Just to learn I'm doing some calculations on my poker results. I'm trying to figure out the probability of given winrate.
The available statistics I got in my database are:
Hands: $30 000$
Winrate: $2$ bets per $100$ hands
Expected winrate (what our winrate would be if we had gained all of our EV) : $8$ bets per $100$ hands
StdDev: $8$ bets per $100$ hands
What's the probability of our winrate per $100$ hands being less than $2$ given that our expected winrate is $8$?
I'm thinking like this:
Central limit theorem can be applied and therefore normalized
Use this formula: $t = \dfrac{2-8}{8/(3k^{0.5})}$
And then look up $t$ in a $z$-table? ($t$ will be very close to $z$ because of the large sample).
Am I doing this right?
Looks fine, except that I don't know what $k$ is.
Standard error $=\frac{0.08}{\sqrt{30000}}$, $z=\frac{0.08-0.02}{\text{standard error}}$