Hypothesis Test for Longterm Winrate -- Please Help

[sthief09]

Please tell me if/where I'm going wrong. I'm trying to figure out how many hands a person needs to tell if he's a winning player given a certain SD and winrate.

The way I'm thinking of it is in samples of 100 hands. Winrate is x and SD is s. Since n is in terms of 100 hand samples (number of hands divided by 100), I need to do a t-test. The null hypothesis would be that x is greater than 0, or in other words, the player is a winning player on a 95% CI.

we reject if T < t

t can't be exact since we're solving for n, but for a = .05, and v somewhere between 40 and >100, so it's around 1.65-1.69
T = (x - 0)/(SD/sqrt(n)) = x*sqrt(n)/SD

for me, x = 4.46 and SD is 17.24, so

T = .259*sqrt(n) < 1.69 (1.69 since we're starting for the smallest value of n)
n > (1.69/.259)^2
n > 42.57

so according to this, with a winrate of 4.46 BB/100 and a SD of 17.24/100, you'd only need 4,257 hands to be a proven winner. that doesn't make any sense to me. Please tell me where I went wrong.

[tech]

Let me first say that I am not sure that a T test is really appropriate here, simply because some of the key assumptions probably do not hold. Specifically, the distribution of x is likely quite skewed. This makes the results much more difficult to interpret meaningfully.

With that said, I think your calculations are fine. Think about it this way. For someone with the same SD but a winrate of only 1.5BB/100, now a sample size of over 37K hands is required.

Also, this test says nothing about being able to sustain the 4.46 winrate. It simply examines whether the true winrate is likely to be greater than 0. Further, you are only going to be accurate roughly 95% of the time.

[sthief09]

good points. thank you!

[southerndog]

How about this.. Since -300 BB's at a given level shows you are a losing player, why can't +300 bets show you are a winning player?

[scrub]

[ QUOTE ]
How about this.. Since -300 BB's at a given level shows you are a losing player, why can't +300 bets show you are a winning player?

[/ QUOTE ]

Neither of these statements is particularly accurate.

scrub

[southerndog]

b

[sthief09]

because it doesn't prove anything. people say a winning player shouldn't lose more than 300 BB. if you lose 300 BB, you're probably a losing player. but winning 300 BB doesn't prove anything. you could have an enormous SD and small number of hands played, and it'll be insignificant.

[Tapped]

You are pretty much correct on the math. As others have said the distributions isn't symmetrical so it skews a bit, but an approximation is close enough in this case.

Instead of 95%, I use 98%, 2 stds outside mean, because it's a bit more certain.

4.46/100 in 5900 hands will have the same expected gain as 2 stds (1030 BBs at 1.7 BB/hand).

If you play 4 times as much, 24,000 hands, with 4.46/100, you're likely to be at least 2.23 BB/100.