Interesting but I would have thought that

(line vs line variance)/(card v card variance) = winrate

or something to that effect.

I guess you are talking about PTBB/100 winrate.
But then again you can easily 4+ table FR cashgames and therefore have a bigger hourly winrate as opposed to HU hourly winrate.

6-max is golden middle in sustaining high winrate, IMHO.
Black, you r right, it's easy to play even 10-12 tables FR, 8-10 tables 6-max, but not more than 2 tables of HU cash, because in HU it is the most hard and tough spots to fight for, and you have to pick up on every read of opponents.
I quit HU Cash for some time, because it is killing my nerves to crush HU for very long, and then fall of a clip for long time. It is just toooooooo much variance.

I'm talking about both. 2 tables of HU = 8 tables of FR. I can 3 table relatively comfortably, and lots 4+ table.

Don't you think that playing so many tables is part of the reason variance is so high?

I think once you reach your limit of tables you can play at a time while still playing your A game it doesnt affect variance at all

Just wanted to say that this is wrong. If a winning player somehow did play for an infinite time, then his bankroll could either go bust or converge to infinity. I think a lot of the BR calculations out there do calculate the percent chance that you would ever go bust at your stakes given a certain winrate. The only way you'd be guaranteed to eventually go bust is if you continually cashed yourself out down to a point where you had an extremely small ROR instead of continuously growing your bankroll.

Define "A" game. I can four table profitably at 6-max with a good win-rate. If I was single-tabling, my win-rate would increase because I would be better at pressing smaller edges, that while they may be adding to fluctuation, these fluctuations are negated by better play. Also, there are plenty of call-downs or value bets that I would do while single-tabling that I do not make a habit of while multi-tabling. I am leaving some money on the table when I multi-table, there is no denying it. If I can add 1 bb/100 to my wr and shave 5bb/100 off my SD, my bankroll needs would dramatically decrease.

It is simple mathematics. Playing one table at 12bb/100 is less profitable than playing four tables at 4bb/100. By nature, the person with the lower win-rate is going to either have a larger SD or a SD that is going to have a larger effect on the win-rate and bank-roll needs.

I disagree, his bankroll will always be finite, and thus the chance of him going bust never undefined. Even at a billion trillion jillion $ bankroll, the odds of losing a billion trillion 70/30s is still not 0. Converges pretty much at 0 but still possible.

If any of you guys ever become immortal I hope you will have enough money set aside for at least one reload.

Knowing your winrate within +-1ptbb/100 when you have a 13ptbb/100 winrate seems a bit over the top though, if you're content with knowing your winrate within 1ptbb/100 for a 5ptbb/100 winrate (a very good 6m winrate). If you want to know your true winrate within +-20% of your current winrate, at any given confidence, you should be able to drastically decrease the number of hands needed in these calcs.

Is it not more interesting to compare HU and 6m in this manner instead? It seems pointless comparing absolute numbers like this since the potential winrates are so different. For example knowing your true winrate is within your current winrate +-10ptbb/100 is more usefull, and probably enough accurate, when you have a winrate of 100ptbb/100 compared to 1ptbb/100. A bit exteme, but you get the point.

I'm not sure what do you mean. So I'm not probably that guy About the simulator, I promised to let you guys have it once it ready but I haven't really got the time to finish it in such manner that it would be user friendly enough. Anyway, I hope I'll be able to let you have it in near future.

Good post LJ. It's interesting to see just how big a factor variance can be. However, essentially we are unsure of how much we are actually making until we put in the time over years and years to figure it out.

One thing I have been thinking about lately is, what if there was a program created to calculate just how lucky or unlucky we are? I know that pokerev is a great tool, but it doesn't really go into too much depth; something that could really give us a good idea of how we are doing after a mere 50 or 100 thousand hands.

I mean, you're only analyzing the base statistics to determine around what your winrate should be, and how "off" it could be. But if a program was to analyze individual hands much more in-depth than even pokerev does, it would give the player a HUGE understanding of how good they are doing.

I've heard people say that something like this wouldn't be that useful, because we shouldn't be too concerned with results and only with our own play. But knowing whether you are beating the limit you're playing at for how much you would like to be beating it for is obviously invaluable information.

Anyways, I've already read information on pretty much all that has been talked about here; but it is very clear to me that still, people just have no idea how ridiculous variance is. After playing 50K hands at a reasonably high SD, not many people would be able to swallow the fact that their winrate may be off by 5 or 6 PTBB/100.

Scansion, for a program to work like that, it would have to be created by a player that can beat all the limits.

multi-tabling does not change SD at all.

No, it may not change the SD, but it may lower your win-rate, which makes the same SD have a larger impact.

I don't really follow what you're trying to say here.

I think everyone benefits from knowing what their "true" winrate is. +/- 20% is still 2.8 PTBB for a 14 PTBB winrate and takes 335k hands if you have an SD like mine.

You don't have to talk in absolute numbers, that's why I gave you guys access to the spreadsheet. Work out your own numbers and figure out whatever it is you want to. You can change the winrate resolution on the spreadsheet to see how many hands it takes to get within +/- the input resolution (default is 1 PTBB/100).

Quite the opposite imo. In a reasonable sample size of 100k hands you can have a very clear idea if you are winning or losing. Yes, if you want an exact long term winrate, it's going to take a while, but that's the beauty of confidence intervals.

For example, if I keep my winrate over the next 35k hands (80k total) my chance of being a longterm winner is 99.99987%. That's pretty powerful to know. Also, my winrate becomes something between ~8 and ~19.5 PTBB/100 with 95% confidence. Again, not pinpoint, but it's certainly powerful to know.

So you can definitely get a good idea of where you stand in 2-4 months of hands played.

The only thing I was saying is that the difference is smaller between 6m and HU than what comes off in the thread, that's all.

+-20% for a 5ptbb/100 winner with a SD of 30 also takes 345k hands (SD stat taken out of my arse, but meant to represent a big 6m winner).

Basically I just reacted on that maybe one shouldn't compare 6m and HU calcs with absolute numbers, which I think many are doing. And when calcing in % instead you notice that the diff isn't really that big between 6m and HU.

Yes this what I meant, of course you will have a pretty accurate idea of whether you are a winning player but the amount that you could be off by is pretty astounding.

However one thing that I haven't seen mentioned is that players improve their game. I've been playing 1000nl for some time and I don't even count my first ~15k hands because they occurred before I took lessons.

So I guess technically these calculations are theoretical because I would be surprised if anyone played over two million hands of heads up and did not improve.

Srry for bumping this but it's a good post so w/e.

In fact, masterLJ, variance is even sicker than you describe.


Let's say you have a 10ptbb winrate over 100k hands. You might think the chances of your true winrate being 5ptbb or lower are equal to your true winrate being 15ptbb or higher, but that's not true.

The population of winrates isn't normally distributed, there are much more true winrates of 7ptbb then there are of 13ptbb. So, when you have a 10ptbb winrate over 100k hands, your true winrate is indeed between [10-x,10+x] with a certain confidence (obviously the confidence you want, together with your SD, determines x), but it's not symmetrical*! You have higher chance of your true winrate being [-infinity, 10] than of your true winrate being [10,infinity].

Unfortunately, we don't know how true winrates are distributed. We know it's 'weighted downwards': 7pbb winrates are more likely than 13ptbb winrates. But we don't know how much this effect plays (the higher your observed winrate it the more it plays though, for obvious reasons). In addition to that, you will get better. I guess the point is when you have an observed winrate that you are crushing the game, not only do you have the standard confidence interval putting your two feets in the ground, there is also another effect in play, making it even more likely you are 'just' a good player running hot instead of the next durrr (becausere there are more good players than durrrrrs)


English isn't my first language so it's kinda hard to put my thoughts into words, I'll just refer to mathematics of poker chapter 3 (page 40-43 in particular)

*the chance of the results of the next 100 hand sample being either [-inf,9] or [11,inf] is the same/symmetrical though

1) Playing 300/600 against durr might make your winrate at 25/50 higher (both by caring less about the money and by getting better) (although that argument applies more to a good nl1k reg/nl2k bumhunter playing the very best nl2k regs -- the space between 25/50 and 300/600 is just too big)
2) If you have a stoploss, what's the problem with taking a ~coinflip against someone you have a 4ptbb edge over at 3/6? If someone offered you a free 5k to flip for 50k (assuming that's like 1/20th of your bankroll), wouldn't you do it?

Also, it seems weird intuitivily that the fact that you actually play more hands/100 (as in, you fold less preflop, thus more and bigger possible manifestations of your edge) in HU as opposed to FR has no influence at all on these types of calculations.

I think the point was that its impossible to say your edge is 4ptbb and be confident about it without playing millions of hands. We basically have no clue who is the better player between Ivey and Antonius is and they cant be certain either, especially in such a high level match where each player is aware of what they are doing and will actively mix it up.

I think mean/SD are calculated hand by hand. It's simply the mean and SD of each hand we play. That's the right way to calculate it, although PT2 does it incorrectly