I guess one of the really key points here is estimating your own a priori win rate. How do you think about this? Do you think about say spots where people can be exploited, how frequently they occur and how much the exploit is worth? Do you think this is worth doing? Or is it more an experience judgement (or previous data).
I think using tools like simple postflop trainer to estimate your loss rate vs equilibrium per 100 as well as your opponents’ can give you a fairly reasonable baseline.
Excellent content Sauce, thanks for this! Im very interested in digging and seeing an extended extrapolation of how the standard deviation could play out over deep NLHE and PLO with antes in an effort to try to quantify just how swingy the outlier bad runs and good runs can be.
One other point is that people look at poker dope when they are in a downswing which so it’s not a truly random sample. The other issue is that the probability of an X buy in dowswing over Y Hands has the issue that we are repeatedly looking at how we are doing. So in 1M Hands we don’t have 20 50k samples looked at another way we have 1M 50k samples. Now we don’t really have that either as those samples are highly correlated so the effective number of 50k samples is somewhere between those two.
How should I think about varience in general?... Or I must try to not think about it and just go with my daily grind routine. I'm aware that next 100k hands can happen XYZ in terms of swings and varience. I can interfer with XYZ: by just change game (not reasonable of course, maybe I'm 500z reg and playing only that), by improving (well adding extra 0,05bb each month won't make huge picture), by .... .
Anything else comes to your mind??
To me seems like: ''yeah there is varience and let's carry on''
Hey Ben, great video - really enjoy the analysis of this part of the game. Just wanted to ask a question about pokerdope.
Lets say I run at 10bb/100 over a 100k sample - if I use these inputs for a pokerdope simulation (10bb w/r, sample 100k hands, st/dev 100) and it gives me a 95% confidence interval of 3.5bb-16bb. Is it safe to say that theres a 95% chance that my true winrate falls within this interval? Or am I interpreting that incorrectly?
Is this an iff? I guess Ben said yes below so I’m inclined to believe him but I never realized that. A priori, what it is actually saying is that “if you’re true winrate is 10 then over 100k hands you can be 95% sure you’ll be in this window”
If Ben says that the converse is also true I believe him, but it’s definitely not what the graph is saying directly.
"“if you’re true winrate is 10 then over 100k hands you can be 95% sure you’ll be in this window”-- this is correct. OP however is trying to infer their true WR from a sample.
Makes sense, so if we were to apply Bayesian thinking to that output would it just be the upper bound of the interval that would be effected (I.e something more like 3.5bb-9bb) or would the lower bound be effected too.
I guess im just trying to understand whether or not running at 10bb over that sample can be reason to assume that the player is extremely likely to be a solid winning player in those games.
The lower bound would probably be affected as well but it would depend on your exact choice of prior. To implement what Ben is suggesting you could choose a Gaussian prior with say mean -rake at your level / 6 then you have to take a guess at the stdev on the basis of how many profitable players you think there are at that level.
"If my true winrate was 10bb/100, then there is a 95% chance I will be between 3.5bb and 16bb/100 over 100k hands"
You are making the statement:
"If I observe a winrate of 10bb/100 over 100k hands, then there is a 95% chance my true winrate is between 3.5bb and 16bb/100"
A priori, as someone (me) who doesn't know anything about statistics, it's not obvious those statements are equivalent. But I believe you if you say that they are.
Yeah they are not completely equivalent. But in this case as we have well behaved distributions if you know the true variance (gets slightly more complicated if you don't, but not really) and follow the estimating procedure to estimate a 5% confidence interval (roughly compute the mean and add and subtract 1.96 sigma then the true value will lie in this range 95% of the time.
If you start with the true rate assume a normal distribution with that and the true sigma the observed value will lie within plus/minus 1.96 * sigma 95% of the time. So in this case they end up being the same. If you were estimating the stdev you would need the value of the t-distribution in the first paragraph which might be slightly different but basically as long as the distributions are reasonably well behaved (finite variance) you don't lose very much.
Hi Ben, any advice trying to estimate Standard Dev in live games? My friends and I have ranges from 160-1000 in NLHE, i guess it varies a lot due to open sizes,straddles, depth etc, in the UK its not uncommon to be £1k deep at 1/1. But assuming there are no straddles, playing relatively deep with 5-15x opens for instance?
Been loving your vids for like 6 years now, just never commented since I just enjoy the content oh so very much. But now as a content creator, I appreciate the value of comments.
So just wanted to say I thoroughly enjoyed this video!
Also, what software did you use for your powerpoint-type presentation? I really liked the layout.
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first!
I was so close...
"If you're not first, you're last!"
very excited for this topic, thanks Ben!
I guess one of the really key points here is estimating your own a priori win rate. How do you think about this? Do you think about say spots where people can be exploited, how frequently they occur and how much the exploit is worth? Do you think this is worth doing? Or is it more an experience judgement (or previous data).
Excellent question!
I think using tools like simple postflop trainer to estimate your loss rate vs equilibrium per 100 as well as your opponents’ can give you a fairly reasonable baseline.
Excellent content Sauce, thanks for this! Im very interested in digging and seeing an extended extrapolation of how the standard deviation could play out over deep NLHE and PLO with antes in an effort to try to quantify just how swingy the outlier bad runs and good runs can be.
One other point is that people look at poker dope when they are in a downswing which so it’s not a truly random sample. The other issue is that the probability of an X buy in dowswing over Y Hands has the issue that we are repeatedly looking at how we are doing. So in 1M Hands we don’t have 20 50k samples looked at another way we have 1M 50k samples. Now we don’t really have that either as those samples are highly correlated so the effective number of 50k samples is somewhere between those two.
Just check out PT4/HM. It can get as high as 250-300 in really wild plo games
You’re right holonomy. But you can fix this issue by picking regular intervals to look at pokerdope so that you don’t bias yourself
Shouldn’t we also be removing rake from the total being given up by the bad players at the table before we divide it between the regs?
Yes but I’m assuming reg winrates are less rake as this is how they appear in the tracking software
Hello Ben, nice video as usual
How should I think about varience in general?... Or I must try to not think about it and just go with my daily grind routine. I'm aware that next 100k hands can happen XYZ in terms of swings and varience. I can interfer with XYZ: by just change game (not reasonable of course, maybe I'm 500z reg and playing only that), by improving (well adding extra 0,05bb each month won't make huge picture), by .... .
Anything else comes to your mind??
To me seems like: ''yeah there is varience and let's carry on''
If quantitative reminders about variance aren't positive for you, by all means do whatever works.
Hey Ben, great video - really enjoy the analysis of this part of the game. Just wanted to ask a question about pokerdope.
Lets say I run at 10bb/100 over a 100k sample - if I use these inputs for a pokerdope simulation (10bb w/r, sample 100k hands, st/dev 100) and it gives me a 95% confidence interval of 3.5bb-16bb. Is it safe to say that theres a 95% chance that my true winrate falls within this interval? Or am I interpreting that incorrectly?
That’s right in the Gaussian sense.
As a Bayesian it hurts my heart to think like that bc no one in history of game has won at 16bb but about a zillion people have won at 3.5bb.
Is this an iff? I guess Ben said yes below so I’m inclined to believe him but I never realized that. A priori, what it is actually saying is that “if you’re true winrate is 10 then over 100k hands you can be 95% sure you’ll be in this window”
If Ben says that the converse is also true I believe him, but it’s definitely not what the graph is saying directly.
RTW, not sure I understand your post.
"“if you’re true winrate is 10 then over 100k hands you can be 95% sure you’ll be in this window”-- this is correct. OP however is trying to infer their true WR from a sample.
Makes sense, so if we were to apply Bayesian thinking to that output would it just be the upper bound of the interval that would be effected (I.e something more like 3.5bb-9bb) or would the lower bound be effected too.
I guess im just trying to understand whether or not running at 10bb over that sample can be reason to assume that the player is extremely likely to be a solid winning player in those games.
Yes from a frequentist perspective. If you want a good illustration of the difference between frequentist and bayesian thinking have a look at this.
https://xkcd.com/1132/
The lower bound would probably be affected as well but it would depend on your exact choice of prior. To implement what Ben is suggesting you could choose a Gaussian prior with say mean -rake at your level / 6 then you have to take a guess at the stdev on the basis of how many profitable players you think there are at that level.
I meant, pokerdope makes this statement:
"If my true winrate was 10bb/100, then there is a 95% chance I will be between 3.5bb and 16bb/100 over 100k hands"
You are making the statement:
"If I observe a winrate of 10bb/100 over 100k hands, then there is a 95% chance my true winrate is between 3.5bb and 16bb/100"
A priori, as someone (me) who doesn't know anything about statistics, it's not obvious those statements are equivalent. But I believe you if you say that they are.
Yeah they are not completely equivalent. But in this case as we have well behaved distributions if you know the true variance (gets slightly more complicated if you don't, but not really) and follow the estimating procedure to estimate a 5% confidence interval (roughly compute the mean and add and subtract 1.96 sigma then the true value will lie in this range 95% of the time.
If you start with the true rate assume a normal distribution with that and the true sigma the observed value will lie within plus/minus 1.96 * sigma 95% of the time. So in this case they end up being the same. If you were estimating the stdev you would need the value of the t-distribution in the first paragraph which might be slightly different but basically as long as the distributions are reasonably well behaved (finite variance) you don't lose very much.
Thanks Holonomy, that's helpful.
Hi Ben, any advice trying to estimate Standard Dev in live games? My friends and I have ranges from 160-1000 in NLHE, i guess it varies a lot due to open sizes,straddles, depth etc, in the UK its not uncommon to be £1k deep at 1/1. But assuming there are no straddles, playing relatively deep with 5-15x opens for instance?
okay 2nd and last question from me: Does RunitThreetimes and Insurance (not 1% of pot, 0% of the pot - well maybe someday) will reduce varience a lot?
I don't know
In a practical manner yes it lowers variance from your results
You are really just reducing the effective size of the game though not making the game any less variable
Hey Ben Sulsky
Been loving your vids for like 6 years now, just never commented since I just enjoy the content oh so very much. But now as a content creator, I appreciate the value of comments.
So just wanted to say I thoroughly enjoyed this video!
Also, what software did you use for your powerpoint-type presentation? I really liked the layout.
Cheers,
Tariq
Thank you for the kind words Tariq! I wish you continued success on the content creation side :)
I have to confess, I often submit audio to RIO and they produce the slides for me.
I know, I'm spoiled.
They really do a fantastic job though! My thanks for making me look organized, meticulous and smart!!
Loved this video!
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