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.

[KurtSF]

I truly believe that you must embrace variance if you want to play and win at poker. Most people don't have a clue how much influence it has on results. Its nuts!

For example, checkout this post (http://forumserver.twoplustwo.com/showflat.php?Cat=0&Board=microplnl&Number=9030561) . OP has 7800 hands. Frankly it looks to me like he's crushing the games, but who knows?

Nice work raistlinx. Good post.

[raistlinx]

Someone requested these links be fixed so I thought I would bump this for anyone new who hadn't seen it.

[yntm3]

Fantastic post I really like this one.

[ama0330]

Nice post, some analyses like these have been done before but I think these are clear and concise.

I would recommend that this thread be stickied for whine reference

[greggg230]

Thanks for this. Sometimes I think I'm the worst poker player ever after sitting down for 4 hours and losing 1 BI. It's nice to have some empirical reminders of what we already know: That's poker.

[corsakh]

[ QUOTE ]
Thanks for this. Sometimes I think I'm the worst poker player ever after sitting down for 4 hours and losing 1 BI. It's nice to have some empirical reminders of what we already know: That's poker.

[/ QUOTE ]

Lol.. in my case its usually 4 BI /images/graemlins/smile.gif

[bozzer]

very helpful, thanks.

would it be possible for you to add a link to the spreadsheet (it is available somewhere on the forums, but i can't remember where)?

[Quester]

[ QUOTE ]
Thanks for this. Sometimes I think I'm the worst poker player ever after sitting down for 4 hours and losing 1 BI. It's nice to have some empirical reminders of what we already know: That's poker.

[/ QUOTE ]

Geez, I lost 6 BI in 30 minutes last night and you're worried about 1 BI in 4 hours.

[greggg230]

[ QUOTE ]
[ QUOTE ]
Thanks for this. Sometimes I think I'm the worst poker player ever after sitting down for 4 hours and losing 1 BI. It's nice to have some empirical reminders of what we already know: That's poker.

[/ QUOTE ]

Geez, I lost 6 BI in 30 minutes last night and you're worried about 1 BI in 4 hours.

[/ QUOTE ]

Hehe, I've definitely lost more than 1 BI in 4 hours; I just meant I get easily discouraged. /images/graemlins/smile.gif

[monkover]

nice post

[raistlinx]

[ QUOTE ]
very helpful, thanks.

would it be possible for you to add a link to the spreadsheet (it is available somewhere on the forums, but i can't remember where)?

[/ QUOTE ]I'm currently working with another poster in the FR forum to put this and an expectation calculator of his into one spreadsheet. Part of the plan is to put this into a more user friendly format where you just enter in your values and it will graph it for you via a macro.

When that's done I'll make sure it is posted in both forums.

[johndenver]

Over my first 7K hands of 10 NL, I won ~16 ptbb/100

I thought I was a soon to be poker legend

Now, 11 K hands later, my total winrate has settled to a standard 5 ptbb /100, who knows what it will be 10, 20, 50 K hands down the road

Dont get too high or too low

[DMBFan23]

Virtually everyone underestimates the variance in poker, this has been true ever since I've been a member of 2p2. I do it too.

[Speedlimits]

good post. im on the positive side of variance right now and loving it.

[vixticator]

[ QUOTE ]
Over my first 7K hands of 10 NL, I won ~16 ptbb/100

Now, 11 K hands later, my total winrate has settled to a standard 5 ptbb /100, who knows what it will be 10, 20, 50 K hands down the road

[/ QUOTE ]This is what I'm going through now. I was DESTROYING 10NL through about 7-8k. The last 4k have been painful. Still winning at a good clip overall but ouch this downswing stuff really messes with my head.

[Win.by.TKo]

With variance being such a large part of poker, how does one know when to move up? I'm at 2NL and would like to advance, but I'm not sure what I should use to make that determination.

[WHITEBOYAEHS]

[ QUOTE ]
With variance being such a large part of poker, how does one know when to move up? I'm at 2NL and would like to advance, but I'm not sure what I should use to make that determination.

[/ QUOTE ]

at around $100 in your bankroll...generally it is said that you should have atleast 20 buyins for any given level