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Calculating Poker Tournament Expectation

By dgillis | Published Oct 23 2008, 05:09 PM |

After reading countless books, studying videos, and talking poker for more hours than I care to admit I have noticed that most topics have been well covered in some way. In a recent World Series of Poker episode Daniel Negreanu said "In the long run the most successful poker players are great money managers." You’ve heard the commentators on the WSOP mention that the average pro values each tournaments at X number of buy-ins, but I found myself wondering, how do I get to X and what the heck does it mean?

Almost everyone will express the importance of bankroll management; however it seems to me that finding a proper explanation of how to value your tournaments can be difficult. So for my first article on PocketFives I decided to take a crack at offering a detailed explanation of this important part of bankroll management.

There's a lot of math, but hey we’re poker players so no problem right? In my first attempt to write this I ended up with something that looked like an advanced game theory text book. I decided it was best to scrap that and just tell you where to find the numbers and give a basic explanation of where they come from and what they mean.

I know if you’re a regular reader on this site you have heard countless times that you should be maintaining a spreadsheet. Well guess what, if you’ve been doing that this whole process will be a breeze. If you’re like me and the spreadsheet is missing a few days worth of info there’s no other way to do this than to actually count your results. To use as an example I decided to take my $2.20 180 man turbo results.

I chose these in particular because I spent plenty of time playing them trying to build my bankroll, so I have a pretty decent sample size. This brings me to another point. When dealing with statistics and odds bigger is better; when we’re talking sample size that is, the more events you have considered the more reliable your information will be.

Ok on to the math, hang with me through this and then we will get into what it means and how to use it. In order to find out how much you can expect to make over the long run playing tournaments we need to find your average cash and multiply it by the odds of cashing. To find our average cash we add up all cashes for that buy-in\field size then divide by the number of tournaments that you cashed in. My numbers looked like this…


AC = total $’s cashed/ total tournaments cashed in
AC = $1857/84
AC = $22.10


Ok, now that we know our AC we need to know how often we can expect to cash, or your In the Money percentage (ITM). Now we also know from sleeping through math class we can find our ITM by taking the total times you cashed and dividing it by the total tournaments of this kind that you played. Again my numbers looked like this…


ITM = total cashed/total played
ITM = 84/596
ITM = .14 or 14%


In other words I could expect to cash for about $22.10 once out of every six tournaments that I played. With those two numbers we can figure out what your profit per tournament is (for simplicity let’s call this X). To find X we need to first multiply our buy-in (BI) and rake (R) by 6. Remember that my ITM ratio was 14% or about 1 of every 6, so we will be basing this on a six game span. Once we have that number we will subtract it from our AC then divide by 6. It looks something like…


X= AC - 6(BI+R)/6
X= 22.10 – 6(2.00+.20)/6
X= 22.10 – 13.20/6
X= 8.90/6
X= $1.48


Now that we have X, what does it mean and why should you care? Well the obvious answer to that is it means that I can expect to profit $1.48 for every tournament I play at that level, assuming that my skill or the average player’s skill doesn’t increase or decrease. At this level it might not be so important, but when if you are considering taking the plunge to the pro life having this formula can tell you just how much you would make over a given number of tournaments.

So for instance let’s say that I was playing $220 tournaments and was able to maintain the same results (not likely but let’s go with it for this example). If I wanted to know how much I could expect to make over the course of a year I would multiply X by the number of tournaments I could fit in. Let’s say I could fit in 20 a week with X= 148.00 I would expect to make about $154K… much better than my current salary, but of course I would need a solid sample size before I felt comfortable telling my boss where to put his job.

Yeah yeah, I hear you… what does this mean for the average player? The micro guy just playing to build his bankroll could use this to estimate how long it will be before he can make his next jump in levels. Say you’ve already moved up a level or two and can afford to pull out a few dollars here and there; but you know you really want to buy that TV you saw in big box electronics the other day, well if you know your X then you would know just how long it will take.

I hope you enjoyed my musings and that this has been in some way helpful. Remember Rome wasn’t built in a day, so be patient and use good bankroll management. Good luck at the tables!


---

Comments
lpaper 

lpaper said:

very good article imo

October 23, 2008 11:56 PM
krispycream 

krispycream said:

Nice first article. Keep em coming.

i prefer having at least 60% of my roll in one game at any time, but to each his own.

October 24, 2008 12:42 AM
Livew1re 

Livew1re said:

i understood that till you got to this part

"X= AC - 6(BI+R)/6

X= 22.10 – 6(2.00+.20)/6

X= 22.10 – 13.20/6

X= 8.90/6

X= $1.48

"

then i got completely lost. lol.

October 24, 2008 1:09 AM
jokajon00 

jokajon00 said:

Excellent article!!! Now I know how many sng's I gotta play to get another monitor!!!

October 24, 2008 1:27 AM
ripomatic 

ripomatic said:

I may be wrong here but isn't 14% = 1/7.1  

Thanks for making a fairly simple calculation a little more confusing...

October 24, 2008 2:37 AM
seal 

seal said:

Being a math teacher I can confirm that ripomatic is completely right in that 14% does equal 1 out of 7.1 not 1 out of 6 as in the article.

As simple as possible, the formula the author puts forth just says that if your avg buy in is greater than your avg cash then you play at a loss every time by that amount. If your avg cash is greater than your avg buy in then you play at a profit every time by that amount.

October 24, 2008 4:20 AM
dgillis 

dgillis said:

I used 15% just to make it easier to understand which came out to about 6.67, I chose to round down and go with the more aggressive ratio really just to make it easier to compute, techinically it should have been seven. I def. should have notated that, my mistake.  That said if you follow the steps then my actual numbers shouldnt matter to much, you should get a correctly solved equation when your done.

October 24, 2008 6:00 AM
hisnibs2000 

hisnibs2000 said:

i pwn

October 24, 2008 6:19 AM
NightPrince 

NightPrince said:

Finding your expectation in a tournament is easy, it's the number of buyins you need to play a tournament which is where people go wrong.

October 24, 2008 6:37 AM
Pastwind 

Pastwind said:

I like the part where X = 1.48$ becomes X = 148$. A sure bankroll booster!

October 24, 2008 6:55 AM
Paulieballz 

Paulieballz said:

The formula should actually have ( ) around the subtraction as well otherwise the division portion is supposed to be done first.  Therefore, X= (22.10 – 6(2.00+.20))/6 is really the way the formula should be written.

October 24, 2008 7:34 AM
dgillis 

dgillis said:

again your correct, sorry but I had to rewrite this at 5 am due to my hard drive failing the night wen. night.  it should be {22.10-6(2.00+.20)}/6 thanks pualie that is key... thanks for bearing with me through the first article kinks!

October 24, 2008 8:06 AM
Spaceh0g 

Spaceh0g said:

wait, why don't you just take ($1,857/596)-$2.20 to get "X"...?

October 24, 2008 8:09 AM
Zunga 

Zunga said:

Why don't you all become Grade 12 Mathematics Teachers, and not correct every fucking thing that's said.  1/6 or 1/7, brackets or not.  Close enough.  Who gives a shit.  Keep it to yourselves.  

October 24, 2008 8:48 AM
Nate Avenson 

Nate Avenson said:

"wait, why don't you just take ($1,857/596)-$2.20 to get "X"...?"

This.

October 24, 2008 1:30 PM
Zpaceman 

Zpaceman said:

lol, this article is bad, but what else can i expect when i haven't written any myself recently. a whole article for a trivial calculation that might make 1 paragraph of a good article and then he gets the math wrong. the actual answer, as earlier posters correctly showed, is X = $0.92 (quite a difference, huh!) and, ldo, 596 trials at 180-man SNGs is not even close to a good sample size. nice try, but come back with some stats when u've played like 2k times. having said that ~40% ROI at $2.20 180-man SNGs seems reasonable for anyone with modest poker skills. no way, however, can this ever be translated to an expection of 40% ROI at $220 abi like this author risibly attempted here. epic fail imo. next please...

October 24, 2008 1:54 PM
dgillis 

dgillis said:

its the same thing... but without the longer equation it would be harder to manipulate for other adjustments, and I felt the specific formula offered a better handle on what components went into the number and how they effected the outcome. either way will work just fine.

October 24, 2008 1:54 PM
Nate Avenson 

Nate Avenson said:

I'm a little confused. What does this formula calculate? It doesn't calculate ROI, And I always thought Expectation = ROI

October 24, 2008 7:53 PM
grapsfan 

grapsfan said:

Stu, for someone who has gotten BURIED by his peers more than anyone else who has ever written for this site...I might have expected a little more support for someone making his first attempt at this.

Stay classy, San Diego.

October 24, 2008 8:26 PM
Zpaceman 

Zpaceman said:

sorry graps (and dgillis), my response was somewhat of a pastiche of the kind of shit i sometimes get, but i probably chose the wrong target. stu.

October 25, 2008 5:41 AM
Fear Le55 

Fear Le55 said:

ur just an ass hole , fuck you

November 1, 2008 3:32 PM
Neoattitude 

Neoattitude said:

Awesome Article!!!! I enjoyed reading it.

Just one minor error to ur equation that a math major like me would catch.

You wrote:

X= AC - 6(BI+R)/6

X= 22.10 – 6(2.00+.20)/6

X= 22.10 – 13.20/6

X= 8.90/6

X= $1.48

You are just missing paranthesis ( ) or brackets [ ] before AC and after R). so it should like this:

X= [AC - 6(BI+R)]/6

X= [22.10 – 6(2.00+.20)]/6

X= [22.10 – 13.20]/6

X= 8.90/6

X= $1.48

again... i guess this is just a minor error and it doesnt change the fact that this article is awesome and very informative.

Thank you very much for posting it!

November 5, 2008 8:04 AM
tigertonkin 

tigertonkin said:

LMAO, the guy spends ages writing this and every 1 on here just rips it to shreds. Im not maths genuis but i understand what hes saying.

But also if maths is such a big factor in poker then i would expect all of the people above to be great players and massive bankrolls, but i doubt it. which proves fcuk the maths and play the cards.

p.s good effort stu, i appreciated it.

November 29, 2008 9:37 PM

About dgillis

"Prohibition will work great injury to the cause of temperance. It is a species of intemperance within itself, for it goes beyond the bounds of reason in that it attempts to control a man's appetite by legislation, and makes a crime out of things that are not crimes. A Prohibition law strikes a blow at the very principles upon which our government was founded. -Abraham Lincoln"


 
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