Bases for Bankroll Recommendations?

[stuey_thekid]

What figures are the 300BB limit and 20 buy-in no-limit recommendations based on? Considering you can miss draws many times in a row even while being given correct odds (hell, even drop the gloves big, open-ended straight flush draws). And sometimes repeated draw outs take place against your big pairs, two-pairs and sets even after being denied proper odds. Is there some sort of assumption that variance will only step the numbers X amount outside of expectation within a certain number of trials?

[Dangeresque]

Well, basically. It's called the Kelly Criterion, which is based on expectation and standard deviation, however I've too few brain cells left right now to explain that. But, I've heard, as a more secure roll, 550BB and 40BI and I rather prefer those numbers. If you're playing solid winning poker it would take some sort of fourth order standard deviation to punish you that horribly, and normally you would move down at that point.

[tarheeljks]

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Is there some sort of assumption that variance will only step the numbers X amount outside of expectation within a certain number of trials?

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the short answer is yes-- the suggested br #'s should be large enough to w/stand a reasonable amount of variance.

[insyder19]

Like losing with AA 8 times in a row moved all-in preflop.

[emerson]

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What figures are the 300BB limit and 20 buy-in no-limit recommendations based on? Considering you can miss draws many times in a row even while being given correct odds (hell, even drop the gloves big, open-ended straight flush draws). And sometimes repeated draw outs take place against your big pairs, two-pairs and sets even after being denied proper odds. Is there some sort of assumption that variance will only step the numbers X amount outside of expectation within a certain number of trials?

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To do any calculations you need to make an approximation of your win rate per hand and SD per hand. If you have per hour or per hundred figures that will do fine also. I play limit holdem and know that my SD per 100 online is about 18 to 20. Live it is about 12 BB per hour.

If you also approximate your win rate then you can figure the likelihood of having certain size downswings within a given period of time. But you need a starting point. Generic figures are not very accurate. An aggressive player who bluffs frequently will need a much bigger bank than a more conservative player.

[XxGeneralxX]

I play my best poker with a monster roll so that I never think about the money. I currently have 68 BI for the level I am playing. If I were playing w/ 20 BI I would be making my decisions based on absolute dollars which can force me to make bad decisions. With a bigger bankroll I can focus on relative dollars.

[pzhon]

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What figures are the 300BB limit and 20 buy-in no-limit recommendations based on?

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Once upon a time, these were based on something. Maybe it wasn't obvious that they were based on different things (20 buy-ins is significantly more conservative than 300 BB in typical games). Now, they are repeated because they are traditional. Unfortunately, they are not correct for most people, and they are highly misleading in both directions, but repeating them is a lot easier than thinking.

If someone asks you how to play top pair, you'd start with, "It depends," because it depends. When someone asks what size bankroll they need, the correct answer starts with, "It depends," because it depends. However, the common, unthinking response of too many posters here is to give a specific answer which does not depend on anything, or the right quantities. Even the SSNL FAQ is wrong about this.

Please don't say 20 buy-ins unless you know what is wrong with that response, and still think it is the best thing to say in that context. Otherwise, you are just spreading misinformation.

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Is there some sort of assumption that variance will only step the numbers X amount outside of expectation within a certain number of trials?

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That's not an assumption. That's a result, or rather, a type of result. For example, the Cebyshev (multiple spellings) Inequality says that the probability that you are n or more standard deviations away from the mean is at most 1/n^2, and there are effective versions of the Central Limit Theorem which bound how far you are away from a normal distribution (which falls off faster than exponentially rather than only quadratically).

One way to get bankroll recommendations is to choose a risk of ruin, then approximate your poker play by a series of coinflips with the same win rate and standard deviation. Then you solve for the risk of ruin explicitly in the coin flip model, and choose the bankroll with the desired risk of ruin. As long as you are not playing with a very deep stack in NL, the approximation by a coinflip is quite good.

For example, suppose you win 2 BB/100 with a standard deviation of 15 BB/100, which is 0.02 BB/hand with a standard deviation of 1.5 BB/hand. You can approximate a hand by a coin-toss for 1.5 BB where you win with the probability 50.67% = 38/75 that gives you an average win rate of 0.02. The probability that you bust out with n*3/2 BB is (37/38)^n. If you want a 1/1000 risk of ruin, set this equal to 1/1000, which happens when n=259, which corresponds to a bankroll of 389 big bets.

There have been many poor, overly complicated articles on bankroll management. It's not trivial, but the basics are simple. Use c * SD^2/WR, where SD is your standard deviation per period, WR is your true win rate per period, and c is your desired comfort level, which depends on your personal risk tolerance and ability/willingness to move down. Most people are happy with a comfort level from 2 to 4. If you stay at the same level, your risk of ruin is about e^-2c.

The 300 BB guideline is reasonable for some professionals in soft live games. If you assume it applies to tough online games, you are making a mistake which may cost you your bankroll. If you assume that a bankroll suddenly gives you professional's skills, you are making a mistake. If you think you need to grind your way up to $30 at $0.01-$0.02 to safely take a shot at $0.05-$0.10, you are wasting your time by applying that heuristic ridiculously far out of context.

Some people don't want a bankroll. They want a security blanket. They need a certain amount of money in the bank to feel safe. That's fine, get a crutch if that's what you need to feel safe, but it has nothing to do with protecting a winning player from busting out.

Cue the chimpanzee to scream I must be wrong because I've said something correct but unpopular, hence worth saying.

[UtzChips]

http://support3.com/poker/bankroll/bankroll.asp

[Gonso]

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Use c * SD^2/WR, where SD is your standard deviation per period, WR is your true win rate per period, and c is your desired comfort level

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Could you show what happens to the RoR if you drop down a limit once your effective BR drops to 50% of starting strength? Rather than playing that limit until busto.

Assume you're playing 2000NL with a 1BB/100 WR and 20BB/100 SD. You can drop to 1000NL where you're 2BB/100, and if you drop to 50% of that roll, on to 500NL with a 4BB/100 WR (no drop down from here, win or you bust). Roughly the percentages of hitting the floor of each limit multiplied by one another, no? Except that your BR for the higher two limits is halved in the calculation?

Also

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Cue the chimpanzee to scream

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what's up with you and screaming chimpanzees

[stuey_thekid]

Interesting response that was, admittedly, over my head at points. Have any favorite statistics textbooks containing good explanations of your main statistical concepts?