Variance in poker: Living with the Beast

[raistlinx]

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.