Bankroll Requirements

[teamdonkey]

Phzon, i absolutely disagree in several spots:

-20k hands is about 480k short of what you'd need to tell if there's any real difference in your winrate when buying in short. Actually closer to a million: half buying full, half buying in short. Do the calculations for yourself... i'm not joking. I don't think anyone would argue your buyin amount would make more than 3 or 4 BB/100 difference, and since you can't narrow your winrate down to a range that proves this difference without at least a half a million hands, you'll never be able to make that statement with any sort of credibility.

-Tommy Angelo / ElDiablo are talking about buying in short until you get a feel for the table, then buying in for more. Not buying in short and staying there.

-in small stakes NL, not buying in for the max because the other big stacks are good is close to rediculous. There's only 2 situations where it's a disadvantage:
1. your post flop play is poor. If this is the case, you should be actively working to improve it (which you need larger stacks for) or playing a game where it isn't as important (MTTs, STTs).
2. the big stacks at the table are much better than you. If this is the case, you have no business being at that table. The rake is too hard to beat by itself without having to deal with losing chips over time to better players also. I'd argue strongly that if you're not at least very close to the best player at your table, in almost all cases you're losing money.

Buying in small makes your decisions easier. It certainly allows for plays and situations not available to you when you're deep. But it's the complexity of poker that makes it difficult (and profitable), and the difficult decisions you face when playing deep should be where the majority of your edge against bad players comes from. In the long term there really shouldn't be any arguement as to which is more +EV to a winning player.

[pzhon]

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-20k hands is about 480k short of what you'd need to tell if there's any real difference in your winrate when buying in short.

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There seems to be a folklore about how many hands you need to be able to draw conclusions about your win rate. Below whatever number someone wants to give in an argument, they will say your sample size is negligible. (By contrast, thedustustr offered NO evidence for his assertion that buying in short should cut my win rate proportionately. I have offered numerical and logical arguments against it.) As a mathematician, I prefer the much more accurate idea that rather than using an arbitrary threshold (chosen beforehand, or adjusted later to try to disqualify my evidence), we can recognize that the observed win rate smoothly becomes increasingly accurate with more evidence. A very high number of hands is needed to pin down a win rate within 1 BB/100. A much lower number of hands is needed to provide substantial evidence that my win rate is not cut in half when I buy in short.

20k hands each is enough that I would notice if buying in short were to cut my win rate in half the vast majority of the time. The 95% confidence interval from the last 20k hands does not include winning only 6.5 BB/100. (33 PTBB/Sqrt(200) = 2.33 PTBB/100.) While I don't have strong evidence that I would not win 13 PTBB/100 by buying in for 100 BB, I don't believe it.

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I don't think anyone would argue your buyin amount would make more than 3 or 4 BB/100 difference,

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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.

I'll respond to the rest later.

[teamdonkey]

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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).

[rachelwxm]

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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.

[pzhon]

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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.