’s can be found in poker tracker. A live player would enter BB/Hour and SD/Hour here.4. In cell F1 enter “2” and in F2 enter “15”. These are the value’s we will be using for this example.5. In cell B1, enter “=(F$2*NORMSINV(A1))+F$1”. This converts your random number to your win for those 100 hands based on your win rate and standard deviation. Copy paste cell B1 into B2-B1000.6. In cell C1, enter “=B1”. In C2, enter “=C1+B2”. Finally, copy cell C2 into cells C3-C1000. This is the total # of BB’s you’ve won after X amount of hands.7. Next, goto Insert -> Chart. Select Chart Type = XY Scatter and Chart Sub-Type = Scatter with data points connected by smoothed Lines without markers.8. Click Next. Under Data Range, enter “=Sheet1!$C$1:$C$1000”. Make sure Series In = Column.9. Click Next. Call the X-axis “Hands x 100”. Call the Y-axis “BB”. Note: Remember, the X-axis is 1000 sets of 100 hands, therefore it represents 100,000 hands. That’s why we call it Hands x 100.10. Click Next. Select “As New Sheet” and click Finish.11. Voila! A chart should appear now which looks very much like the one’s I posted above.If you’ve done everything correctly, what you have in front of you is the results of a 2BB/100 player with a standard deviation of 15 BB/100 after 100,000 hands. It will look something like this:If you press F9, a new set of data for the same player will be generated. It’s interesting to see how one set of 100,000 hands maybe completely different from another set. For example, in one of my sets the player won about 2650 BB after 100k hands. In another, he won only 1300 BB, less than half the amount of the previous set!However, these graphs are not that interesting, since they are pretty smooth and also because not many of us have a bunch of 100k hand samples. Also, you’ll rarely see a break even graph after 100k hands, and even more rare will be a graph where the player is losing after 100k hands. A much more interesting sample to analyze is one with 10k hands. That sample can change a lot from one to the next, as you can see from the first 3 graphs I posted. Also, many of us have played 10k hands where we were invincible, and others where we looked like fish. We’ve always been told that, “that’s variance”, well now we can actually see with our own eyes how much variance can affect the game of poker.12. Right click the chart and select “Source Data”. In Data Range, enter “=Sheet1!$C$1:$C$100”.Now, we have the same player after only 10k hands played. This graph won’t quite look like the one’s we get from programs such as Poker Patterns because those programs graph each hand. On the other hand, our graph graph’s sets of 100 hands, and therefore looks less “pointy”.If we press F9 and go thru the graph’s, we can clearly see that the results for this same player are vastly different. Most of the time he’s winning (he is a 2bb/100 player afterall), but sometimes he breaks even or even loses. His biggest downswings are generally about 150 BB.Now, you can experiment with different kinds of data. Take a look at the swings a 1 BB/100 with a 15 BB/100 standard deviation goes thru. You’ll notice a few things, namely: he has bigger downswings, and they are more frequent. Look at a player who wins only 0.5 BB/100, and the magnitude and frequency of the downswings will be more pronounced. You can also change the number of hands played to 100k, and look at a break even player say. You’ll notice a bunch of 300 BB+ downswings, maybe even a 1000 BB downswing.So now that we have a better idea of the variance involved in SH, wouldn’t it be nice to know how often downswing will occur? For that, we’ll need to work with Normal Distributions. You can find a detailed explanation about Normal Distributions as it relates to poker in the book Mathematics of Poker. We used the Normal Distribution to calculate the above graphs, and we’ll use it for calculating the probability of a downswing of a given magnitude to occur given our winrate and standard deviation.Part 2 will be up shortly.

[crazyplaya6 0]

dude...that's sickmy two cents: while poker is, at its core, a game of mathematics in a technical sense, big winners play more on feel than straight numbers or stats. Not saying that knowing the math isn't important, because it definitely is, but a sklansonian comprehension isn't necessary. My advice, pick up theory of poker, read it, then play a micro limit cash game where you play EVERY hand for 100 hands or so, in order to learn some feel. Im of the opinion that when feel players, they win on avg more than the mathematics-based players, because while the math guy will take the 5% edge, the feel player may pass in order to gain a 20% or 30% edge later down the road. just my thoughts.

[aim786 0]

dude...that's sickmy two cents: while poker is, at its core, a game of mathematics in a technical sense, big winners play more on feel than straight numbers or stats. Not saying that knowing the math isn't important, because it definitely is, but a sklansonian comprehension isn't necessary. My advice, pick up theory of poker, read it, then play a micro limit cash game where you play EVERY hand for 100 hands or so, in order to learn some feel. Im of the opinion that when feel players, they win on avg more than the mathematics-based players, because while the math guy will take the 5% edge, the feel player may pass in order to gain a 20% or 30% edge later down the road. just my thoughts.

1) I agree. Big winners usually have a very good read on their opponents, and know how an opponent will play a certain hand. More important than stats is knowing your opponent and his tendencies.2) This statement is somewhat iffy. There are basically 2 ways to play poker: the math way or the reading players way. Successful players are usually a combination of both, although some players are much more talented in one approach than the other. However, the poker community is dominated by "feel" players, since most players find that approach more challenging, rewarding, and entertaining than the math approach. Because of the fact that there are so many "feel" players, it is only natural that most of the big winners come from this school of thought.In reality, and this is my opinion, both approaches are the same and in order to be successful you have to be good at both. A math player, given an opponents range of hands, his own hand, and the size of the pot, can usually come up with the "optimal" solution to the situation (assuming that the situation is not too complex). However, if he does not play a lot of poker and sits down in a game trying to apply his approach, he will most likely run into the following problem: he won't be able to assign accurate ranges to his opponents.A feel player on the other hand, can probably give you a pretty good estimate as to what an opponent holding's are. However, if he does not use this information properly, ie knows what his action should be given his read, then he is no better off than the math player.

[navybuttons 15]

dude...that's sickmy two cents: while poker is, at its core, a game of mathematics in a technical sense, big winners play more on feel than straight numbers or stats. Not saying that knowing the math isn't important, because it definitely is, but a sklansonian comprehension isn't necessary. My advice, pick up theory of poker, read it, then play a micro limit cash game where you play EVERY hand for 100 hands or so, in order to learn some feel. Im of the opinion that when feel players, they win on avg more than the mathematics-based players, because while the math guy will take the 5% edge, the feel player may pass in order to gain a 20% or 30% edge later down the road. just my thoughts.

the OP isn't a guide to playing poker by mathematics. it is mathematics explaining the varaince that occurs naturally at a given winrate and standard deviation. a feel player giving up a 5%-10% edge is a huge leak. it doesn't matter if a feel player has a higher winrate then a math player, he is still going to encounter variance and losing streaks, just smaller ones then the player whose winrate is not as high. if a math player has a higher winrate than a feel player he will have the same occurance.you'd be suprised but there is not much difference between winning "feel" players and winning "math" players.

[antistuff 0]

feel players play by the math too they just do it intuitively and don't know they are doing it.

[navybuttons 15]

feel players play by the math too they just do it intuitively and don't know they are doing it.

sactly

[Frez 0]

dude...that's sickbecause while the math guy will take the 5% edge, the feel player may pass in order to gain a 20% or 30% edge later down the road.

dude...there's no way "feel" is 4-6 times more useful than math. Very useful, but not 400% more useful. Besides, I'll spend a little time on sudying math away from the table and put it into play at the same time I'm learning feel from experience.Plus, "feel" players who are skilled at putting their opponent on a hand or a range of hands use that information to make mathematically correct bets.

[sixsixtie 0]

I am having one of those right now myself. Holy god is it ever frustrating

[CobaltBlue 662]

This is pretty cool. More people should check it out.

[vbnautilus 48]

Was there ever a part 2?

[RISEorFall 0]

then play a micro limit cash game where you play EVERY hand for 100 hands or so, in order to learn some feel.

thats one of the most ridiculous things ive ever heard in my entire life

[aim786 0]

Was there ever a part 2?

I was going to write one, however very few people responded to the OP so I felt that most of the posters were not really interested in the subject. If there are some more responses, when I get back from vegas I'll write up part 2.

[Flushgarden 0]

thats one of the most ridiculous things ive ever heard in my entire life

Actually DN himself said this is a good exercise.

[sennin 0]

Great post, maybe there is hope for me afterall in cash games. Looking forward to part 2 if you decide to do it

[RISEorFall 0]

Actually DN himself said this is a good exercise.

at micro limits? good luckand i think 100 hands is far too few to gain any real feel.