Thanks. I tried yesterday and seemed could only get it with kindle unlimited. I was able to get it with your link.

I hope you enjoy it and find it well worthwhile. I'll also try to answer any questions you might have,

Mason

I'm going to post a 10minute clip of a coaching lesson (once I get the okay from the student) so people have a better idea.

I show you the data and I record the session and send it to you via email. But no I don't give you the data.

You can stop the video and take pictures of it though so you have it and you will always have the video to refer too.

Yes, also people play worse when they run bad and play better when they run good. That's something this experiment doesn't even take into account so variance is actually greater than 13bb over 500k hands.

One thing I learned from your book was that I was approaching preflop completely incorrectly wrt to live poker. Online there are usually 4 -5 regs and 1-2 fish so you want to isolate preflop against the fish.

In live poker you need to take the opposite approach. Since it's usually 6-7 fish/2-3 regs you limp/over limp more and rarely isolate.

What do you even mean when you are saying that variance (you mean standard deviation btw) is 13bb over 500k hands?

Zamadhi I'm not nearly as technical as you so forgive my math ignorance.

I am saying the gap between wins/losses over 500k hands was 13.1bb.

I'm not particularly technical btw (not compared to others in this thread, at least).

But my point is that it's a question of probabilities and confidence intervals.
What do you think is the probability of running 6.5bb/100 over or under EV over 500k hands with a 100bb/100 std.dev?

According to primedope it's 1/500,000. Even if primedope underestimates it, it's still very unlikely.

That's not the standard deviation (or variance). These terms have very precise statistical meaning. However, using a basic knowledge of statistics and an educated guess, the standard deviation of the estimated win rate of zero (since all the players are the same bot) after 500,000 hands is probably around 3BB. This assumes the difference between the largest difference is approximately four standard deviations.

Mason

Stnd dev over 500k is close to 1.5bb/100, so two players are 4 stand dev off the expected value. This seems absurd.

Maybe there is bug. One bot lost a lot and only one bot won almost everything.

It’s why you should choose a lower variance format (online NLHE cash being one of the best in this aspect) and plan ahead to put in good amount of volume if you don’t want the results of your career to be massively decided by luck

Let's see if we can figure this out. The standard deviation (sd) for 100 hands is 100bb. So 500,000 hands is actually a sample of 5,000 (100 hands at a time). The square root of 5,000 is approximately 70. So the sd on the estimate after a sample of 500,000 hands should be approximately 100BB divided by 70 which is 1.4BB. Then if you're 6.5BB above the expected EV (or mean) that means you're approximately 4.6 standard deviations above the mean.

I don't have Table of Normal Distributions in front of me, but 1/500,000 sounds about right.

Mason

I don't know if "absurd" is the right word but extremely unlikely for sure.

Good chance there is a bug.

Mason

The important thing about this chart is that it implies that in this particular game the standard deviation for your result in any particular 100 hundred hands is about 200 big blinds, Do you see why?

Only if you are using only your results to come to a conclusion. You need a much smaller sample if you are also using your observations of how they play. If you eliminate the possibility of being cheated, how many hands would you need to see where most of those hands had six people seeing the flop, before you knew your short term break even result couldn't mean you were a 6.5 bb loser?

I am a complete neophyte when it comes to statistics but I like learning so I'll give it a shot. Please let me know the answer either way though.

Okay screw this I'm cheating, I'd still like to know the math though.

6.5 million hand sample.

100 Standard Deviation.



200 Standard Deviation.



Since the + or - is .78 at 100bbs and the actual result is 1.7. It has a standard deviation of 200 (actually slightly over).

I still want to see the math though. I think it is the square root of 65000 (6.5 million divided by 100) which is 254 so 100/254 = .39 so it should be + or - .78 but since it is + or - 1.7 we know the standard deviation is more than twice 100.

One comment. This is a bit "cherry picked", as the conclusion always is the difference between best and worst. With six bots you can combine the results in 5+4+3+2+1=15 ways, but here always picking the greatest difference of those 15 possible.

May make it look worse than it is.

I didn't do the fancy calculations. I just realized that the results of the chart would be about what would be expected if the standard deviation was two hundred due to the square root thingy.

This is obvious even without playing millions of hands and a big reason why a lot of talented players choose to pursue poker purely as a hobby.

That's why it says "Biggest W/L gap" and not "conclusion"

Ok, let's say "result advertised"

I'm going to change my policy on this actually. I'll update my coaching thread. I'm going to start giving students the data for the spots we go over in a lesson so they get max value out of the coaching session. Too many coaches doodle and waste time during the hour so this will increase efficiency for the student.

Will be uploading a 10min video on my coaching thread as well if interested in some free MDA.

The lowest variance format is the one in which your skill edge is the greatest compared to your opponents', regardless of game type. Variance is a function of winrate which is a reflection of skill gap (in general). This assumes a game in which starting hand selection has a meaningful role in your chance of winning.

In my experience, live PLO (4 or 5) is probably lower variance than online NLHE simply because the skill gap between the better pros and the average recs is much wider and more than makes up for the relative closeness of preflop equities. One factor that contributes to this disparity in skill is the lack of study resources.

In this vein, the thread title obviously assumes similar skill among opponents. As the skill gap widens, luck becomes a much less important factor over both short and long term. For example, a skilled pro may not have the best hand at showdown in a given hand but may get his or her opponent to fold a better hand using their knowledge of blockers or ranges. A strong pro may lose a few 60/40s or 70/30s over a few sessions but over time getting it in ahead versus the lesser opponent will net positive for their bottom line.

I agree with much of what you're saying but you're not saying it right. And that's because with a higher win rate you can certainly have a higher variance/standard deviation.

But what does often happen is that the relationship between your expectation and standard deviation improves, and that drives many of the good things that can happen at the poker table. And as usual, see my book Gambling Theory and Other Topics - Expanded Edition for more discussion of this important topic,

Mason

Mason you’re awesome, natural salesman haha.