Ahaa, so he was a clever one!

Thanks for your help, sir

Great point!

And I have to admit, I did made a mistake.
It's not a 1%, it's 1.2% chance to be break even or better in the game where 200BB lost in 1000 hands with assumed SD 25.

This is getting lame, Guy auto sits fresh table after .. I hate PTR :

Dealer: ItsADAMyay joins the table at seat #1
Dealer: A new game will start in 15 seconds
Dealer: AzNRonWu is sitting out
AzNRonWu: brb
AzNRonWu: gotta take a bathroom
Dealer: AzNRonWu leaves the table

same guy did it to me before , then he came back played 20 hands quit 1bet up.

Got him!

PokerStars Game #37569217978: Hold'em Limit ($3/$6 USD) - 2010/01/02 21:54:42 PT [2010/01/03 0:54:42 ET]
Table 'Antilia' 2-max Seat #1 is the button
Seat 1: ItsADAMyay ($420 in chips)
Seat 2: AzNRonWu ($58.50 in chips)
ItsADAMyay: posts small blind $1
AzNRonWu: posts big blind $3
*** HOLE CARDS ***
Dealt to ItsADAMyay [Qd 6h]
ItsADAMyay: raises $3 to $6
AzNRonWu: folds
Uncalled bet ($3) returned to ItsADAMyay
AzNRonWu is sitting out
ItsADAMyay collected $6 from pot
ItsADAMyay: doesn't show hand
*** SUMMARY ***
Total pot $6 | Rake $0
Seat 1: ItsADAMyay (button) (small blind) collected ($6)
Seat 2: AzNRonWu (big blind) folded before Flop

Damn. He hit and ran himself!

Your 1% number is only true if you completely ignore any Bayesian analysis, which is very silly imo. No one is a 20 BB loser, so observing a 20 BB lossrate over a 1000 hands and drawing a normal distribution around -20 BB/100 is just ridiculous. To do a reasonable analysis, you'd have to combine the -20 BB/100 distribution with a distribution of possible winrates and lossrates, centered around zero minus the rake.

Your analysis would suggest that it is equally likely that JR has a winrate of -40 BB/100 and 0 BB/100. Which is obviously lol.

ding ding ding

So, all this must be wrong then?

[IMG][/IMG]

The upper bound of the confidence interval is calculated as

W-Φ-1(p)σ√P

and the lower bound is

W+Φ-1(p)σ√P.

Win rate is simulated by

Wn={Wn-1+ΔP[ W+Φ-1(p)σ/√ΔP ]}/P

while total winnings are

Tn=Tn-1+ΔP[ W+Φ-1(p)σ/√ΔP ].

P is total number of periods, T is current total winnings, W is win rate, σ is the standard deviation of the win rate, ΔP is some fraction of P (ΔP=P/200 is used for convenience in graphing), Φ-1() is the inverse standard normal cumulative distribution, and p is the probability of achieving a particular win rate. The value of p ranges between 0 and 1 and is generated randomly.

But it surly looks like

though

Did you not read and understand what I wrote? According to your analysis, is it equally likely that JR's true winrate is -40 BB and 0 BB/100?

edit: I guess you do have some probability of various winrates in your simulation. But your results seem rather far off from what I would expect. Could you plot your distribution of possible winrates?

I read and I understood.

I just don't see why you keep on coming up with those silly numbers when it's painfully clear from the graph that it is equally likely that JR's "true winrate" is somewhere in between -19.86 BB and +19.86 BB/100 with -20BB/100 result being outside of 98.8% confidence.

Sorry, I should have read more closely. Could you post a graph of the distribution of winrates you used?

well i guess it's outside that 1% then

That's also assuming he and all his opponents play the same at all times, right?

Well, again...

It is 0.00BB/100 that is outside of 1%.

1BB/100 has 0.7% probability
2BB/100 - 0.5%

If you want to give yourself 3BB/100 badge, then you have have to accept the fact that chances of that are 3 in 1000.

So my question stands.

With practically guaranteed enormous variance and and practically guaranteed no long term benefits - why even get involved?

Aha, now we are getting somewhere!!!

Are we looking for any assumption when we proudly claim to be a 4BB/100 winner over 87K hands or to be within 0.5% confidence from our "real" ROI over 10k SNGs?
Or we just simply use statistical modeling as an undeniable mathematical prove of our superiority (conveniently disregarding the fact that the whole thing is based on dynamic flow of a huge amount of incomplete, ever changing information).

But as soon as our beloved bell curve delivers a knock out blow to our ego in a form of "unpleasant truth",
we start looking for "assumptions" to bail us out of something we don't really want to accept.
Interesting.

Copoka,

Are you really saying that against this opponent you think there is like a 15% chance JR's true winrate is between -20 and -10 BB/100? That is what your analysis implies.

At least that's what I think it implies. I'm not sure quite what you're doing. Could you post a graph of the probability of JR having various winrates versus this guy?

What I am really saying or think does not matter much.

But what statistical analyse is "saying" is that it is equally likely that JR's "true winrate" is somewhere in between -19.86 BB and +19.86 BB/100 with -20BB/100 result being outside of 98.8% confidence.

If you what to take out of this range anything that you consider impossible and leave only what would fit your understanding of the situation - be my guest. I don't care.
Just don't kill the massinger. Take it up with bell curve, not me.

Edit.
Sorry for not posting.
Here it is. http://www.castrovalva.com/~la/win.htm

I'm asking if that's what the statistical analysis implies. Are you able to post a graph showing the probability of JR's true winrate given his -20 session?

Did you get that link?

Yes.

So whose up for HULA 2010? I played it last year and found it really fun, mostly because I'm a game selection nit.

I'll probably be in, it's 500 right? What site would I need an account on?