ITH Poker Forum

[toronexti]

Alright I was wondering if someone could do a little math for me since I'm not really sure how to do it.

Assumptions:
2PTBB/100 earn rate at NL HE
Standard deviation of 40PTBB/100

So after 10k hands what's the chances that the player will be in the red?
At what point is the chance under 5%?

[the_hawk]

Can't be bothered to show my working but I reckon the chances now you're in the red are about 16%, and with that true earn and SD you have a less than 5% chance of being in the red after 27k hands.

[Fenris78]

After 10k hands your expected win value is 200PTBB and your standard deviation is 400PTB (here is where I might be mistaken, but my guess is 40*sqrt(100) should be sigma for 10k when 40 is sigma for 10k)

This means the zero point of your distribution curve is at -200/400 = -0.5, and the area under the curve from 0 to -0.5 is 0.1915. This means the chance you are in the red after 10k hands is 0.5-0.1915 or 30.85% chance of being down after 10k hands.

When is your chance greater than 95% to be up? Well, that's easy I guess. It's greater 95% once the relation between expected value and standard deviation is greater than 1.645.

X is the number of hands played. Your win rate is 0.02PTBB*X, your standard deviation is 4PTBB*sqrt(X). Thus we need 0.005*sqrt(X) to be equal 1.645, which yields X = 108,241

So it seems you need roughly 110k hands to get the chance of being down below 5%.

If anyone wonders, where I got all the stuff from, it's from this very good post:

Thoughts about winrates and variance

I am certainly not a statistics guy, so if anyone who knows what they are doing would check my math, I would be glad

[Bugsbunny]

After 10k hands your expected win value is 200PTBB and your standard deviation is 400PTB (here is where I might be mistaken, but my guess is 40*sqrt(100) should be sigma for 10k when 40 is sigma for 10k)

This means the zero point of your distribution curve is at -200/400 = -0.5, and the area under the curve from 0 to -0.5 is 0.1915. This means the chance you are in the red after 10k hands is 0.5-0.1915 or 30.85% chance of being down after 10k hands.

When is your chance greater than 95% to be up? Well, that's easy I guess. It's greater 95% once the relation between expected value and standard deviation is greater than 1.645.

X is the number of hands played. Your win rate is 0.02PTBB*X, your standard deviation is 4PTBB*sqrt(X). Thus we need 0.005*sqrt(X) to be equal 1.645, which yields X = 108,241

So it seems you need roughly 110k hands to get the chance of being down below 5%.

If anyone wonders, where I got all the stuff from, it's from this very good post:

Thoughts about winrates and variance

I am certainly not a statistics guy, so if anyone who knows what they are doing would check my math, I would be glad

The numbers you gave are accurate. The Excel formula for chance of being behind is:
=NORMSDIST(-$A$2/$B$2*SQRT(A4))

Where:
A2 = Earn in BB/100
B2 = Standard Deviation/100
A4 = number of hands/100

[toronexti]

Bugs I'm trying to plug this formula into excel and put in:

A2 - 2
A4 - 10000
B2 - 40

and the answer I get is 2.86652E-07

Which I have no idea what that means.

[Bugsbunny]

Bugs I'm trying to plug this formula into excel and put in:

A2 - 2
A4 - 10000
B2 - 40

and the answer I get is 2.86652E-07

Which I have no idea what that means.

Try 10000/100 = 100 for A4

You should end up with .3085375387 (depending on how many decimal places you show). Convert to a percentage you get 30.85+%

The way you ran it is for 1,000,000 (1 million) hands. And the percentage would be .0000286652%, or about 1.4/50,000

For 100K hands it's about 5.7%

[toronexti]

I love how with my current earn/SD rate after 200k hands on any given 100 hands I'm only 53% to be up.