Standard deviation for SNG\'s and sample size for CASH games
 

I'm not sure if anyone has written extensively on this topic in regard to heads up games but I'll try to explain things as simple as possible .

Your standard deviation for heads up sng's is a function of your win rate . If you assume that your win rate is ~60% , then your standard deviation will remain fixed for any player who shares the same win rate . A simple calculation proceeds as follows :

Var(x)=E(x^2)-E(x)^2 where E(x) is your win rate(or mean) for a random variable x . For this particular case , we regard the variable x as +1 for when we win 1 unit and -1.05 for when we lose one buyin which also includes the rake .

So assuming you win 60% of the time , your s.d is simply the square root of your variance or var(x) .

E(x^2)=1^2*0.6 +(-1.05)^2*.4
E(x^2)= 1.041

Also E(x)=1*0.6-1*0.4 -0.05
E(x)=0.15

Var(x)=1.041-0.15^2
Var(x)=1.0185

S.D(x)=sqrt(1.0185)~ 1.0092

This means that if your win rate is 60% , then your s.d is approximately equivalent to 1 buyin , no matter what !

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Our standard deviation for cash games may be different for two players who share the same win rate . As I explained earlier , this is not the case for sng's .

To compute our standard deviation for cash games , we need at least 30 cash game sessions to ascertain that our s.d converges to a steady number . We need not even know our win rate which is why the central limit theorem is so very useful in situations like this . Using the numbers that Jakeduke provided , I will calculate the number of hands needed to determine with 95% confidence, our win rate interval .

Lets say after 50k hands , our win rate is (10 bb)/100 hands and bb is not to be mistaken for big bets .

Our standard deviation , using jakeduke's numbers is ~ 11 big blinds/100 hands .

xbar is our sample mean (10 bb/100 hands)
z= our confidence level which is approximately 2 s.d's above and below the mean .
sigma bar is our sample standard deviation .

In this case , sigma bar is 11/sqrt(500)~ 0.4919 per 100 hands .

10 +- 2*0.4919 Which means that we are 95% confident that Jakeduke's win rate lies between 9.0162 to 10.98 BB's per 100 hands .

Using z=3 , we are about 99% confident that Jake's win rate lies between 10 +- 3*0.4919 or between 8.52 to 11.47 BB's per 100 hands .

Re: Standard deviation for SNG\'s and sample size for CASH games
 

but per how many hu sngs?

it's not 1 per 1000 games.

does my question make sense?

Re: Standard deviation for SNG\'s and sample size for CASH games
 

You lost me right after "simple math".


But I dont even understand the concept of SD so I guess... yeah.

Re: Standard deviation for SNG\'s and sample size for CASH games
 

One correction .

Instead of S.D =11BB/100 hands I meant to put S.D=110bb's/100 hands . No wonder why things weren't adding up .

Jake's true s.d in terms of big blinds is 110bb/100 hands .

Sigma bar becomes 110/sqrt500 = 4.919/100 hands .

Our confidence interval becomes :

10+-2*4.919

and so we're 95% confident that his true win rate lies between 0.162 to 19.838 . All this tells us is that we're pretty confident that he's a winner.

This is one of the reasons why they say 50k hands is sufficient to determine that you're a profitable poker player .

Re: Standard deviation for SNG\'s and sample size for CASH games
 

[ QUOTE ]
but per how many hu sngs?

it's not 1 per 1000 games.

does my question make sense?

[/ QUOTE ]

For each 1 sng , your standard deviation is +1 unit from your mean . For a 9 player sng , your standard deviation will be close to 1.7 for each 1 sng .

Re: Standard deviation for SNG\'s and sample size for CASH games
 

Tnixon , here is the day you've been waiting for [img]/images/graemlins/smile.gif[/img]

Jakes s.d for NL100 is 110 bb's/100 hands .
Lets make a hypothetical assumption that an average sng lasts 30 hands . So playing a $100+5 buyin sng at a 60% win rate is equivalent to a s.d of about $100/30 hands which is about THREE times higher than your variance playing in cash games !!

Re: Standard deviation for SNG\'s and sample size for CASH games
 

One other minor correction .

If we include rakes into this discussion for an sng , then this means (as a 60% winner) that you will win 0.95 units , 60% of the time , and lose 1.05 units , 40% of the time .

So for my original variance calculation , we should replace +1 with +0.95 but this doesn't change things much .

E(x^2) = 0.95^2*0.6 + (-1.05)^2*0.4
E(x^2)=0.9825

var(x)= 0.9825 - 0.15^2
var(x)=0.96
s.d(x)=0.97979797 or almost 1 buyin per sng .

Re: Standard deviation for SNG\'s and sample size for CASH games
 

[ QUOTE ]
Tnixon , here is the day you've been waiting for

[/ QUOTE ]

The day I've been waiting for? You mean the day where you run through the same calculations that I already showed in another thread (although to be fair, my numbers were off, and showed SNGs being lower variance than they really are, because I incorrectly put the winrate inside the squared terms instead of outside, where it belonged), and ended up basically restating the same conclusion that I already came to in another post, without any acknowledgement whatsoever that it even existed, even though I know for a fact that you at least browsed it?

Wow. You're right. I've totally been waiting for that. In fact, my face is blue, I've been holding my breath for so long.

Re: Standard deviation for SNG\'s and sample size for CASH games
 

It's worth pointing out a couple of things.

First of all, we only have one data point for cash game variance, jakeduke.

Second, we only have one data point for average hands per SNG, and jay didn't even use that number, instead picking an even smaller number, which doesn't seem realistic given that I suspect my games are typically shorter than many, because I would guess that I make a rather large number of high-variance plays compared to many other winning players.

But you can help!

http://forumserver.twoplustwo.com/showfl...=1#Post12263671

Re: Standard deviation for SNG\'s and sample size for CASH games
 

Tnixon , I thought I was helping you out and you're actually criticizing me ? What's wrong with you?

You've never arrived at a standard deviation of 1 unit which is a common total for sng's . You cannot compare s.d's unless you have a reasonable estimate for both sng's and cash games which I've clearly shown in my example .

Please do not ruin this thread with your gibberish .In fact , I would prefer it if Leader locket it .