What is a solid win rate at party .50/1?

[tytygoodnuts]

And how many hands do you have to play before you can consider your win rate accurate with your quality of play?

[Vern]

[ QUOTE ]
And how many hands do you have to play before you can consider your win rate accurate with your quality of play?

[/ QUOTE ]

If your Standard Deviation is the typical ~15BB/100 hands, you need 202.5K hands to be ~99% confident that your true win rate is within +/- 1BB of your apparent win rate.

Math

Condifence for ~99% = 3 Standard Deviations / Square root of hand samples.

Hands are sampled in 100 hand units, so for this to resolve to +/- 1BB, you need (15*3)/SQRT(x)=1, which is the same as SQRT(x)=45, so square both sides and you get x=2025. That is 2025 Hand samples, of 100 hands, so the result is 202,500 hands.

Vern

Standard Disclaimer, I am by no means an expert at any of this.

[MrWookie47]

You can check the FAQ for most stat questions, but convergence of win rate isn't discussed there. Few posters discuss win rates over fewer than 100k hands. It depends on the variance of your style of play. A typical standard devaition per 100 hands is 15-17, so you can divide that by the square root of the number of hands you've played divided by 100 to get the uncertainty of your win rate thus far. If you're looking at your win rate at 10k hands, be happy with anything >0 [img]/images/graemlins/smile.gif[/img], and if you're worried that it's too low, post more hands for more critique.

[MrWookie47]

To pseudo-hijack the thread, is there a place in PT that records your SD/100 (I can't seem to find it), or do we just assume 15 for the typical player?

[Vern]

[ QUOTE ]
To pseudo-hijack the thread, is there a place in PT that records your SD/100 (I can't seem to find it), or do we just assume 15 for the typical player?

[/ QUOTE ]

Under the sessions tab, click the More Detail button.

[Vern]

[ QUOTE ]
[ QUOTE ]
And how many hands do you have to play before you can consider your win rate accurate with your quality of play?

[/ QUOTE ]

If your Standard Deviation is the typical ~15BB/100 hands, you need 202.5K hands to be ~99% confident that your true win rate is within +/- 1BB of your apparent win rate.

Math

Condifence for ~99% = 3 Standard Deviations / Square root of hand samples.

Hands are sampled in 100 hand units, so for this to resolve to +/- 1BB, you need (15*3)/SQRT(x)=1, which is the same as SQRT(x)=45, so square both sides and you get x=2025. That is 2025 Hand samples, of 100 hands, so the result is 202,500 hands.

Vern

Standard Disclaimer, I am by no means an expert at any of this.

[/ QUOTE ]

Oh, and if you want to find out the ~99% confidence that you are a winning player, instead of Hands=((3 * Standard Deviation in BB/100)^2)*100, use

Hands = ((3 * Standard Deviation in BB/100Hands)/ Win Rate in BB/100Hands))^2) * 100)

So if you have an apparent win rate of 2.56BB/100 and a SD 15BB/100, you get

Hands = (((3*15)/2.56)^2)*100
Hands = ((45/2.56)^2)*100
Hands = (17.58^2)*100
Hands = 309 * 100 = 30,900 hands

So if your win rate is 2.56BB/100 hands, you can be ~99% confident your true win rate is between 0BB/100 and 5.12BB/100 hands (Therefor a winning player) after only 30,900 hands if your SD is 15BB/100. If your SD grows or shrinks, so does the sample size needed. As the Win rate increases the sample size decreases, and if the win rate drops, the sample size must increase. This is just for the "Am I a winning player calculation."

Vern

Standard Disclaimer, I am by no means an expert at any of this.

[memphis57]

[ QUOTE ]
you need 202.5K hands to be ~99% confident that your true win rate is within +/- 1BB of your apparent win rate.


[/ QUOTE ]

BTW, this is 202,500 hands played with a consistent style, against a consistent level of competition. If you change your playing style, learn new things, or if the quality of the competition changes, you have to start over on counting the 202,500 hands.

In other words, you'll never have a big enough sample size to be mathematically sure, but you should get a feel after 10K hands, and that feel will get more precise at 20K and 40K hands. But the important point is, if you get to 20K and you're +6 BB/100, it doesn't mean you're god, and if it's -1, it doesn't mean you're bad. Look more at how you play each hand.

Oh, and don't think you can get away with stopping at 200,000 hands - the 202,500 is a precisely calculated number and we can't guarantee your results if you fail to get there.



Just kidding on that last point, of course.


Anyhow, now that we've whipped you around the appropriate degree about sample size, I guess we can answer your original question in the title of this post. Others will correct me if I'm wrong, but I believe the concensus here is that 2 BB/100 is good over the long, long haul, 1 BB/100 is decent, 3 BB/100 is very good, and 4+ is probably not sustainable.

[DavidC]

I'm sitting at 3.5 after 16k or so, but probably 2.5 over 50k.

[Vern]

[ QUOTE ]
[ QUOTE ]
you need 202.5K hands to be ~99% confident that your true win rate is within +/- 1BB of your apparent win rate.


[/ QUOTE ]
Anyhow, now that we've whipped you around the appropriate degree about sample size, I guess we can answer your original question in the title of this post. Others will correct me if I'm wrong, but I believe the concensus here is that 2 BB/100 is good over the long, long haul, 1 BB/100 is decent, 3 BB/100 is very good, and 4+ is probably not sustainable.

[/ QUOTE ]

Good point Memphis, I never did post that BB/Range. I think your numbers are low for Party Skins though, by about .5BB/100, just because the compitetion is so bad. At Stars I think it would be too high by about .5BB/100 just because of the competition is so much tougher.

I think 1.5 is ok, 2.5 is good, 3.5 is great, but agree anything over 4 would be difficult to sustain.

Vern

[memphis57]

[ QUOTE ]
Oh, and if you want to find out the ~99% confidence that you are a winning player....

[/ QUOTE ]

(Sorry I keep quoting you, Vern, to reply to the OP, but you say all the right things.)

One more thing - even if you play 202,500 hands with a style that never varies, and you 24-table it 24-hours-a-day so you get it done in 2 weeks and can therefore say that the level of competition remained fairly constant, and you average 1 BB/100 over it all, you still can't be 100% sure that you are a winning player - only 99% sure. And 1% is a sizeable chunk of chance. Ever been dealt AA or KK? The odds of getting dealt one of those hands is about 1 in a hundred. So if you meet all the conditions and do the calculations to prove that you are a winning player, every time you get an AA or KK you should doubt your conclusion.

(Okay, I'm getting down from my mathematical high horse now.)