bankroll management

[cardplayer52]

I started to use a new BRM system and figured I'd share. I just hope I can explain it clearly enough. OK here goes.

1st You need to decide the amount of buyins for a given stake you want to keep. I wouldnt recommend less than 50 for cash games. I would use 100 for SnGs and maybe 200 for larger tourneys.

2nd You need to decide the amount of tables you have open per session. Add the total amount of buyins and devide that by the number of tables.(this will be the same if all buyins are equal). This amount shouldn't be larger than 4% of your total bankroll.(believe me there's nothing like losing power while 20 tabling).

3rd If you take the number from the prior step and multiply it by 100, this will be the amount you need to have in your BR to start the session.

The reason I use an average of the buyins is for when I want to move up in stakes. If I four table I would average amount of 3 lesser buyins and one higher buyin x100. When I have that amount in my BR I could start to add one higher buyin to my sessions.

I figure out the amount I'd need to add more and more tables. Until I had enough buyins to play at the higher level. I do this unless I dip below the last treshold. Then I drop higher buyins as my BRM system allows.

Also you need to keep the same ratio of smaller to higher buyins the same. So if you bust in a higher buyin you need to wait till you finish all the lower buyins before you add another higher buyin.

 

[micalupagoo]

Nice write up
BRM is very important!

 

[BelFish]

In general, bankroll management most likely needs to use a normal distribution and a level of confidence. First, the distance is played, then, based on the expectation and variance obtained for you personally, estimates of the confidence intervals are made. And the lower limit is sought in such a way that the probability of a complete collapse is, for example, 5%. Or 3%. For some it will turn out that 10 buy-ins will be enough, for others 50 will not be enough... It all depends on the level of play of a particular person.

Later i will give some calculations...

 

[BelFish]

expected value and variance can be taken from trackers. Or keep statistics ourselves.

I will show how to apply these formulas using the example of SnGs HU. For example, a person plays a $7 limit and has a win/loss rate of 55% / 45% over the long run.

Then the mathematical expectation and variance will be as follows:

MO = 6.42$ * 0.55 - 7$ * 0.45 = 0.381$
S.D. = 6.702$ (square root of variance).

Then the confidence interval is calculated using the formula in Excel:

= CONFIDENCE (1-A1, A2, A3)

Cell A1 contains the required reliability of the results. We install it ourselves. Usually this number is greater than 0.9.
Cell A2 - standard deviation (S.D.)
Cell A3 is the sample size, i.e. the number of SnGs HU games for which we will look at the result. For example, you play 1000 SnGs per month.

= CONFIDENCE (1-0.9, 6.702, 1000) = 0.3486

Then for the upper and lower profit margins we get:

(0.381-0.3486) * 1000 = 32.4 $
(0.381 + 0.3486) * 1000 = $ 874

And for the average profit value: 0.381 * 1000 = $ 381

In order to determine the BRM for a given player, it is necessary to select such a number of games at which there will be a maximum drawdown, i.e. the bottom line of the profit will be the most negative. This number is 211 games. In this case, the lower limit is equal to: -79.73 $.

Because we chose 0.9 confidence, which means that 90% of the time we don't walk out of these limits. In 5% of cases, the result will be better than the upper limit ($ 305.94 for 211 games), and in only 5% of cases it will be below the 11.4 buy-ins (11.4 * $ 7 = $ 79.8). So, there must be BRM = 12 buy-ins for this player if he wants to have no more than 5% chance of a crash.

A more conservative BRM can be calculated, for example, for a 2% crash probability. By analogy, you can calculate BRM for cash games, for tournaments. But this requires large statistics for specific games ...

 

[deputat777]

Thanks for the useful information.

 

[BelFish]

If we counted for a more experienced SnG HU player, for example, with statistics of win/loss = 60% / 40%, then using the same formulas it would turn out that the maximum drawdown for a confidence level of 0.9 would be $ 28.6 at about 25-30 SnGs played. For such a player, it would be possible to play at brm = 5 BI (almost 4BI would be enough, but you need to round up to integers). Although this is quite an aggressive BRM, for such a player the chance of collapse is less than 5% for a given BRM.
It is possible and 4BI, just the chance of collapse then will be a little more than 5%.

Or you can use a conservative brm with a 2% chance of collapse. Then, according to the formulas, we get the largest drawdown for the reliability of 0.96 (only 2% of the results are worse than the lower limit according to the formula), equal to -44.7 $ for about 42-43 games.

$ 44.7 / $ 7 = 6.4, i.e. for a given player, the conservative BRM = 7 Buy-ins.

If we count for SnG HU player with statistics of win / loss = 52% / 48% at a long distance, then the correct BRM for him will be equal to 0 BI, i.e. he'd better stop playing at all

 

[BelFish]

Someone may want to play with BRM, in which the chance of crash is no more than 1%.

The 20 or 30 BI rule is for beginners. At the same time, a fairly large margin of safety.

But of course it is worthwhile to understand that all this calculations is conditional. For cases when you sit down to play each game at a different time. Because if, for example, a very strong player starts to sit down to you all the time, then the BRM should be much higher against him!

P.S. So it's best always to have a bankroll with some margin of safety...

 

[fundiver199]

I think, the ideas layed out by OP are a bit of the conservative side. If you really hate losing money and is prone to tilt, you can go with these numbers, but for people trying to build up a bankroll, it will take very long time this way. So I would suggest moving to the next level, when you have 30 BIs for cash games, 50 BIs for SnGs and 100 BIs for MTTs. Or at least start taking some "shots".

If for instance you have 400$ and play SnGs on pokerstars, then play a mixture of 3,5$ and 7$ games and stop playing the 7$ games, if you drop below 350$. In that way you still have 100 BIs for the level, you are going to drop back down to, and this is quite conservative already. What goes wrong for most people is, that they dont move down, when they start to lose, and in my opinion this is way more important than being very conservative about moving up.

Also there is no mathematical logic behind letting your bankroll requirement depend on, how many tournaments you are playing per session. If you play very long sessions, you are also more likely to cash in some of the tournaments, and the risk of ruin is just the same, regardless if you play 1 tournament per day or 30 tournaments the last day of the month just to take some extreme examples.

Instead you might select to implement some sort of stop loss strategy, if you are prone to tilt. For cash game players its usually calculated as the amount of big blinds, you are down, and a reasonable stop loss could be somewhere between 300 and 500BB. If you got felted 3-5 times in a cash game session, you are usually tilting to some extend, or at least that was my experience, when I played cash.

 

[cardplayer52]

Also there is no mathematical logic behind letting your bankroll requirement depend on, how many tournaments you are playing per session.

The rule was not more than 5% at risk at a time. It wasn't to do with how many games per session it was how many open tables per session. I've lose 20 buyins do to a power outage. I've also lost some buyins when Ive experienced internet connection problems.

Building a bankroll is one thing. But if you count on that bankroll to make you money, you dont want to lose it. It doesnt grow per say as you will withdrawing most of the profits.

My write up wasnt really meant to suggest the amount of buyins one needed. It was more how to figure how to allow oneself to move into a higher buyin, by taking an average of the buyins.

So me using 100 buyins for SnGs would play $3.50s until I got upto $437.50(which is 100x[($3.5×3)+7]/4 tables).
At $525 Id add another $7 or drop back down at $350.

 

[fundiver199]

I've lose 20 buyins do to a power outage. I've also lost some buyins when Ive experienced internet connection problems.

This might be a concern, if you live in an area with unstable electricity supply and/or internet connection. But for the vast majority its not something to worry about in my opinion. Also we should probably not be 20 tabling anyway, since we are then trading to much quality for quantity, and its easy to end up burning yourself out.

 

[messats]

I started to use a new BRM system and figured I'd share. I just hope I can explain it clearly enough. OK here goes.

1st You need to decide the amount of buyins for a given stake you want to keep. I wouldnt recommend less than 50 for cash games. I would use 100 for SnGs and maybe 200 for larger tourneys.

2nd You need to decide the amount of tables you have open per session. Add the total amount of buyins and devide that by the number of tables.(this will be the same if all buyins are equal). This amount shouldn't be larger than 4% of your total bankroll.(believe me there's nothing like losing power while 20 tabling).

3rd If you take the number from the prior step and multiply it by 100, this will be the amount you need to have in your BR to start the session.

The reason I use an average of the buyins is for when I want to move up in stakes. If I four table I would average amount of 3 lesser buyins and one higher buyin x100. When I have that amount in my BR I could start to add one higher buyin to my sessions.

I figure out the amount I'd need to add more and more tables. Until I had enough buyins to play at the higher level. I do this unless I dip below the last treshold. Then I drop higher buyins as my BRM system allows.

Also you need to keep the same ratio of smaller to higher buyins the same. So if you bust in a higher buyin you need to wait till you finish all the lower buyins before you add another higher buyin.

this is one of my weak areas as i have won many games had a bank roll of up to 1000 and lost it all many times over, this is where am focused on working

 

[cardplayer52]

MO = 6.42$ * 0.55 - 7$ * 0.45 = 0.381$
S.D. = 6.702$ (square root of variance)

I read all your comments but can't follow all your math. I no longer had a HUD so how can I get the standard deviation? I read a cash HU player the standard deviation is anywhere from 50-100bb/100, with 80bb/100 suggested. The other thing I don't understand is the 5% risk of ruin. 5% is 20:1 so if I played 21 sessions would I go broke(assuming I cashed out all my profits)?

The formula I've seen used is B=((S2/(2m))In(1/R).
B= bankroll
S= standard deviation
M=win rate
R= risk of ruin

I'm not quite sure how to convert a 6% ROI into a win rate. Or how does 55/44 or 60/40 convert to a win rate.

 

[BelFish]

Well, when you know the frequency of the winnings, then the variance can be determined from it.

I did a simulations of the game in Excel and it turned out that ruin occurs with greater frequency. This is because if we have reached a minimum (for a drawdown), then the graph will not necessarily go up statistically. That is, later than this moment, sometimes an even larger drawdown will occur. Since we will not stop playing after the number of games at which this minimum of graph will reached.

Maybe a good formula for BRM would be to multiply the number obtained by this method by a factor from 1.5 to 2. Maybe the results for any win rates and reliability will correspond well to simulations of the game in Excel. I'll check it later.

-----------------------

Can't you tell where exactly you saw that formula? And was there a solution or just a final formula?

I'll look at the formula for now and try to apply it to different cases. Maybe i'll figure out how to solve it myself.

 

[funfellow888]

bankroll

not sure but i think ya need a bankroll to do bankroll managment:joyman:

 

[BelFish]

The other thing I don't understand is the 5% risk of ruin. 5% is 20:1 so if I played 21 sessions would I go broke(assuming I cashed out all my profits)?

This refers to the full risk of ruin with a given BRM. If the winning player plays for a very long time, then statistically, his graph will eventually turn out to be a plus. But if at the same time 5% of the graphs cross the negative mark by a number equal to the number of buy-ins, then he simply will not be able to play further in order to reach a plus, which is later achieved on the graphs.
If during simulations 5% of all graphs cross this mark, then this means that ruin occurs in 5% of cases.

 

[BelFish]

I'm not quite sure how to convert a 6% ROI into a win rate. Or how does 55/44 or 60/40 convert to a win rate.

In the formula that you quoted just the conversion of the frequency of wins to winrate. But this is specifically for SnG HU. It depend of the rake. In case of a loss, we lose $ 7, and in case of a win, we receive only $ 6.42.

ROI can also be converted in a similar way into an absolute amount of money.

P.S. It is even more correct to say that the formula does not contain winrate, but the mathematical expectation of one game (one SnG HU in this case).

In English, it is better to replace MO in the formula with ME

 

[CallmeFloppy]

I think one of the main things here too is understanding what your winrate is.

If you are a losing player, no bankroll management system is going to keep you from going broke, all you can hope for is to spread out our losses.

Other is do not expect that your winrate is the same for all types of play. You will likely find that different stakes will greatly affect your win rate. You also need to understand how many tables you can handle.

Now I am just a recreational player, but I found that my peak was when playing 4-6 tables. I would stay more engaged and take less chances when I stayed in this zone. If I played less, I would get bored and lose focus and play hands I shouldn't, or miss opportunities I would otherwise take advantage of. Over 6 and I would find that may ability to keep track of the games dropped off and I would get frustrated.

Find your sweet spot and stick to that when applying the other information above.

 

[1nsomn1a]

The main thing is not to spend too much time on mastering micro limits, too strict bankroll management can keep you at these limits for a long time, since the micro game is too dispersive and you can spend a lot of time. And time is the most important thing, and it's not just in poker.

 

[BelFish]

Regarding the formula for BRM with a logarithm: if we consider 2 cases (the chance of ruin 5% and the chance of ruin 3%), then the formula for these cases will take the form:

B5 = 3D/2m, for a 5% ruin chance

B3 = 3.5D/2m, for a ruin chance of 3%

Then, applying the formula to SnG HU, we get for the case of the frequency of winnings at a distance equal to 55%:

B5 = 3 * 6.7 ^ 2 / (2 * 0.381) = 58.9 $ =( 58.9 / 7) BI = 8.4 BI

B3 = 10 BI

B1=13 BI, for a ruin chance of 1%

 

[BelFish]

Sorry, mistake

B(5%)=25.3 BI
B(3%)=29.5 BI

B(1%)=39 BI

 

[BelFish]

Here's what i noticed: if at the point of maximum drawdown we put about three times the standard deviation from the average expectation down, then the distance from zero to the resulting point will be approximately equal to the required BRM. More precisely, it is necessary to postpone about 3.2 standard deviations.

For example, for the case of a win rate of 55%, the maximum drawdown will occur on average with 211 games. In this case, the mathematical expectation of a win will be 211*0.381$=80.4$.
(80.4$+79.73$)/1.96=81.7$ Then, postponing 3.2 standard deviations down from the average, we get a drawdown below zero equal to (80.4$-3.2*81.7$)/7$=25.9 BI. And this is about 26 full buy-ins, as according to the formula with the logarithm.

For the case of reliability different from 5%, we also obtain the value of the sum for the BRM very close to the value obtained by the formula with the logarithm.

 

[ph_il]

i think my brm plan is overly simplified based on these post. my brm plan is:

do i have 100+ buy-ins and can i beat this level?

a. yes, yes = play
b. yes, no = take stabs
c. no, yes = take stabs at 75+ buy-ins
d. no, no = don't play

 

[fundiver199]

i think my brm plan is overly simplified based on these post. my brm plan is:

do i have 100+ buy-ins and can i beat this level?

a. yes, yes = play
b. yes, no = take stabs
c. no, yes = take stabs at 75+ buy-ins
d. no, no = don't play

Sounds totally reasonable for me, if you are talking about MTTs. b) is to dip your toe in and gain experience with, how higher limit games tend to play. c) is known as "shot taking", and for that even 75 BIs is pretty conservative. If for instance you have a 1.000$ bankroll and want to play a 22$ tournament like the recent MicroMillions main event on PokerStars, then you still have 978$ left to play with, if you fail to cash, which is essentially the same as 1.000$. So as long as "shots" are really just that, they are completely fine. The problem only start to arise, if you then decide to also play the 22$ "big", the 16,5$ "hot" and the 33$ PKO "on demand", because then you are no longer taking "shots" but simply playing above your bankroll.

 

[ph_il]

Sounds totally reasonable for me, if you are talking about MTTs. b) is to dip your toe in and gain experience with, how higher limit games tend to play. c) is known as "shot taking", and for that even 75 BIs is pretty conservative. If for instance you have a 1.000$ bankroll and want to play a 22$ tournament like the recent MicroMillions main event on PokerStars, then you still have 978$ left to play with, if you fail to cash, which is essentially the same as 1.000$. So as long as "shots" are really just that, they are completely fine. The problem only start to arise, if you then decide to also play the 22$ "big", the 16,5$ "hot" and the 33$ PKO "on demand", because then you are no longer taking "shots" but simply playing above your bankroll.

good points. 75 buy-ins might be a bit conservative for shot taking, but it also helps with the mental game that i sometimes struggle with. to be honest, after some though, i think i'd change it to 'take shots at 95+ buy-ins.'

luckily, i don't take shots too often because i just don't have that confidence in my ability anymore. even right now, i'm struggling to play the games i am bankrolled for and often settle for playing mtts i'm way over rolled for just because of my lack of confidence.

 

[fundiver199]

luckily, i don't take shots too often because i just don't have that confidence in my ability anymore. even right now, i'm struggling to play the games i am bankrolled for and often settle for playing mtts i'm way over rolled for just because of my lack of confidence.

Its clearly best to take "shots", when you are on a sunrun, because then you are more confident and just giving back some of your recent winnings, if the shot fails. If on the other hand you a struggling a bit and lacking confidence, being overrolled makes it a lot easier to cope with the bad part of variance.