Variance in poker: Living with the Beast
 

I posted this in the microstakes forum a while back. I got a request to update the links so I figured I'd cross post this here for those who hadn't seen it.


We all worry about our win rate, it is of course why most of us play. However some people worry after playing one two or even 5 thousand hands. Most people who understand variance suggest having at least 100,000 hands before trying to analyse your BB/100, I am going to present some visual evidence for this.

We will look at two types of players, a successful player and a losing player. The winner has a true win rate of 5BB/hr and the losing player -2BB/hr, or roughly 8.5BB/100 and -5BB/100. I have assumed a standard deviation of roughly 50BB every 100 hands. In other words, for every 100 hand you can be up or down a full buy in.

The good player should be "killing" the game and in the first graph after 100 hours (6,500 hands) he clearly is.

http://www.celticchef.com/poker/files/5BBGood.JPG

Our hero is running very well crushing the game at 11 BB/hr or possibly 17BB/100

In the second graph however, he is not doing so well:

http://www.celticchef.com/poker/files/5BBWTF.JPG

Wow... some wild swings ending up around -0.8BB/hr or -1.5BB/100

But check out the third graph

http://www.celticchef.com/poker/files/5BBBad.JPG

Ouch! -7.5BB/hr or something like -12BB/100. How many people would call this player a losing player if he posted this graph after 6500 hands? In truth he is crushing the game in the long run.

Now let's look at the 1600 hours or roughly 100,000 hands

http://www.celticchef.com/poker/files/5BB1600.JPG

much more "normal looking" at around 4.5BB/hr, just a little off his "real" rate

Now for the losing player. You know what's coming so I’ll just post the links.

http://www.celticchef.com/poker/files/Neg2BBGood.JPG
http://www.celticchef.com/poker/files/Neg2BBBad.JPG
http://www.celticchef.com/poker/files/Neg2BBWTF.JPG

And the "long run":
http://www.celticchef.com/poker/files/Neg2BB1600.JPG

Again we see the same kind of graphs. The losing player can actually be running +5BB/hr when in reality he is a losing player.

So we see the value of not jumping to conclusions until we have a large number of hands in. But is even 100,000 enough? One final graph will prove my point:

http://www.celticchef.com/poker/files/OMGWTFBBQ.JPG

Here we see that our -2BB/hr loosing player can still break even over a large number of hands. This is why we should take 100,000 hands as a minimum before we seriously worry about our BB/100.

Where does that leave the recreational player who likes to play 10 hours a week? About three years worth of playing to reach 100K hands. Of course, if you are crushing the game it is much more likely you won't face this long term downswing, but it does happen.

Welcome to poker country... variance lives here and you are on her turf. She likes to play rough and when she does it is a bumpy ride. Don't let her throw you off your game and just take each hand as it comes. Just play each hand the best way you know how... and buckle up.

Re: Variance in poker: Living with the Beast
 

NH, Raistlinx. Thanks for cross-posting as I hadn't seen it before.

Re: Variance in poker: Living with the Beast
 

[ QUOTE ]
I have assumed a standard deviation of roughly 50BB every 100 hands.

[/ QUOTE ]

This is gonna make your whole post invalid, which sucks because I see where you were going with it.

Even most 6maxers have a SD of less than this.

Very well thought out post though. Would love to see this with more accurate numbers.

Re: Variance in poker: Living with the Beast
 

Thanks Raistlinx...this is my first full month grinding out 2K+ hands a day every day and some of the swings I've seen have made my head spin. It's nice to read this stuff and see it in concrete terms since sometimes it feels like the Poker God has singled you out for annihilation.

Your statement about playing every hand as best you can really stands out. I've been trying to focus on every single decision as it comes and ignore everything else. Definitely not easy, but it looks like the only way to make it long term at this game.

Re: Variance in poker: Living with the Beast
 

[ QUOTE ]


Your statement about playing every hand as best you can really stands out. I've been trying to focus on every single decision as it comes and ignore everything else. Definitely not easy, but it looks like the only way to make it long term at this game.

[/ QUOTE ]

On a related not it is also important not to think of your stack as anything but a tool.

Ever-aware of it, one must be. Consumed by its girth will lead to the dark side. [img]/images/graemlins/smile.gif[/img]

Re: Variance in poker: Living with the Beast
 

[ QUOTE ]
[ QUOTE ]
I have assumed a standard deviation of roughly 50BB every 100 hands.

[/ QUOTE ]

This is gonna make your whole post invalid, which sucks because I see where you were going with it.

Even most 6maxers have a SD of less than this.

Very well thought out post though. Would love to see this with more accurate numbers.

[/ QUOTE ]
I did choose an SD a bit higher than what would be normal. This was done to make large swings more likely when I was running the simulations to find some graphs to post and save time.

However, I don't think it invalidates the post in anyway. The post is saying two things: 1) Small samples (say < 100,000) are almost meaningless when estimating win rate, and 2) these are some extreme swings that are possible (not probable) so if you are experiencing a run (good or bad) don't assume that is the way it will always be. Don't quit when you are down if you feel you are playing correctly and don't start thinking you are God when you are running hot.

These wild swings are still possible with a more realistic STDEV, just more unlikely, so I think the post is still valid (if maybe a bit misleading) since the message is the same.

I am planning to add this simulator with the expectation calculator jhill posted yesterday in the next few days. People will be able to run simulations with their own parameters to see what kind of swings are possible.

Re: Variance in poker: Living with the Beast
 

[ QUOTE ]
[ QUOTE ]


Your statement about playing every hand as best you can really stands out. I've been trying to focus on every single decision as it comes and ignore everything else. Definitely not easy, but it looks like the only way to make it long term at this game.

[/ QUOTE ]

On a related not it is also important not to think of your stack as anything but a tool.

Ever-aware of it, one must be. Consumed by its girth will lead to the dark side. [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]

It's a good point and I think it extends to your bankroll in general. The money and stakes I currently play at mean absolutely zero to me in a financial well-being sense and yet I constantly look at my balance. Obviously the goal is to make money but I am definitely guilty of always focusing on the winning and losing aspect of it when in reality life is one huge poker game.

The real problem is that I am the most competitive person that ever lived and have been hardheaded enough to think that I can will myself to win like in other sports. The variance factor though can just spit you out and chew you up. Dealing with it is my biggest obstacle to moving up.

Re: Variance in poker: Living with the Beast
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]


Your statement about playing every hand as best you can really stands out. I've been trying to focus on every single decision as it comes and ignore everything else. Definitely not easy, but it looks like the only way to make it long term at this game.

[/ QUOTE ]

On a related not it is also important not to think of your stack as anything but a tool.

Ever-aware of it, one must be. Consumed by its girth will lead to the dark side. [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]

It's a good point and I think it extends to your bankroll in general. The money and stakes I currently play at mean absolutely zero to me in a financial well-being sense and yet I constantly look at my balance. Obviously the goal is to make money but I am definitely guilty of always focusing on the winning and losing aspect of it when in reality life is one huge poker game.

[/ QUOTE ]

I look at it too much as well. In fact, that is on my list of things to fix. Someone should write an AHK script that won't me look at the cashier screen. [img]/images/graemlins/smile.gif[/img]

Re: Variance in poker: Living with the Beast
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
I have assumed a standard deviation of roughly 50BB every 100 hands.

[/ QUOTE ]

This is gonna make your whole post invalid, which sucks because I see where you were going with it.

Even most 6maxers have a SD of less than this.

Very well thought out post though. Would love to see this with more accurate numbers.

[/ QUOTE ]
I did choose an SD a bit higher than what would be normal. This was done to make large swings more likely when I was running the simulations to find some graphs to post and save time.

[/ QUOTE ]
Doesn't this mean that 100k isn't a large enough sample size?

[ QUOTE ]
I am planning to add this simulator with the expectation calculator jhill posted yesterday in the next few days. People will be able to run simulations with their own parameters to see what kind of swings are possible.

[/ QUOTE ]
That would be great.

Re: Variance in poker: Living with the Beast
 

That last graph is so sick. =(