Buried in Variance?

[Redd]

Hey, first-time poster in Probability but long-time reader of the brain-teasers. I have a general (and probably basic) question that I think about alot while getting sucked out in the nanolimits:

It's obvious that the really bad play that I see in the nanolimits is +EV for me, and +variance. As my bankroll flips around wildly at these highly random tables, it's occurred to me that if I sat at a hypothetical game where I won +1BB/100, with a deviation of 100,000BB/100, my win rate would be so miniscule that it really wouldn't be evident over any reasonable number of hands.

Subsequently, it seems to me there exists some EV/Variance ratio where EV becomes insignificant. Although I took my single stats course a while ago, I kinda-sorta seem to recall there being an actual test for significance in a situation like this? My two questions are:

1) Is there any way to determine a number of hands, X, for a given BB/Variance ratio, where one's win rate is insignificant for <X hands played?

2) Is an insignificant win rate ever attainable in a real game for a 'reasonably' large X, say 100,000 hands?

[Dov]

Without being one of the math geniuses here, I will attempt to reply to your post with a logical point of view.

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Is there any way to determine a number of hands, X, for a given BB/Variance ratio, where one's win rate is insignificant for <X hands played?

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We know that there is a way to determine your win rate from std dev and number of hands played. You can imply from this that with an inadequate sample size, your win rate will be meaningless. (I have a feeling that you may have meant something else when you said insignificant, but without enough hands, it will definitely be a range which is not very useful)

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Is an insignificant win rate ever attainable in a real game for a 'reasonably' large X, say 100,000 hands?

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Wouldn't this be the definition of a break even player?

[Redd]

Yeah, perhaps my question is more about sample size. I was thinking more along the lines of when a scientific study determines that their trials have made a useful finding. When publishing a research paper, isn't there some sort of standard boolean identifier between significance and insignificance?

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Wouldn't this be the definition of a break even player?

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I was more thinking along the lines of someone who was actually playing a +EV game, but you wouldn't know it due to variance. Like in my 1(+/-)100,000BB/100 example, the player is winning, but he'd never know it. But again, I suppose this could just be a sample-size question in disguise.