Re: buying in short
 

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That's precisely what people are arguing when they say you must cut your stakes in half and buy in for 100 BB instead of buying in for $50 at a NL $100 table.

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I agree with you, thats a stupid arguement. And i'll retract my figure of 500k hands needed.... using my standard deviation, just shy of 250k hand samples would narrow your win rate to a 3BB/100 range (95% confidence), and you could statistically claim at that point, if your observed win rate was exactly the same for both sets of data, that the difference (if any) in buying in short vs big was not more than 3BB/100. With 20k hands all you can say is it's not costing you 10.75BB/100 (again using my SD, and assuming observed win rate for both is exactly the same).

Re: buying in short
 

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That's precisely what people are arguing when they say you must cut your stakes in half and buy in for 100 BB instead of buying in for $50 at a NL $100 table.

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I agree with you, thats a stupid arguement. And i'll retract my figure of 500k hands needed.... using my standard deviation, just shy of 250k hand samples would narrow your win rate to a 3BB/100 range (95% confidence), and you could statistically claim at that point, if your observed win rate was exactly the same for both sets of data, that the difference (if any) in buying in short vs big was not more than 3BB/100. With 20k hands all you can say is it's not costing you 10.75BB/100 (again using my SD, and assuming observed win rate for both is exactly the same).

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I think the assumption of 2 sample t-test in this situation is violated because buyin short and full are highly correlated.

Re: Bankroll Requirements
 

I've been learning and playing only SSNL for the last month (before this I was primarily playing STT's/MTT's). FWIW, whenever I see someone join my table without buying in full, especially if they only buy in for around half or less, I immediately categorize them as weak-tight/scared money/fish until they show me otherwise. Perhaps this is another advantage of buying in short at a higher level -- that many opponents will erroneously think you're weak-tight/scared money/fish when you buy in short, and thus won't play correctly against you (at least in the short term).

Re: buying in short
 

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using my standard deviation, just shy of 250k hand samples would narrow your win rate to a 3BB/100 range (95% confidence),

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Your standard deviation appears to be much higher than mine. A side benefit of buying in short is that my SD is lower.

I don't think your win rate is so much lower that you need to get the 95% confidence interval to be so small to reject the hypothesis that buying in for 50 BB is only half as profitable as buying in for 100 BB.

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With 20k hands all you can say is it's not costing you 10.75BB/100 (again using my SD, and assuming observed win rate for both is exactly the same).


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That's not true. Even if that were roughly 2 joint standard deviations (it's a lot higher than mine), you don't need 2 standard deviations of evidence before you can say anything. A Bayesian approach might say that you should reweight the hypothesis of equality upward by a factor of 3.1 relative to the hypothesis that there is a 1.5 standard deviation difference. (3.1 = exp(1.5^2/2)) So if you started with the assumption that the two were equally likely, you would update that to saying that equality is a 3.1:1 favorite over the difference in win rates that would be 1.5 standard deviations away from the observation. That's not bulletproof, but it would be a lot better than NO evidence, which is what thedustbustr offered.