Losing streak length, is this ridonculous?

[littletrogdor]

Anyone have an opinion on how long a losing streak can get before mathematically its almost impossible for it to continue? I consider myself to be a good but not great player, I average about 2.5 bb/100 on $50 nl tables over about 40k hands the past year.

Lately though, I've been averaging -2 bb/100 over the last 10k hands. Everyone hates it when bad beats conspire to put a huge dent in your bankroll, but I think this is getting a little ridiculous.

Anyone have thoughts? And please dont tell me 10k hands is nothing :P

[Fnord]

10k hands is nothing and your win-rate isn't amazing.

Full table? 12%VP$IP/5% PFR? Or are you tighter than that?

[Demiparadigm]

What's your standard deviation?
You may have just been running good for 40K hands.

[littletrogdor]

This is full table, i play about 15% of the hands, raise the top 10 hands, sometimes position raises depending on the feel of the table. I never said my win rate was amazing One reason my it was 2.5 instead of a higher is I had a similar losing streak and dropped half my br a while back from bad beats.

Just lookin for some other peoples experiences thats all...

On another note, statistics is what it is. Talking about 40k hands as if someone is running hot or cold is a load of bs. Most players don't get anywhere near that many hands in a year, and they have a great feel for how they are doing. I know you many of you play a hell lot of hands, 8 tables at once, whatever, but the deviations you'll see from analyzing 10k hands vs 100k hands are quite small.

To put it into an example, on average over 40k hands youll see aces 182 times. If you see a flop 50% of those times (im being conservative), thats 91 events. You only need 30 to draw a normal distribution for a statistical event... say having your aces cracked.

[Fnord]

On another note, statistics is what it is. Talking about 40k hands as if someone is running hot or cold is a load of bs.

It's not, although your style will have less variance than most.

You have some horrible misconceptions about NLHE and all of your money comes from taking less than your fair share of money from the uber-donators, while giving up very little outside of your blinds (and your opponents are putting very little pressure there anyway.)

[KoRnholio]

re: post title

New word to spread around: Ridonkulous

Definition: A ridiculously bad poker play made by a donkey; often involving a suckout.

Usage: Man, I can't believe what a ridonkulous play that guy made on the flop, it's almost like he knew he'd turn that 2-outer.

[BIGandRICH]

My expierience...

I dropped a large proportion of my bankroll, and thought it was bad beats.. until i really analised the play, and though some people got lucky i still made alot of fucked up plays...

I dont have enough expierence to know how much of a sample 10K is.. but i'm pretty sure i'd be hard put to be down over 10K hands without screwing up along the way.

[Fnord]

I dont have enough expierence to know how much of a sample 10K is.. but i'm pretty sure i'd be hard put to be down over 10K hands without screwing up along the way.

It is, but the answer isn't simple and depends a lot on your win-rate, etc.

[Checkways]

Anyone have an opinion on how long a losing streak can get before mathematically its almost impossible for it to continue? I consider myself to be a good but not great player, I average about 2.5 bb/100 on $50 nl tables over about 40k hands the past year.

Lately though, I've been averaging -2 bb/100 over the last 10k hands. Everyone hates it when bad beats conspire to put a huge dent in your bankroll, but I think this is getting a little ridiculous.

Anyone have thoughts? And please dont tell me 10k hands is nothing :P

Personally, I've never had a losing streak that long before. Have you been playing break even/losing for the last 10k hands? If so, then that's a bad sign. If you were mostly winning, but then hit a couple of really bad streaks then it may just be variance.

Take a break and analyze your game. Don't be satisfied with 2.5bb/100. You should definitely start looking to improve your game overall.

[littletrogdor]

Fnord I know your the man and all, but if I have horrible misconceptions about nlhe, why am I up so much money? Your pinning me as a TAG player who only goes fishing. I take money from everyone at the table, not just the fish, and make the laydowns that I need to.

I guess I'll just ride it out. If you guys are waiting for enough hands to draw a 99% confidence interval in your stats, your out of your mind. And if you don't understand exactly what that statement means, you should take a statistics course before you make comments on what is or isn't enough hands to draw conclusions on your play.

Thanks to those who responded.

[johnny_fish]

Fnord I know your the man and all, but if I have horrible misconceptions about nlhe, why am I up so much money? Your pinning me as a TAG player who only goes fishing. I take money from everyone at the table, not just the fish, and make the laydowns that I need to.

I guess I'll just ride it out. If you guys are waiting for enough hands to draw a 99% confidence interval in your stats, your out of your mind. And if you don't understand exactly what that statement means, you should take a statistics course before you make comments on what is or isn't enough hands to draw conclusions on your play.

Thanks to those who responded.

I don't get it. You say 10K is enough to be a reliable estimate, but when it shows a negative result, you'll think of it as variance and you'll ''ride it out''..

If you think it's reliable: Make adjustments to your game, or stop playing.
If you don't think it's reliable: Keep playing till you get a reliable sample size.

[sandstorm]

I guess I'll just ride it out. If you guys are waiting for enough hands to draw a 99% confidence interval in your stats, your out of your mind. And if you don't understand exactly what that statement means, you should take a statistics course before you make comments on what is or isn't enough hands to draw conclusions on your play.

We don't need 99% confidence here, but still, 10k hands in poker is not much. Post some more of your stats here, and I'm sure you'll get a few really good tips!

[Aceofone]

If your losing consistently over 10,000 hands, you have leaks to plug.

[sandstorm]

http://www.flopturnriver.com/phpBB2/...ic.php?t=22058

[TalentedTom]

If your losing consistently over 10,000 hands, you have leaks to plug.

Yeah, 2.5bb/100 isnt too great either, you are barley beating the games and now they are barley beating you.
There are leaks, its your job to find them.

[Miffed22001]

my losing streaks last for one hand
i lose my stack and leave

so my longest is two hands. Both KK vs AA back to back at different tables
meh

[r8ed]

Like others mention, you should anaylze your play periodically to find leaks whether you are winning or losing. Plus, despite the large volume of fish out there, many of the usual players are getting better and smarter. Even some newbies are getting smarter right when they start thanks to places like FTR. Everyone and their uncle is continuation betting their prelop raises these days. That wasn't happening as often say 6 months ago. I'm sure you know how to adjust, but you should always hunt for leaks.

[Pyroxene]

I guess I'll just ride it out. If you guys are waiting for enough hands to draw a 99% confidence interval in your stats, your out of your mind. And if you don't understand exactly what that statement means, you should take a statistics course before you make comments on what is or isn't enough hands to draw conclusions on your play.

Honestly, Fnord's comments about 10K being a small sample are right on the money; and it is fairly easy to demonstrate.

The odds of being dealt a pocket pair are 1 in 17. The odds of flopping quads with that PP are about 1 in 400. On the average, in 10K hands you have only seen it once (33.8%). It would be easy to have not seen it at all (22.9%), leaving 43.3% of the people that saw it more than once*. It is possible another guy saw it 3 times. Assuming you got it the average one time, did someone else have a boat or an over-pair they could not put down; allowing you to destack them? If so, were both stacks quite deep? Or, the one time it happened to you did you get no action? That can literally make a 2xbuy-in difference in your total BR right there in that one wonderful hand. But there is a 20% chance you got it while you were in the blinds, out of position you try to slow play; no one bets.

And that is just flopped hidden quads.

In 10K hands you will get pocket Aces roughly 45 times. Roughly 2 of those times someone else will be dealt pocket Kings. Did you get your fair share of two (there is a 9.9% chance that this never happened to you in 10K hands)? Did you get him All-In and win the hand? Or did an Ace flop and scare him off? It's likely only happened twice to you in 10K hands so the variance is quite large. That is the type of thing that could put your bankroll up by 2xbuy-ins. But it is entirely possible that you lost both times to the KKs, there is a little more than 3% chance of it in fact. So in a sample of 25 people, each who have played 10K hands, it likely will have happened to 1 of them. What's more, 7 of those 25 people will have lost one of them and won one of them coming out even for the experience assumming equal stacks both times. The other 17 people have a 2xBuy-In bankroll advantage over those 7 and a 4xBuy-In over the one poor guy.**

In 10K hands there are honestly not that many monster vs monster (someone is going to lose a stack) opportunities. It is quite possible that you have not seen a straight flush using both your hole cards, while someone else saw two and got big action both times. It is entirely possible that one person got 15 of these monster vs. monster opportunities, got action on 12 of them and won 11. It is also entirely possible that one person got 9 of these opportunities, got action on 5 of them and won only 3.

I do agree that 10K hands is likely enough to minimize the variance of your standard decent hand vs decent hand. But it is not nearly enough for your big Buy-In (or even multi-Buy-In) swinging hands to even out to the expected distribution.

That can have an enormous impact on your BB/100 hands. Consider stack depths of 100 BB. Using the examples above just for AA vs KK. For 17 of the 25 people the AA vs KK hands will have contributed 100 BB * 2 / 10K hands which is 2 BB/100 hands. Seven people will be +0 BB / 100 hands and the one poor guy will literally be -2 BB / 100 hands just from the variance because the sample is small. Judging from your BB/100 that you mention, whether you are one of the 17 or one of the 7 or the one unlucky joe will cause a variance in your BB / 100 roughly equal to its current value.

And the AA vs KK fight works both ways. In 10K hands you likely have been the KK vs an AA two times; but there is a 9.9% chance that it has not happened to you at all. Assuming it did, did the AA guy slowplay PF only for an Ace to flop and cause you to back off? Or did he push hard both times and get you All-In PF destacking you both times. Were you the lucky 1 guy in 25 that won BOTH times that happened, or one of the 7 that is even for the experience, or one of the 17 whose BB/100 is down by 2 just from those two hands?

With a larger sample size these differences even out. While 1 guy in 25 will lose all of his AA vs. KK matchups in 10K hands (hitting his BB/100 for a -2), only 1 guy in 29.8 million will keep up that losing rate for 50K hands. While 17 in 25 will win all of their AA vs. KK matchups (adding +2 BB/100) only 1 in 7 will keep up that win rate for 50K hands. Everyone else begins to approach the expected win rate of roughly 4 out of 5.

So, I hope I made the numeric case for why a 10K sample size is insufficient to determine a meaningful BB / 100.

* For a quick breakdown to illustrate the variance, with a sample size of 10K events with each event having a 1 in 6800 chance of being positive:

22.97% of no positives 0 per 10K
33.79% of 1 positive 1 per 10K
24.84% of 2 positives 2 per 10K
12.17% of 3 positives 3 per 10K
4.47% of 4 positives 4 per 10K
1.325 of 5 positives. 5 per 10K

So the typical person will flop hidden quands 1 time in 10K hands, but better than 175 will flop it 3 or more times. The BB/100 of the lucky 17% will reflect this.

Compare that to 50K samples

4.24% of 3 positives .6 per 10K
7.8% of 4 positives .8 per 10K
11.48% of 5 positives 1 per 10K
14.06% of 6 positives 1.2 per 10K
14.77% of 7 positives 1.4 per 10K
13.58% of 8 positives 1.6 per 10K
11.09% of 9 positives 1.8 per 10K
8.16% of 10 positives 2 per 10K
5.45% of 11 positives 2.2 per 10K
...
0.99% of 14 positives 2.8 per 10K

Notice the significantly tighter distributiuon. With only 10K samples, almost 18% of the people will experience 3 times the number of quads as the typical person. But by the time we get to 50K samples, less than 1% of the people will expereince triple the expected occurance count.

** AA vs KK is a 81.9 to 18.1 fight. Odds of losing 2 for 2 are (0.181 * 0.181) = 3.2%. Odds of winning both are (0.819 * 0.819) = 67.0 %. Odds of 1 win and 1 lose are (100 - 67.0 - 3.2) = 29.8%

[sejje]

Yeah, I don't understand this.

It's late, so maybe my thinking/math is way off here. But -2BB/100 for 10K hands amounts to 2 buy-ins, right?

Hell, I swing 2 buy-ins ALL THE TIME. I swing 5 now and then, and I've lost 10 in a couple of days before.

What if you played to +2BB for 9,900 hands, and in the last 100 hands you lost four buy-ins to suckouts? That's some sweet variance for you. 10K hands isn't enough.

[r8ed]

Isn't -2BB/100 =
-2 Big Bets/100 hands where Big Bets are 2x Big Blind?

That's -$1/100 which is pretty much even. If you can play that way and collect bonuses or rakeback, then you will make a profit. It's harder to do that these days since the Party breakaway.

[aislephive]

Switch to limit if you want less variance.

[TalentedTom]

I guess I'll just ride it out. If you guys are waiting for enough hands to draw a 99% confidence interval in your stats, your out of your mind. And if you don't understand exactly what that statement means, you should take a statistics course before you make comments on what is or isn't enough hands to draw conclusions on your play.

Honestly, Fnord's comments about 10K being a small sample are right on the money; and it is fairly easy to demonstrate.

The odds of being dealt a pocket pair are 1 in 17. The odds of flopping quads with that PP are about 1 in 400. On the average, in 10K hands you have only seen it once (33.8%). It would be easy to have not seen it at all (22.9%), leaving 43.3% of the people that saw it more than once*. It is possible another guy saw it 3 times. Assuming you got it the average one time, did someone else have a boat or an over-pair they could not put down; allowing you to destack them? If so, were both stacks quite deep? Or, the one time it happened to you did you get no action? That can literally make a 2xbuy-in difference in your total BR right there in that one wonderful hand. But there is a 20% chance you got it while you were in the blinds, out of position you try to slow play; no one bets.

And that is just flopped hidden quads.

In 10K hands you will get pocket Aces roughly 45 times. Roughly 2 of those times someone else will be dealt pocket Kings. Did you get your fair share of two (there is a 9.9% chance that this never happened to you in 10K hands)? Did you get him All-In and win the hand? Or did an Ace flop and scare him off? It's likely only happened twice to you in 10K hands so the variance is quite large. That is the type of thing that could put your bankroll up by 2xbuy-ins. But it is entirely possible that you lost both times to the KKs, there is a little more than 3% chance of it in fact. So in a sample of 25 people, each who have played 10K hands, it likely will have happened to 1 of them. What's more, 7 of those 25 people will have lost one of them and won one of them coming out even for the experience assumming equal stacks both times. The other 17 people have a 2xBuy-In bankroll advantage over those 7 and a 4xBuy-In over the one poor guy.**

In 10K hands there are honestly not that many monster vs monster (someone is going to lose a stack) opportunities. It is quite possible that you have not seen a straight flush using both your hole cards, while someone else saw two and got big action both times. It is entirely possible that one person got 15 of these monster vs. monster opportunities, got action on 12 of them and won 11. It is also entirely possible that one person got 9 of these opportunities, got action on 5 of them and won only 3.

I do agree that 10K hands is likely enough to minimize the variance of your standard decent hand vs decent hand. But it is not nearly enough for your big Buy-In (or even multi-Buy-In) swinging hands to even out to the expected distribution.

That can have an enormous impact on your BB/100 hands. Consider stack depths of 100 BB. Using the examples above just for AA vs KK. For 17 of the 25 people the AA vs KK hands will have contributed 100 BB * 2 / 10K hands which is 2 BB/100 hands. Seven people will be +0 BB / 100 hands and the one poor guy will literally be -2 BB / 100 hands just from the variance because the sample is small. Judging from your BB/100 that you mention, whether you are one of the 17 or one of the 7 or the one unlucky joe will cause a variance in your BB / 100 roughly equal to its current value.

And the AA vs KK fight works both ways. In 10K hands you likely have been the KK vs an AA two times; but there is a 9.9% chance that it has not happened to you at all. Assuming it did, did the AA guy slowplay PF only for an Ace to flop and cause you to back off? Or did he push hard both times and get you All-In PF destacking you both times. Were you the lucky 1 guy in 25 that won BOTH times that happened, or one of the 7 that is even for the experience, or one of the 17 whose BB/100 is down by 2 just from those two hands?

With a larger sample size these differences even out. While 1 guy in 25 will lose all of his AA vs. KK matchups in 10K hands (hitting his BB/100 for a -2), only 1 guy in 29.8 million will keep up that losing rate for 50K hands. While 17 in 25 will win all of their AA vs. KK matchups (adding +2 BB/100) only 1 in 7 will keep up that win rate for 50K hands. Everyone else begins to approach the expected win rate of roughly 4 out of 5.

So, I hope I made the numeric case for why a 10K sample size is insufficient to determine a meaningful BB / 100.

* For a quick breakdown to illustrate the variance, with a sample size of 10K events with each event having a 1 in 6800 chance of being positive:

22.97% of no positives 0 per 10K
33.79% of 1 positive 1 per 10K
24.84% of 2 positives 2 per 10K
12.17% of 3 positives 3 per 10K
4.47% of 4 positives 4 per 10K
1.325 of 5 positives. 5 per 10K

So the typical person will flop hidden quands 1 time in 10K hands, but better than 175 will flop it 3 or more times. The BB/100 of the lucky 17% will reflect this.

Compare that to 50K samples

4.24% of 3 positives .6 per 10K
7.8% of 4 positives .8 per 10K
11.48% of 5 positives 1 per 10K
14.06% of 6 positives 1.2 per 10K
14.77% of 7 positives 1.4 per 10K
13.58% of 8 positives 1.6 per 10K
11.09% of 9 positives 1.8 per 10K
8.16% of 10 positives 2 per 10K
5.45% of 11 positives 2.2 per 10K
...
0.99% of 14 positives 2.8 per 10K

Notice the significantly tighter distributiuon. With only 10K samples, almost 18% of the people will experience 3 times the number of quads as the typical person. But by the time we get to 50K samples, less than 1% of the people will expereince triple the expected occurance count.

** AA vs KK is a 81.9 to 18.1 fight. Odds of losing 2 for 2 are (0.181 * 0.181) = 3.2%. Odds of winning both are (0.819 * 0.819) = 67.0 %. Odds of 1 win and 1 lose are (100 - 67.0 - 3.2) = 29.8%

Jeez that's a long post. I read the first sentance bookmarked it, and will continue later, it looks like a lot of good stuff. This is the longest post I have ever seen, you should gather all this stuff up and write a book, everyone is doing it these days you can make a killing. I would buy a copy just to show it off to everyone.

[Checkways]

I guess I'll just ride it out. If you guys are waiting for enough hands to draw a 99% confidence interval in your stats, your out of your mind. And if you don't understand exactly what that statement means, you should take a statistics course before you make comments on what is or isn't enough hands to draw conclusions on your play.

Honestly, Fnord's comments about 10K being a small sample are right on the money; and it is fairly easy to demonstrate.

The odds of being dealt a pocket pair are 1 in 17. The odds of flopping quads with that PP are about 1 in 400. On the average, in 10K hands you have only seen it once (33.8%). It would be easy to have not seen it at all (22.9%), leaving 43.3% of the people that saw it more than once*. It is possible another guy saw it 3 times. Assuming you got it the average one time, did someone else have a boat or an over-pair they could not put down; allowing you to destack them? If so, were both stacks quite deep? Or, the one time it happened to you did you get no action? That can literally make a 2xbuy-in difference in your total BR right there in that one wonderful hand. But there is a 20% chance you got it while you were in the blinds, out of position you try to slow play; no one bets.

And that is just flopped hidden quads.

In 10K hands you will get pocket Aces roughly 45 times. Roughly 2 of those times someone else will be dealt pocket Kings. Did you get your fair share of two (there is a 9.9% chance that this never happened to you in 10K hands)? Did you get him All-In and win the hand? Or did an Ace flop and scare him off? It's likely only happened twice to you in 10K hands so the variance is quite large. That is the type of thing that could put your bankroll up by 2xbuy-ins. But it is entirely possible that you lost both times to the KKs, there is a little more than 3% chance of it in fact. So in a sample of 25 people, each who have played 10K hands, it likely will have happened to 1 of them. What's more, 7 of those 25 people will have lost one of them and won one of them coming out even for the experience assumming equal stacks both times. The other 17 people have a 2xBuy-In bankroll advantage over those 7 and a 4xBuy-In over the one poor guy.**

In 10K hands there are honestly not that many monster vs monster (someone is going to lose a stack) opportunities. It is quite possible that you have not seen a straight flush using both your hole cards, while someone else saw two and got big action both times. It is entirely possible that one person got 15 of these monster vs. monster opportunities, got action on 12 of them and won 11. It is also entirely possible that one person got 9 of these opportunities, got action on 5 of them and won only 3.

I do agree that 10K hands is likely enough to minimize the variance of your standard decent hand vs decent hand. But it is not nearly enough for your big Buy-In (or even multi-Buy-In) swinging hands to even out to the expected distribution.

That can have an enormous impact on your BB/100 hands. Consider stack depths of 100 BB. Using the examples above just for AA vs KK. For 17 of the 25 people the AA vs KK hands will have contributed 100 BB * 2 / 10K hands which is 2 BB/100 hands. Seven people will be +0 BB / 100 hands and the one poor guy will literally be -2 BB / 100 hands just from the variance because the sample is small. Judging from your BB/100 that you mention, whether you are one of the 17 or one of the 7 or the one unlucky joe will cause a variance in your BB / 100 roughly equal to its current value.

And the AA vs KK fight works both ways. In 10K hands you likely have been the KK vs an AA two times; but there is a 9.9% chance that it has not happened to you at all. Assuming it did, did the AA guy slowplay PF only for an Ace to flop and cause you to back off? Or did he push hard both times and get you All-In PF destacking you both times. Were you the lucky 1 guy in 25 that won BOTH times that happened, or one of the 7 that is even for the experience, or one of the 17 whose BB/100 is down by 2 just from those two hands?

Nice post. So how many hands is a good sample size in your opinion?

[WhooFleuryScores]

I dropped a large proportion of my bankroll, and thought it was bad beats.. until i really analised the play, and though some people got lucky i still made alot of fucked up plays...

Had that happen to me last month during my October losing skid.Realized that I had been overplaying my PP sometimes as well as raising my straights or flushes despite a paired board.Ended up on the losing end of course.Also tended to miss many value bets on the river against passive calling stations and thus leaving money on the table.

[Demiparadigm]

Switch to limit if you want less variance.

limit has more variance.


Good luck.

[Molinero]

"Poker Statistics for Dummies" by Pyroxene (2005) FlopTurnRiver Press

[r8ed]

Also tended to miss many value bets on the river against passive calling stations and thus leaving money on the table.

I gotta improve there too. You wonder what they are calling you down with and don't want to get reraised. Then you check the river and they have one pair or Ace high. Even extracting only 10% more on the river should add up over time.

[SinkRox]

welcome to poker varience. U've either had a bad [long lasting] run or played bads/have leaks to anylise - probablky a bit of everything.

Checkout my last 68k hands and my varience (.1/.2NL 10max) and my loosing sessions post here: http://www.flopturnriver.com/phpBB2/...osing+sessions

[WhooFleuryScores]

[img]
[/img]

Had the same issues too.Working my way back though.

[boyobach]

Hey, Sinkrox....

how'd you pull that graph off pokertracker?

I have PT but aint sussed graphs yet

[Pyroxene]

I guess I'll just ride it out. If you guys are waiting for enough hands to draw a 99% confidence interval in your stats, your out of your mind. And if you don't understand exactly what that statement means, you should take a statistics course before you make comments on what is or isn't enough hands to draw conclusions on your play.

Honestly, Fnord's comments about 10K being a small sample are right on the money; and it is fairly easy to demonstrate.

...

Nice post. So how many hands is a good sample size in your opinion?

That is a very good question. I have been thinking on it for the last couple of days, trying to make sure my answer was meaningful.

In words, I will put it forth this way: The sample needs to large enough that the effect of monster vs. monster does not shift the BB/100 of the vast majority of people by an amount they find significant.

A Few Definitions and One or Two Arguable Assumptions

1) Monster vs. monster

I am talking about pre-flop and flop collisions of hands where, regardless of skill, both players have every reason to believe they are strongly ahead.

I am not talking about just any old hand where two people go All-In. A lot of people go All-In more often than they should and a lot of people do not go All-In as often as they should. That is a matter of skill and it SHOULD affect their BB/100.

I am talking about the fairly rare collision of cards that neither side has any reason to back down on. Hands like AA vs KK preflop, top set vs. second set on a rainbow disconected board, AA vs. AK on a AKK flop, top boat against hidden quads.

These hands happen and when they happen someone usually gets destacked and the other person doubles up. Yet the -100 BB vs +100 BB bankroll swing hand had nothing to do with skill. Because EVERY player is trying to get their chips in the pot because 99% of the time they have the best hand in that position.

** ASSUMPTION **: I am going to assume that for any given individual, about 1 hand in 500 is like this. As an example, a specific person will be dealt AA when one (or two) of his opponents are dealt KK 1 in 5013 hands at a 10 man table. Obviously, that person will be dealt KK against an opponents AA the same rate of 1 in 5013 hands. So roughly 20% of these monsters vs. monsters are AA vs KK pre-flop. So, I feel my assumption is good but if people want to argue it, I am willing to listen.

2) Vast majority of the people

I am going to go with 92% here. That leaves 4% of the people being unlucky and 4% being lucky. Both of these 4% will say my analysis is wrong because they will find it hard to believe they are that far on the edge. I can live with that.

3) Shifting by an amount they find significant

If you are +BB/100 then you are making money (amazing insight there I know). But, the studies show only about 30% of the poker players are in that range. In turn, the BB/100 range of the 80th percentile is quite different from the BB/100 range of the 97th percentile. If I say 2BB/100 is a good rate, the upper crust will laugh and say that is peanuts. If I say 12 BB/100 is a good rate, a lot of money making players will say I am dreaming.

With that in mind, I am going to settle on 5 BB/100 hands as a solid rate. In turn, I am going to say that I want the sample size to be large enough that the monster vs. monster collisions are not swinging it by +/- 20%.

Putting it all together, I am saying the sample has to be large enough that the outcome of the rare (1 in 500) collision of monster vs monster hands has a less than +/- 1BB/100 effect on 92% of the population.

So, what does that leave?

I did a lot of heavy math for this. Enough that I think I will write up a whole post on variance. I am not going to go into enormous detail on the math because it will just bog down this short post. I will put all the math and analysis in a longer post some other day. Until then, trust my math.

For the one paragraph of what I did:

I determined the distribution of people that would have a certain number of monster vs. monster hands in various sample sizes. Within each number of such hands, I computed the distribution of outcomes based on a 50/50 chance of winning or losing (if it was not 50/50 then it was really a skill based hand that someone played wrong). Using the second set of distributions multiplied by the likelyhood from the first distribution, this gives me a percentage of people that experience a certain number of 100 BB loses or gains. I total all of those percentages for all of those distributions then I divided by the number of (10K hands) that the sample represents. This last step is the step that takes into acount a 100 BB loss over 10K hands is -1BB/100, but a 100 BB loss over 100K hands is only a -0.1BB/100.

What do we know?

We know that 10K hands is laughably small. I made some charts that I will include in the larger write up. But here are the numbers from the middle of the distribution of 10K hands:

BB/100     percent
-5	      4.74
-4	      5.96
-3	      7.12
-2	      8.10
-1	      8.73
 0	      8.97
 1	      8.73
 2	      8.10
 3	      7.12
 4	      5.96
 5	      4.74

Less than 9% of the population will be within the tolerance I wanted. An amazing 91% of the population will have a +/- 1BB/100 hand swing OR MORE because of these monsters. Perhaps even more interesting, slighly better than 30% of the population will have a +/- 5BB/100 swing. Remember back to my 5BB/100 hands being a good rate. What this is saying is that in a set of TOTALLY EQUAL players ALL of whom can make 5BB/100 hands over the very long term, 15% will be at 0BB/100 or WORSE and 15% will be at 10BB/100 or BETTER just from these 1/500 coin flip hands. Over 3% of the population will have experienced an amazing +/- 10BB/100 shift.

I hope then that everyone can agree 10K is too small.

How does 50K look ... better ... but not there yet

BB/100     percent
-3  	      1.29
-2.8	      1.49
-2.6	      1.71
-2.4	      1.94
-2.2	      2.18
-2  	      2.42
-1.8	      2.66
-1.6	      2.90
-1.4	      3.12
-1.2	      3.33
-1  	      3.52
-0.8	      3.69
-0.6	      3.82
-0.4	      3.91
-0.2	      3.97
 0  	      3.99
 0.2	      3.97
 0.4	      3.91
 0.6	      3.82
 0.8	      3.69
 1  	      3.52
 1.2	      3.33
 1.4	      3.12
 1.6	      2.90
 1.8	      2.66 
 2  	      2.42
 2.2	      2.18
 2.4	      1.94
 2.6	      1.71
 2.8	      1.49
 3  	      1.29

64% of the population is still outside of my 1BB/100 swing target. But that is a huge improvement. Also, gone are the +/- 10BB/100 swings. Only about 1 in 500 people are experiencing more than a +/- 5.6BB/100 shift.

But this does not meet my goals.

Scotty, I need more samples!

100K hands yields:

BB/100     percent
-2  	      1.04
-1.9	      1.14
-1.8	      1.25
-1.7	      1.37
-1.6	      1.49
-1.5	      1.61
-1.4	      1.73
-1.3	      1.85
-1.2	      1.97
-1.1	      2.08
-1  	      2.20
-0.9	      2.30
-0.8	      2.40
-0.7	      2.50
-0.6	      2.58
-0.5	      2.65
-0.4	      2.71
-0.3	      2.76
-0.2	      2.79
-0.1	      2.82
 0  	      2.82
 0.1	      2.82
 0.2	      2.79
 0.3	      2.76
 0.4	      2.71
 0.5	      2.65
 0.6	      2.58
 0.7	      2.50
 0.8	      2.40
 0.9	      2.30
 1  	      2.20
 1.1	      2.08
 1.2	      1.97
 1.3	      1.85
 1.4	      1.73
 1.5	      1.61
 1.6	      1.49
 1.7	      1.37
 1.8	      1.25
 1.9	      1.14 
 2  	      1.04

49% are outside my range, but we are getting better. Also, only about 2% experience more than a 3BB/100 swing.

Beyond that, my computer programs are still cranking out the numbers. I knew a large number of samples would be necessary but I had thought that 100K samples would be closer than it actually was.

I will say this, if you are a solid 5BB/100 player, the effects of these monsters cannot throw you negative in 100K hands. If you drift into the 1BB/100 or below then you are going to have to look for something else to blame.

I hope these numbers really illustrate what so many of the good players on FTR try to re-enforce, 'Poker is a long term game.'

[salsa4ever]

that is easily the best fukn post i've seen in my entire life!

GOGOGO!

please post the rest of the math. I *always* thought statistics was an utterly useless subject. Now I know it's just that at Uni, they don't apply it to anything useful.

[Irisheyes]

Yea amazing post, I can tell a load of work went into that. Thanks.

Must say I never thought this rare of a situation would have that large an affect over what I considered to be a ample sample size.

[SinkRox]

Hey, Sinkrox....

how'd you pull that graph off pokertracker?

I have PT but aint sussed graphs yet

http://www.flopturnriver.com/phpBB2/...=poker+grapher

[BankItDrew]

Let's ASSUME that 200k hands would be a good indicator of where a player is with the bb/100 scale. This is only an indicator of how this player ranks based on his/her previous 200k hands. I know that 200k hands from now, I will be a much better player than I am today. Unfortunatly, I can't scale my improvement.

Unless, one were to graph each set of each 25k hands, and observe the trends on a line.

[swiggidy]

To save your computer the effort of cruching numbers (and for whomever wanted more math)...

The data matches a normal (Gaussian) distribution exactly. So to make this chart:

BB/100 percent
-5 4.74
-4 5.96
-3 7.12
-2 8.10
-1 8.73
0 8.97
1 8.73
2 8.10
3 7.12
4 5.96
5 4.74

use:
percent = 100*i/sqrt(2*pi*s) * exp(-b^2/(2*s))

where:
i = BB/100 increment (i = 1 for 10k, 0.2 for 50k, 0.1 for 100k)
s = 200k/sample set size (s = 20 for 10k, 4 for 50k, 2 for 100k)
b = BB/100 (first column)

s = sigma^2 in the guassian formula. 2*sigma represents 95% of the population, so set:
v= acceptable BB/100 variation (+-1 for Pyroxene)

then:
Desired sample set size = 200k/v^2

by Pyroxene's method and thinking:
v = 1 => Desired sample set = 200k

If +-2 BB is acceptable then 200k/4 = 50k is a satisfactory sample set.

A sample set of 10k implies a possible variation up to +- 8BB (by Pyroxene's setup)