Calling all Sample Size Nazi's

[pzhon]

After n hands, a 95% confidence interval for your win rate in BB/100 is roughly results +- 300/squareroot(n). So, if you win at a rate of 3 BB/100 for 10k hands, your 95% confidence interval would be 0-6 BB/100. To shrink the interval by a factor of 2, you need to increase the number of hands by a factor of 4.

[aargh57]

[ QUOTE ]
After n hands, a 95% confidence interval for your win rate in BB/100 is roughly results +- 300/squareroot(n). So, if you win at a rate of 3 BB/100 for 10k hands, your 95% confidence interval would be 0-6 BB/100. To shrink the interval by a factor of 2, you need to increase the number of hands by a factor of 4.

[/ QUOTE ]

So then say, for example, I have a 2.0 BB/100 after 40,000 hands my 95% confidence interval would be:

2.0 +/- 300/(squareroot of 40000) =
2.0 +/- 300/200 =
2.0 +/- 1.5 =
between 0.5 and 3.5

In other words I am 95% sure that my "true win rate" would lie between 0.5 and 3.5.

I just wanted to see if I'm calculating this right.

BTW, I am assuming that this formula is in a book somewhere. If so, which one?

[Dov]

I hate to say this, but I think you're asking the wrong questions.

Assuming you have the roll for the game you want to play in, just rail it for a little bit. If you can't tell whether or not you can beat it, then you can't.

If you don't know what I'm talking about, then don't move up yet.

[Dov]

[ QUOTE ]
Listen, heres the thing: If you can't spot the sucker ...

[/ QUOTE ]

Exactly...

[pzhon]

[ QUOTE ]
[ QUOTE ]
results +- 300/squareroot(n)

[/ QUOTE ]

So then say, for example, I have a 2.0 BB/100 after 40,000 hands my 95% confidence interval would be:

2.0 +/- 300/(squareroot of 40000) =
between 0.5 and 3.5

[/ QUOTE ]
Yes, 0.5-3.5 BB/100.

[ QUOTE ]

BTW, I am assuming that this formula is in a book somewhere. If so, which one?

[/ QUOTE ]
I didn't get it from a book. It's an application of basic statistics and the assumption that your standard deviation for 100 hands is about 15 BB. There are analogous formulas for NLHE and for tournaments with other values replacing the 300.

[Killer Man's Son]

Excellent responses. helpmeout & pzhon...thanks for the insite. Very informative.

Dov - I think you probably nailed the question I was asking 'underneath it all'. I have watched higher limit games and know I can beat them. Its just a matter of grabbing my balls and going for it. But, I also understand variance is a bitch. I've been MTing under my normal limit this weekend and things aren't going well. No excuses, just a bad run. Had I decided to move up, I might perceive this as being outplayed which I know is not the case under my normal limit. So, I was looking for a general number of hands I should play before I cry uncle and move back down.

I'm going to keep plugging away under my normal limit for now to see how things go. I'm not a MT junkie like many posters here but I'm working up to it (currently at 3 tables). I can handle playing this w/o a problem so we'll see what the future holds.

Thanks again.