Bases for Bankroll Recommendations?
 

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?

Re: Bases for Bankroll Recommendations?
 

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.

Re: Bases for Bankroll Recommendations?
 

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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.

Re: Bases for Bankroll Recommendations?
 

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

Re: Bases for Bankroll Recommendations?
 

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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.

Re: Bases for Bankroll Recommendations?
 

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.

Re: Bases for Bankroll Recommendations?
 

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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.

Re: Bases for Bankroll Recommendations?
 

Re: Bases for Bankroll Recommendations?
 

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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

Re: Bases for Bankroll Recommendations?
 

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

Re: Bases for Bankroll Recommendations?
 

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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).

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First, that SD/100 is quite low for NL.
Second, with those stats, you are winning the same $/hand at each level, so you should normally play in the game with the least variance. Of course, you might expect that your win rate would rise faster in the tougher game.

To determine the actual risk of ruin, you need to determine your plan for moving back up, if any.

Case 1: You never move back up.
Case 2: If you move down to NL $1k, then double up to your original bankroll, you return to NL $2k. If you move down to NL $500 and double up to half of your original bankroll, you move back to NL $1k.

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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?

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Yes, for Case 1.

Let ROR_n(x) be the risk of ruin if you play at level n forever with a starting bankroll of x.

Then your risk of ruin with this strategy is

ROR_2k(BR/2) * ROR_1k(BR/4) * ROR_500(BR/4)

~ ROR_2k(BR/2) * ROR_2k(BR) * ROR_2k(4 BR)
~ ROR_2k(5.5 BR)
~ ROR_2k(BR)^5.5

So, this strategy has the effect of increasing your bankroll by a factor of 5.5, or raises the risk of ruin to the power 5.5. Just playing at NL $500 in the first place would be a factor of 16 rather than 5.5, since your bankroll is 4 times as many buy-ins, and your win rate is 4 times as great.

Case 2 is more complicated.

What is the probability that you lose everything before reaching n times your initial bankroll? The probability of going to infinity is both 1-ROR(BR), and probability of making it to n*BR, and then failing to bust out.

(1-ROR(BR)) = P(BR->nBR)(1-ROR(n BR))
P(BR->nBR) = (1-ROR(BR))/(1-ROR(n BR))

You can use this to set up a solvable system of equations for the risk of ruin with BR, BR/2, and BR/4, but the answer I get is not worth typing. Returning to the higher stakes games increases your ROR relative to Case 1.

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Cue the chimpanzee to scream

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what's up with you and screaming chimpanzees

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They don't like me? It's hard to tell, since it seems to be a different one each time. I write that so that someone who seriously disagrees will take more effort to distinguish himself from a screaming chimpanzee than is sadly typical, or will look like a joke.

In another forum, someone posted a poll, A or B. It turns out he really wanted people to answer A. I alone voted B, and posted the results of a mathematical model supporting B, and gave some qualitative arguments about why B is better. The responses? "Kill yourself." "Intuition always beats mathematics." I hope we can do better in the 2+2 forums.

Re: Bases for Bankroll Recommendations?
 

Thanks, no my numbers aren't right, I just needed to see how that works. I'm trying to move up to a limit I haven't beat in a couple tries yet. When I gave example numbers I didn't consider the $/he was all the same - of course in that case lowest variance makes for the best game.

Re: Bases for Bankroll Recommendations?
 

A couple of additional points to consider:

1) The 300BB rule assumes you bankroll accumulates. If you consistantly cash down to 300BB you will eventually go broke. Think of flipping coins and counting tails as down swings. If you flip a coin 100 times, 10 tails in a row would be unusual. If you flip a coin one million times, you would expect multiple runs of 15 tails or more. The effect of growing your bankroll is that by the time the larger downswings come, you'll have the bankroll to withstand them.

2) Another point is that you risk of ruin only depends on your current bankroll (assuming win rate and standard deviation stay the same). If you start with 300BB and lose 100BB, you have exactly the same risk of ruin as if you started with 100BB and won 100BB. The consequence of this is that if you want to play with a certain risk of ruin, you need more than you think unless you plan to quit as soon as your bankroll drops.

Paul

Re: Bases for Bankroll Recommendations?
 

an excellent discussion on this in print is in mark blades book. but that really is for limit. the problem i have is what exactly does BUY-IN mean? is it the max buy-in for a capped no-limit game? dont you control that buy-in? is it the minimum buy-in? also when you guys say no-limit$200 or no-limit$500 what the hell does that mean? I know its used for internet games.

Re: Bases for Bankroll Recommendations?
 

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what exactly does BUY-IN mean? is it the max buy-in for a capped no-limit game?

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Yes. A buy-in in NL is the max buy-in for a table.

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also when you guys say no-limit$200 or no-limit$500 what the hell does that mean? I know its used for internet games.

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NL200 means the max buy-in is $200. If you think you need 20 buy-ins to play NL200, you'll need $4000 in your bankroll.

Pzhon is very correct, though. Your bankroll requirements are exactly that. Your bankroll requirements. Before anyone decides how much they need to play at a certain limit/stakes, they should answer a few questions.

- Will I move down if I lose a bunch? (yes - smaller BR)
- Will I be withdrawing from my bankroll? (yes - bigger BR)
- Am I trying to move up to the next level? (yes - bigger BR)
- How good am I at this level? (one of the best - smaller BR)

Each of these questions (and quite a few others) affect how much you want to have in your bankroll.

Edit: I'm currently building a bankroll, and playing with the intent of moving up with around 200-300BB for the limit I'm playing. I don't withdraw (smaller bankroll), consider myself better than the majority of my competition (smaller bankroll), amy trying to move up in stakes (bigger BR), and can move down if I go on a long losing streak (smaller BR).

However, when I reach my target limit, I'm going to want a much larger bankroll than I'd need, because I might not be in the top 10% or so of the field, I'll be withdrawing regularly, I won't be actively attempting to move up in stakes, and moving down will really hurt. At this point, I'll probably want 1000+ big bets in my roll.

Determine your motives for playing, and you can use that information to derive your appropriate bankroll.