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View Full Version : What is your likely ITM%


lorinda
11-09-2004, 08:53 AM
Yes, yes, I know, ROI is far more important.

Anyway, I've given links to this (http://faculty.vassar.edu/lowry/binomialX.html) site a couple of times recently and it's gone down like a lead balloon.
It occured to me that people see all the math formula and turn off, so I figured I'd give a quick guide as to how to use it.

(I have no idea who's site it is, it's probably just some student's project or something, and it's not a gambling site)

It basically tells you the chances of certain yes/no events happening, but you can use it both ways.
Scroll through all the math (Unless it interests you) and go straight to the calculator.

The only data it requires are:
n= (number of events) = number of sit n goes played.
k= (the number of stipulated yes results) = number in the money
p= (the probability of k )= probability of getting in the money

Well it wants p, but p is what we want to know... soooo.

Put in your number of games, we'll use 100 as an example.
Let's say you cashed in 45 of these and want to know your true probability of getting in the money.

put 100 in for n and 45 for k.

You say you feel like you've been unlucky and that you should ITM 51% of the time, so put in p=.51 and let's find out how unlucky you needed to be.

Click calculate.

Now read down to the 45 or fewer section.

You are now reading what odds you are of having won 45 or less from 100 given that your guess of 51% is correct.

You will now see that if you really do ITM 51% of the time, you will win 45 or less from 100 0.1356, or 13.56% of the time.

Now let's do it again with a smaller sample size.

Let's say we played 12 sng's and believe we are a winning player.
We cashed in NINE of those 12, surely we are amazing.

We must get ITM 45% of the time in the long run surely.
So:
n=12
k=9
p=.45

So, we'll get ITM 9 or more times from 12 3.557% of the time, even if our % is 45.
Now 3% might seem small, but 3% shots happen all the time, so you could EASILY be below 45% despite cashing 9 in 12.

Sorry for the convoluted post, but this is a nice little tool for estimating your ITM rate, and also for showing how important sample size is.

Have a little play around, find out your .999 range and your .001 range, you may be surprised.

Lori

dogsballs
11-09-2004, 10:38 PM
Can't for the life of me understand why anyone wouldn't be interested in that site, lori.

SpeakEasy
11-10-2004, 02:54 AM
Huh?

chill888
11-10-2004, 04:52 AM
Hi Lori,

What strikes me as interesting is that there seems that S&G performance results are more analogous to a binomial type distribution than a normal distribution.

Thus (I think) you can use your web link to calculate a far more accurate standard deviation than what has sometimes been used here. For example, in the EXCEL tracking sheet that passes around here sometimes. Desn't it assume a normal distribution?

Sorry in advance if I am offbase.

gl

eastbay
11-10-2004, 06:30 AM
[ QUOTE ]
Hi Lori,

What strikes me as interesting is that there seems that S&G performance results are more analogous to a binomial type distribution than a normal distribution.


[/ QUOTE ]

ITM is a true binomial distribution - you're either in or you're out. So, this is the correct way to relate the various variables: ITM, sample size N, standard dev., etc.

ROI is less clear (to me).

eastbay

jcm4ccc
11-10-2004, 08:01 AM
You can also do the 95% confidence interval for a binomial distribution, to determine your true ITM%.

The formula is:

ITM +- 1.96 (sqrt(ITM*(1-ITM)/# of games))

For instance, assume these stats:

40% ITM
100 games

The formula would be:

.40 +- 1.96 (SQRT(((.40 * (1-.40))/100))=
.40 +- 1.96 (SQRT (.40*.60)/100) =
.40 +- 1.96 (SQRT (.24/100) =
.40 +- 1.96 (SQRT (.0024) =
.40 +- 1.96 (0.049) =
.40 +- (.096)

You add and subtract .096 from 0.40 to get your confidence interval: .304 is the lower range, and .496 is the upper range. So you can be 95% confident that your true ITM is between .304 and .496.

This demonstrates why 100 games is not enough to determine your true ITM.

The more games you play, the smaller the confidence interval.

Still assuming a 40% ITM, your confidence interval would be:

100 games .304 - .496
200 games .332 - .468
300 games .345 - .455
400 games .352 - .448
500 games .357 - .443
1000 games .370 - .430

So even after 1000 games, the range is still greater than .05.

You can use this formula for other binomial distributions, such as the number of times you placed in first place.

Here is a link to a page that will calculate binomial distributions for you. In the "Number of events", enter the number of games you have won. In the "Total sample size" enter the number of games you have played. The numbers obtained are slightly different from the numbers used in the calculations above. This page gets an "exact confidence interval" which I guess is a more precise version of what I outlined above.

http://www.swogstat.org/stat/public/binomial_conf.htm

chill888
11-10-2004, 08:10 AM
[ QUOTE ]
[ QUOTE ]




[/ QUOTE ]

ITM is a true binomial distribution - you're either in or you're out. So, this is the correct way to relate the various variables: ITM, sample size N, standard dev., etc.

ROI is less clear (to me).

eastbay

[/ QUOTE ]


As a start, if you make a simplifying assumption about your
distribution of 1st, 2nd, and 3rds, when you are ITM then I think it is fairly easily applicable to ROI.

For example, say you finish evenly between 1, 2, and 3rd place then for a given ITM% you know your win rate and your win rate follows a binomial distribution of sorts.

So say you play $55 tables and have an average win rate of $103 / games (only count the games where you cash). The binomial would be you either lose $55 or win $103. From that you could have your Standard deviation (which can be changed eaily -see post in this thread - into a confidence interval) around your win rate. This divided into your buy-in gives you ROI - with a confidence interval.

The simplifying assumption I'm making is that you lump all your ITMs into an average $. Not smart enough to know whether this corrupts the exercise or not.

gl