This may kind of sum it up. But with a super high win rate you may overcome it. Online you can see it at play money and especially during the boom at micro stakes. Isolating bad players at live cash games may be the option for a very high expected winrate. I play live mtts, and can't control competition that way. So must prepare to lose, good thing is I can't lose more than the buy in each time (don't rebuy)...

this is actually true and well documented
it used to be ~33% but since people are living longer and longer 1 in 2 people are getting diagnosed with cancer in their lifetime (in the western world)

Small probabilities do happen. But this is extremely tiny, and there's a big difference.

Mason

Sorry, but this stuff can be very tricky and you don't seem to understand how it can actually work.

MM

it's not tricky Mr Malmuth

we're poker players we all played around with primedope variance calculator

Good for you. Since you're knowledgeable, why don't you explain where I got things wrong.

Mason

Not following what is being discussed. But I hope everyone realizes that nothing involving gambling has ever happened randomly that is seven or eight standard deviations away from the mean.

well essentially whether it’s 6 bots playing vs each other or a crusher playing vs 5 fishes, it’s possible for the crusher to run 6.5bb under EV over a period of 500k hands (we are assuming same standard deviation)

that was the point of matt marinelli posting this, that the sample you need for statistical significance is larger than people “feel”

This is easy to estimate. All you need to know is the standard deviation for some length of time, and 100 hands would do just fine.

This sentence shows that you don't understand what statistical significance means. There is no magic sample size number that is required for statistical significance. You can have statistical significance no matter the sample size. You also might want to pick up a basic college level statsics book to get a better grasp of how this works.

Mason

Thinking about this a little more, it's extremely unlikely that 2,000 hands where you flop a set is not a large enough sample size.

MM

I’m not sure if you’re being intentionally obtuse or you’re just misunderstanding the point, your qualifications regarding statistics is irrelevent to the point matt marinelli was attempting tk make

Let's go to the source: https://twitter.com/MatthewMarinel5

I can give Mason that the details are too few. For example standard deviation. Could it be an April's fool? Anyhow, what is a typical standard deviation, then put in that amount of hands, and let's look at some real numbers. We don't need those fancy bots for that. Expected win rate is of course 0bb/100, like for each bot in the twitter (X)

Hell, I may check this for myself. Maybe using three different standard deviations in poker: practically highest and lowest, and "typical"

First:
So regular standard deviation (SD) appears to be 70-100bb/100. What is the biggest and lowest SD you've seen over say 500k hands? Until then, I'll go with these. Could start with 80bb/100

https://www.primedope.com/poker-variance-calculator/

Expected win rate 0bb/100, SD 80bb/100




Then, you are a good player with an expected of 5bb/100
SD 80bb/100:


SD 100bb/100:


So with an expected of 5bb/100 it looks you can start to be "really" confident around 100k hands. At around 30k hands the optimist has it (light green)

And...wait for it...the expected super 10bb/100, 100000 hands instead of the million:


Looks you are MAYBE starting to know something after 10k hands with an expected win rate of 10bb/100. Wait until 30k hands for being "really" confident. You are of course not that one in a thousand guy...

LOL

Ok. Die on the hill that over 2000 flopped sets isn't that much of a sample.

Your misppaced arrogance is quite funny.

Finally, we may want to go back to the OP:



We get this for 100k hands (SD 100):
70% confidence interval Approx difference
[-3.16 BB/100, 3.16 BB/100] 6.3 bb
95% confidence interval
[-6.32 BB/100, 6.32 BB/100] 12.6 bb

500k hands:
70% confidence interval
[-1.41 BB/100, 1.41 BB/100] 2.8 bb
95% confidence interval
[-2.83 BB/100, 2.83 BB/100] 5.7 bb

2M hands:
70% confidence interval
[-0.71 BB/100, 0.71 BB/100] 1.4 bb
95% confidence interval
[-1.41 BB/100, 1.41 BB/100] 2.8 bb

6.5M hands:
70% confidence interval
[-0.39 BB/100, 0.39 BB/100] 0.8bb
95% confidence interval
[-0.78 BB/100, 0.78 BB/100] 1.6bb

All in all the bots give a bit too pessimist picture. Though, for 500k hands with an expected win rate of 5bb/100 luck indeed can mean as much as the expected. Approximately you are between 2.2 and 7.8 bb/100 with 95% confidence. And even with 70% confidence you are between 3.6 and 6.4 bb/100.

At 100k hands luck is indeed expected to mean more than 5bb/100.

And for a 6max PLO player in aggro games with a SD of 220?

i thought mining hand histories is frowned upon these days?

How the hell did you acquire a 245 million hand database?

It's possible with for example SD 200bb/100, so let's see. https://forumserver.twoplustwo.com/3...x-plo-1120206/

Found that the 95% confidence interval for SD 100 is the same as the 70% for SD 200, and the 95% for SD 200 is in turn double that.


SD 200 bb/100, 95% confidence interval:

100k hands
[-12.65 BB/100, 12.65 BB/100]
Approx difference: 25 bb

500k hands:
11 bb

2M hands:
6 bb

6.5M hands:
3 bb

Closer to the bots in some places.

This approximate difference number means nothing. It's the difference between the two most extreme outliers. But what interest us is maximum difference between the extreme outlier and what your results are supposed to be.

Right, if your expectation is 0BB/100 and you are winning at 12.65BB/100 clip, that's the maximum deviation, not 25BB.

it's where 95% are at the large SD of 200bb/100 at 100k hands. So 2.5% fare even worse than -12.65 bb/100 and 2.5% even better than +12.65/100. But, I like to think I'm more in the 70% area than the 95% area, and 100 bb/100, not 200 bb/100. Some posts up is that calculation, much better... and my "difference" just mimicks the bot op Biggest W/L (win/lose) gap (my "difference")

Could also check if the confidence interval is the same with win rates, I assume so. And we could put those six bots to rest, they only confuse.

It was from my old CFP.

Everything in poker is frowned upon. The current zeitgeist in poker is the lesser players nitpick all the tools and ways better players got to be better.

If you were coached---->you didn't have the talent to do it on your own.

If you datamined---->that is frowned upon

If you use MDA----->that is borderline cheating

If you use solvers---->you would have never made it without them

There will always be excuses from people who don't want to put in the work.

There's no maximum deviation sir, it just gets less likely

You and David have got to stop with your "boomer math," this is the second time recently that I have seen either of you make an egregious mathematical or logical error in your posts. Anyone who has ever played NLH poker would/should know that you don't flop a set/fullhouse/quads once every ~150 hands.

To arrive at the correct approximate frequency you can't just take 1 / [(Pairs/Total combos of hands) * (flopped set, full house, or quads frequency)] and completely disregard that you don't see a flop every time you are dealt a pocket pair preflop.

---

Your number of 2000 is inaccurate, but let's use it. Actually "losing money" over a sample of 2,000 flopped sets at >= 100bb NLH for a winning player would be something that no poker player has ever actually experienced or seen happen to anyone else, not even close. This event could actually occur at a significantly higher frequency when combined with a beyond atrocious level of play, but even still would be an exceedingly rare event. The original poster is clearly misremembering or embellishing their story to a significant degree anyway, their post formatting alone should have been a warning sign of a low quality post.



Not exactly the same as NLH (presumably cash) hands on FTP circa 2010, but this is what I have to work with. This is my graph for NLH MTTs at stack sizes > 99bb with flopped hand strength being bottom, middle, or top set and all in preflop = false. Extrapolating this sample with a σ of 595bb/100 to a sample of 2000 gives you this:





Keeping the σ at 595bb/100 you would need to drop the winrate for flopped sets down to ~650bb/100 (huge lol) before a 1/1,000,000 chance of a losing run shows up. Dropping the winrate your variance would actually lower significantly and make the 1/1,000,000 run disappear. Basically losing with flopped sets n = 2000 in any format or any stakes is "impossible" unless you are intentionally trying to lose.

+1 for post of the year. Gg SeaKing.