Another way of thinking about is like the stock market. If your have ever read a prospectus the bold face type says past performance is not indicative of future results. Just because a stock has returned 20% per annum for the last five years (aka your "observed poker win rate") does not mean it will continue returning 20% per annum in the future. Modeling out future results based on a previously observed win rate is a pointless excercise because the previous years' returns were influenced by random variance in the market which can and will be completely different in the future. A win rate simply tells you how you performed in the past given he circumstances, nothing more.

If you want more finance analogies, your win rate is the equivalent of the balance sheet which gives you a snapshot high level picture of where you stand at a particular point in time whereas the income statement or cash flow statement tells you how you are performing in the current ongoing operating environment.

Dude, that's not even two buyins. That can't be correct.

My guess is that you did not enter a realistic standard deviation.

You're falling victim for what what bip and I said earlier:


Your graphs just show a result, they don't show the variance of different outcomes.




If you look at the two graphs you'll notice that each graph has a lot of lines (potential outcomes) both above and below the dotted line (average winrate).

Where people get confused is that most of the lines are always winning over the sample size for the 8 bb winner and are still going up for the most part. Therefore their swing doesn't seem as bad, however if they are only winning 2 bbs for a long stretch that's still far below their expected value of 8 bbs for that stretch.

However for the -1bb loser (ideally this would be a winrate of 0, but too lazy to make another), half the lines are in the negative,therefore they are very aware that they are running below ev.

When people look at variance they focused on the X-axis when they should be focused on the dotted line.

+1. He's not even close on SD. ~75-100 bb/hr would be realistic, which is anywhere from 250-400 bb/100 depending on how many hands per hour you estimate (25-30).

There are also very complex factors to calculate for that differ from online, which factor in greatly to bankroll requirements. I've played in 2/5 games that play as big as a 10/25, and 5/T games that play smaller than a normal 2/5. I used to have a regular 1/2 game that played more like a 5/T.

Plugging the numbers into a formula is a place to start, but it's not the end all be all of bankroll management for live poker.

Thanks Bip and JohnnyBuz and bluegrassplayer I think it all makes more sense to me now.

Basically poker players are frequently conflating variables from a mathematical model of poker with their actual real world poker skills and then cognitive dissonance makes it difficult for them to unpick the model from reality.

Win rate = a measure of my innate but laboriously honed poker genius = persistent reality = means of deciding who is the best.

Variance = downswing = bad luck = anything getting in the way of my rightful winrate.

Risk of ruin = never going to happen


In reality there's just the cards, your decisions and your opponents' decisions. Everything else is a simplified model of reality used in an attempt to understand which are the better decisions ahead of time and thereby increase your chance of coming out ahead in the long run.

How big of a bankroll do I need to move up stakes?



Ultimately moving up stakes and bankroll requirements depends more on personal circumstances. It's rare but there's people out there who should skip 1 2 altogether and just jump into 2 5. Usually they have income to replenish their roll if things don't go well and are good enough that they'd be wasting their time at 1 2.

There's others who might have grinded out 100 buy ins for 2 5 by playing 1 2 and they still might not be ready skillwise to move up.

Also not everyone has a lot of options. If the only games offered near you are 1 2 or 5 10... well surely you aren't going to Grind out 250 buy ins at 1 2 before taking a shot.

Trying to have a steadfast rule "x buy ins to play this game" is pretty ridiculous because looking at someone's personal circumstances and making a decision that suits them and only them is neither that difficult nor time consuming. The most imoprtant thing is that you have enough buy ins that you can comfortably play your best.


Should I include tips/food paid for with chips/bad beat jackpots etc. when calculating my winrate?

Answer: It's typically assumed that when someone posts a winrate that tips ARE included, and most likely small purchases too. It's safe to assume that no one is eating a 60 dollar meal every session, paying for it with chips and still winning at $85/ hour. Winning a bad beat jackpot, or other forms of rakeback such as high hands etc. are usually not included.

However, when calculating your winrate/hourly for yourself you are free to do whatever you want. If you want to take meticulous notes on how you are doing in your player pool then it's best to not calculate tips and to pay for meals out of pocket. Some players even calculate the rake they pay. That way you know exactly what your winrate is, how much the rake is taking out, and you can compare your winrate to other winrates in different locations.

If you are more concerned with how much you make/spend on trips to the casino then include any expenses that you feel are necessary and include a bad beat jackpot or a high hand etc, but be sure to factor that in if you decide to compare your stats with someone else's. Ultimately your winrate is being recorded for you so feel free to record it in whatever way makes sense for you.



Do winning players experience less variance?









If you look at the two graphs you'll notice that each graph has a lot of lines (potential outcomes) both above and below the dotted line (average winrate).

Where people get confused is that most of the lines are always winning over the sample size for the 8 bb winner and are still going up for the most part. Therefore their swing doesn't seem as bad, however if they are only winning 2 bbs for a long stretch that's still far below their expected value of 8 bbs for that stretch.

However for the -1bb loser (ideally this would be a winrate of 0, but too lazy to make another), half the lines are in the negative,therefore they are very aware that they are running below ev.

When people look at variance they are focused on the X-axis when they should be focused on the dotted line.

Err my sims were using a sd of 70 which is perfectly reasonable for 9-10 handed live FR if you play a tighter strat.

Everyone ITT seems to be obfuscating the definition of variance. You play 1k hours with a 5bb/hr WR and your buddy plays 1k hours with a 15bb/hr wr. Both with 70 sd. Yes, technically you and your buddy should deviate from your EV the same amount but the way in which this manifests (I.e. much longer swings) is an aspect of variance that shouldn't be ignored imo. You, as a direct result of your lower WR, will experience several long back to back breakeven/losing months. Your buddy won't. Yes mathematically the sdev doesn't change but in any practical sense, WR does directly affect variance (which is a term that encompasses more than just whether you run above/below EV).

Another way of thinking about it is like this:

In 2015, Steph Curry averaged 30 points per game ("observed win rate") with sample size 'n=80' ("sessions played") and a standard deviation of 9.7 ("square root of variance").

The starting lineup in 2015 was: H. Barnes · A. Bogut · S. Curry · D. Green · K. Thompson

68% of the time (1 Sd.Dev), Steph scored between 20.3 and 39.7 points per game
95% of the time (2 Sd.Dev), Steph scored between 10.6 and 49.4 points per game
99.8% of the time (3 Sd.Dev), Steph scored between 1 and 59.1 points per game

If we were going to model out Curry's variance in 2016, would we use the observed values from 2015? Of course not! We would have to model out some incredibly complex Monte Carlo simulation combining less useful past performance with incredibly opaque future projections.

The variable conditions ("starting lineup" , "changes in other teams' rosters" , "changes in schedule" , "changes in Steph's health" , "changes in Steph's teammates health" , "changes in opponent's health") are so far beyond a static constant that we cannot even begin to consider using Curry's 2015 PPG average to model 2016 results.

The projected starting lineup in 2016 is: K. Durant · Z. Pachulia · S. Curry · D. Green · K. Thompson

And basketball is something I consider infinitely easier to model then the complexities in an ever changing poker environment. We can be reasonably assured that the Warriors will average somewhere between 100-110 points per game and Curry will average somewhere between his career average 22 PPG and career high 30 PPG. The biggest source of "variance" in 2016 will be the added presence of Kevin Durant and continued development of Klay Thompson which will likely push Curry's average down to the 22-25 PPG range.

The point being: past performance is not indicative of future results. Using past performance to model future variance is nonsensical because future variance (in the context of poker hand outcomes) is completely random and not based off anything that has occurred in the past.

Meale: if winrate and variance aren't actual things in reality but merely measures of what happened at a macro level over a period of time does it make sense to say "winrate affects variance"?

What you're actually describing above in terms of variables in a model of reality is a reality where one player makes fewer good decisions and therefore wins less when the cards are favourable, loses more when the cards are unfavourable and suffers longer breakeven and losing periods as a result.

The only thing that can truly be said to affect anything are the decisions made and the fall of the cards. All other variables are modelling some higher level outcome of decisions+cards. The varable in the model are correlated with each other but non of them cause anything.

Pokerdope gives me a bankroll requirement of 2936BB if you use a SD of 280 BB/100 (70 BB/hour, assuming 25 hands per hour) and 183BB if you use a SD of 70 BB/100.

My guess is that it is unrealistic to have a SD of less than twice your win rate.

Yes. If the result of the essentially poor play lead to longer lasting downswings/BE stretches, we can say while this player is losing, they're experiencing negative variance. If they lose for longer, the presence of this negative variance has a larger toll on mental game etc.

I understand the difference mathematically that above posters have been trying to mention, I e. Past results not indicating future results. But that's like saying we can't say someone who won for a mill hours at 50bb/hr will continue to win. Ofc they will. But this is just because we disagree about the definition of variance.

Also asiannit ye my bad I forgot to multiply sdev by 4 lmao

It's a bit more than 30 hands an hour for sure, let's say 32-33 hands per hour. So it's more like 30bb/100.

This is a wrong use of the term variance. Variance means deviation from your mean expected, whereas you mean variance in yhid instance to mean your expected WR.

In general, what a lot of people are saying when they are talking of increased variance is that when you have a lower WR, negative deviation from your expected WR will move you to a temporary losing hourly more often than if your expected WR was higher. Which is true.

But IMO, when the term variance should be used to describe how swingy is your game, the idea that you will have bigger winning and bigger losing sessions than one who's game produces less variance.

No, I did not mean expected WR, I meant variance. I'm fully aware what the terms mean. (You can read my other posts on this page)

When figuring out potential outcomes, like the ones I posted, assumptions are made regarding rake; basically that the rake remains constant throughout these runs. This is pretty true for deep stack (although not 100% and especially not for live poker), but not so much with short stacks. I'm convinced that the difference in rake leads to lower lows for short stackers, as well as higher highs resulting in higher standard deviation and being less likely to be near your mean in any given sample.

Paying more % rake (as a short stack has to) will just mean lower winrate. Variance won't be increased and lows will still be not as low in absolute terms as deep stack because you can't lose as much as quickly short stacked.

Are we all agreed your risk of ruin is lower short stacked assuming you are able to actually win?

I don't know, someone could only get that win rate in extreme conditions e.g. play money tables. They certainly could lose if those extreme conditions changed.

Indeed I'm sure there are many players who posted long winning periods online back in the early 2000's and went on to lose and give up poker all together as the games got tougher and they failed to keep up.

From wikipedia: There's a ton of posts talking about variance where what they mean is either Win Rate or Downswing. To use the Steph Curry posted above, what is difficult to calculate is his PPG, not his variance. That is the deviation he 'll experience from his PPG will in all likelihood remain the same.

And yeah, if your argument is that the rake is higher as a proportion of your stack, then what is affected is your WR, not your variance which as a deviation will stay more or less the same.

Now, may be as a shortstacker, you may experience higher variance than someone who plays deep, because you get to more showdowns. But that's a different argument.

People always reference 25 hands/hr. I dont know where this number comes from. Ive sat and counted on several different occasions over 3 straight days each time (about 12 hrs each time) and every time Ive gotten between 35-42 hands/hr.

Maybe its slower at 1/2 where more people see the flop. Not sure about that.

Rake in proportion to your stack and rake in proportion to profit per hand are very different things. The former is not my argument.

This will go pretty deep into derail territory and affect very few though so not going to get into it.

Yep this. Also, i find these graphs can be misleading because
1) people tend to compare a realization to the mean by projecting onto the mean when they should project down to the x-axis and consider where that projection line crosses the mean. This visually makes it appear like there is less variance.

2) the higher WR results in a graph with much larger range (y-axis) so the noise can appear muted as well.

It should be stressed that if you took a cross sectional slice of these two graphs for a given # of hands and shifted the dotted line to 0, it would be impossible to tell which distribution generated which image.

Quite honestly - more incorrect statements have been posted in the last 24 hours than correct ones. I actually discourage anyone from trying to learn about stats from discussions in here. (Yes, there are several correct things posted - but someone looking to learn won't be able to tell the difference).

The amount of incorrect information ITT is too much to overcome.. the actual message gets lost in the noise, people get defensive, and then thread derails.

I applaud bgp for trying to consolidate some common questions - but I fear it is like writing in the sand at low tide.

Here is the big one I want to address:

How do I play so that I don't go broke?

People always want to believe the answer to this is that there is some low variance winning style. As if in-hand decisions can be made by primarily considering variance. This is cart before the horse..
Try to win first and foremost. The single biggest factor in minimizing risk-of-ruin is to maximize win rate. Winning poker involves aggressive plays that carry risk. Playing scared (weak tight) can be lower variance, but it is not a winning strategy - and the probability of going broke is 100% certain (despite "low variance"). FWIW - I am not advocating LAG play, I am advocating TAG play. Take away the small risky edges... and you are left with no edge.

Yeah that's exactly why it's important to just make a faq as things get discussed. No one will ever be able to tackle everything. Just grab the thing I started and add/remove from it.

A FAQ explaining mean winrate, variance, standard deviation and risk of ruin would be useful to me.

Also bear in mind that a lot of us don't have a strong maths background and stuff that's obvious to someone with good maths skills can be totally opaque to others.

I will write something up on this. Something specific to poker and lighter on the math.