I had a -$13.3k downer in about 35 hours of live 40/80 play. A $15k bankroll for aggressive 40 games is just plain bad, IMO. This was off the heels of running at around 2.5 BB/hour for 100 or so hours of play, too. I couldn't imagine feeling confident in playing at a stake w/out a solid, 500 bet bankroll. Even this year, I'm stuck at live 20/40 to the tune of -0.136 BB/hr over 528 hours (15k-20k hands).

So much of your winrate is encompassed in high variance spots, no matter what the game type (aggressive shorthanded, loose passive FR, etc). Running good or bad in 6 way pots, for example, can make a huge difference (I ran well in these in early to mid 2014, poorly since). But nailing a flush draw on the river could spell the difference between winning a 20+ BB pot or losing it along w/ the 4-5 bets you invested. Mix in a few of these with a RNG determining the result, and you can see some swings.

I've done plenty of ROR calcs over the years. With a very high winrste and an extremely low standard deviation, your suggestion still provides a risk of ruin north of 25%, which is why I say it's an absurd suggestion.

I imagine our difference in opinion stems from the background of the person looking to play. If you are trying to support yourself/family then 25% is crazy, if you have relatively little bills and can work to replenish your bankroll then gamble it up.

Mason, also curious in your example of life expenses are paid for out of this bankroll or if we have 6 months saved up somewhere that we didn't mention. Becusse in reality that's our bankroll as well.

I think you misunderstood by point. The person that can sit in any game and win will win far more money per month/year than a player who game selects extremely well but plays half the hours. The person that wins more money (despite lower winrste) will be far less likely to go busto from life expenses becuse he simply has more money

Ho obi_wang:

If you're far from an expert then you'll need a larger bankroll than an expert. This is partly because the ability to read hands well, and this includes understanding how ranges should impact your strategy, should reduce your standard deviation. So this might be a reason why my numbers are lower than yours.

Another possible reason, and I'm not saying this applies to you, is that I notice that many of today's players are three-betting too much, and three betting with a zero or slightly negative expectation should significantly increase your bankroll requirements.

Best wishes,
Mason

Hi chillrob:

If the games are looser then that should increase your swings. But if the games are more aggressive, they you should play less hands which should decrease your swings. I would have to play in the game for some length of time to be sure, but I suspect that the required bankroll would not be much different.

To put your name on the list The Bellagio will accept call-ins for $10-$20 and $20-$40 limit hold 'em. But for the $40-$80 game or higher, they require that you sign up in person.

Best wishes,
Mason

So you're averaging about 3.5 big bets an hour. I suspect if you keep playing that average will come down.

As in my post above, while I agree that in general $40-$80 is a tougher game than $20-$40, I'm not sure the standard deviation, in terms of units, is much different. Remember, in the bigger game, if you're playing well, you should be playing less hands since you'll more often be against a tight player (for the position).

Best wishes,
Mason

Hi Jon:

You're bringing up a good point. When I say that it's okay to start with bankroll X this assumes you'll not be removing money from the system. For instance, if by removing moving money from your $7,000 $20-$40 limit bankroll you never allow it to grow larger than $7,000, then since it's quite likely that a $7,000 downswing will occur at some point in the future and you'll be broke. But if you let your bankroll grow as you win, then this won't happen.

Best wishes,
Mason

Hi jdr0317:

These aren't my numbers. Also from the above, keep in mind that the best predictor of your future results are your pass results. So when you say you have 528 hours and are a small loser, my response would be that you may not play as well as you think you do. Winning in Tough Hold 'em Games is very good for starting hands in today's games, and the Philip Newall books should help with your strategic play.

I'm not sure this is true and suspect that you are misusing the term "win rate." In a $20-$40 game if you just win the blinds you have won $30. There are very few hands where your win rate for the hand would be higher than $30 if you're called.

Best wishes,
Mason

I would have to see how you're computing the required bankroll. But if you have years worth of playing, then your largest downswing is usually an okay estimate of your required bankroll. And my downswings are consistent with my estimated bankroll.

I addressed this in one of the other posts and yes, it does make a difference.

Best wishes,
Mason

One problem with all of these RoR calcs is that it assumes the games don't change. LHE games have gotten significantly worse in the U.S. in general over the past few years, which implies your winrate will decline over time.

I guess I'm curious where the infinite money to pay for our bills is to come from.
After a mortgage or rent payment, car/gas, health insurance, food, utilities and the money we set aside for taxes it adds up to be considerable monthly expenses.

Unless your talking about people who work full time and want to play poker on he side. In which case it's unlikely (although possible) that most people working a full time job have also managed to put in enough time/study to poker to make 1 bb/hour (it's not easy).

I'm talking, as I usually do, from a theoretical perspective. If you have other issues, my advice is to use your best judgment.

Best wishes,
Mason

mason,

thanks for your replies. it's definitely nice to see admins take something like this seriously; however, i think that you're a bit wayward in your responses and i'd like to clear up a few things:

1. you mentioned both that your br estimates/requirements are based off of a) theoretical math, and b) your personal experience (of your max drawdown being your br requirement). the issue with this is first off, on the face of it, it's highly unlikely your individual experience is a sufficient datapoint to align with the theoretical estimates of win rate and standard deviation.

1a. let's start with the theory. in theory you have a risk of ruin based on your own numbers that is insanely high. like ludicrously high. this could be because you are correct that players who play for a living on this site and who are taking issue with your estimates are incorrect in their assessment of their own play and the games they play it. it is also possible that you are incorrect in your assessment of your own (and others' own) play and/or the games you play in. i don't think that you can be as sure as you seem based off of the information that you've relayed to back up your discussion in this thread.

theory (simple path analysis) indicates that there are a nonzero number of paths at 40/80 w/ a solid 1bb/hr win rate and a stdev in even a tight range where you hit $0 or fewer starting with 40k. this is almost irrespective of game type and playing style assuming win rate is adequately ranged around 1bb/hr.

if you are ok with X% risk of ruin (let's assume not willing to drop down for the moment), then who is to say that other people are also ok with X% RoR?

moving from theory to reality for a moment, have you seriously never seen a solid 40/80 player win or lose 15k in 30-45 hours of play? i'm not god's gift to limit holdem by a LONNGGG shot and i've had a 15k winning weekend in the past 5 months. those who know me also know that while i'm not the best and most solid player around, i simply don't tilt and don't have many leaks that other better players have (i do probably make more mistakes than others, but we're talking fractional bet mistakes, nothing that would allow me to go off the deep end and cap 34s and hit A25 on the flop to make a 30bb pot).

instead during that weekend i had situations where, for example, i won a 35 bb pot and had to fade something like 12-14 cards 2x. that's nearly a 3 rack swing in one singular pot. i just hit everything i had for 35ish hours.

just with that data point alone, you should be able to extrapolate that limit holdem contains a great deal of variance that either a) you haven't seen, or b) you don't believe is possible from nontilting, winning players (i.e. if you have seen it you may have chalked it up to something that doesn't go against your philosophy here as humans with biases are wont to do). i'm just as likely to make this selection bias mistake in human data collection, but given the data i have backing up my claims, i think i'm more likely to be right here.

now, continuing w/ data you haven't seen:

1b. if you're comfortable sharing these data, i'd be curious to take a look:
- what is the total number of 40/80 hours you've played in the past 4-5 years?
- what is the largest drawdown that you've had in the past 4-5 years?
- what is the longest session you tend to play?
- what is the average session length you tend to play?
- what type of games do you typically play in? (let's use a rating system of 1 being equal to a game full of meh but tight and aware playing regs and one bad playing person vs. 10 which would be an off the chart game of 7-9 people to a flop always for 2+ bets)

i bet the answers to these questions will shine some light on the perspective that you're coming from.

finally, in terms of data, do you commiserate with other winning players at the 40/80 limit? again i'm not the end all and be all here and i can separate when i see people overstating their play (and i'm almost surely doing that, as are you even to some small degree), but i can identify when people are likely going through a big drawdown due to tilt or simply getting massacred by the deck. and i've seen the latter very clearly happen to the tune of numbers larger than you're saying are possible within your bankroll structuring discussion. of course in that case there is some poor play, overstating play, etc. but what %? 20% maybe? even so that still leads to numbers beyond what you seem to be willing to accept are possible.

2. you also bring up a clear and good point that this bankroll is one that is flexible in terms of limits. yes if you're willing to drop down then you can have less cash on hand.

3. you are also not talking about drawing any money out of the bankroll, which i also agree with. any expenses should be handled outside of this "cash for the games" bankroll.

so yes, usually you are talking from a theoretical perspective, but here it seems that your discussion hinged on your own observations (reality) along with missing quite a bit in terms of how bad a drawdown can be even if you are a solid, winning, non-tilting player.

i was looking for the graphing site where you can plot 50,000 samples of a few k hours of play to demonstrate just how many of those 50k lines are below the $0 after thousands of hours of play but i couldn't find it (maybe somebody could point it out since i seem to be sucking at google).

anyways, i normally don't post all this detail and drone on like this but you've interjected a controversial (imo) opinion about something that is extremely important to a potentially new limit player.

so my final point would be as the author of the fine books that helped me acquire the skills i have, and as an admin/supermod of your site that has also helped me tremendously, wouldn't it be in your best interest to be as conservative as possible when it comes to discussions of bankroll management theory and practice? just as my own take, it seems to me (my perspective) you are coming off quite cavalier about the swings that can happen in LHE.

thanks again for engaging and may the flop be with you!

not sure if this is what you're looking for, but here's a variance calculator.

if a bankroll was used only for playing poker and not used for life expenses because those were taken care of from another source and you were an expert that doesn't tilt and only plays longer than 8 hours when the game is really good, i think you could get away with 300BB.

Hi Mason , a few questions:

What value for standard deviation are you using for this calculation? What did you use to determine this standard deviation? Have you compared it to online databases?

In my experience playing SoCal 20/40 for several years full time, it's not unlikely to go on a 9k downswing in under 2 years. Not only I have my own data point but a few from winners in the game who play many hours.

As another data point. I had $3000 sessions when I used to play long hours of 8-16 full kill in super action games.

Something doesn't add up, my guess is the standard deviation you are using, or the RoR you are defining as "ok" for a full time professional with normal living expenses.

mason seems to be using his personal experience as his only data point. a couple things should be pointed out about that.

1. the majority of mason's hours are played in a 20/40 that until may of this year was a time game that was $5/half hour. that's only $10/hr of rake. if you're playing in southern california (or anywhere else in the country for that matter), you're easily paying double that amount in rake. lower rake reduces mason's variance.

2. mason, imo, is a nit. he plays fewer hands pre flop than you and i do. this lowers his variance.

3. i've never seen mason play 40/80. i'm not a regular at bellagio, but my guess is that mason rarely if ever plays in the 40 there.

my biggest downswing live is 175BB and online is 450BB.

I'm still curious about how/why Mason thinks $14k can be considered a 40/80 bankroll. I think it's so off that feels like a "social experiment" type of comment.

Losing 4-6 racks in one session is a common occurrence for a ful time player. That's close to half of this "good enough" bankroll (the 25% RoR Jon refers to)

I've played near full time hours this year at 20-40. I've had 2 biggish downswing (180BB and 230BB) and is at 0.8BB/h rate. The Variance is just VERY high. Granted, I'm not super solid and still learning, but it is very hard to imagine a $14k bankroll being sufficient for 40-80 even for an expert. I've talked to multiple pros who has been playing for a living for years and the general consensus is if you play more than 1500 hours it is almost expected that a downswing > 200BB will occur during the year. Not experiencing it is 'running good'.

Hi Chasqui:

First off, I use

BR = [(9)(Var)]/[(4)(WR)]

for the bankroll formula. This formula was first given in my book Poker Essays, published in 1991, but is actually derived from my book Gambling Theory and Other Topics which was first published in 1987. Note that Var is the variance which is the standard deviation squared and WR is the estimated win rate. Also, how to estimate your standard deviation, using the maximum likelihood estimator is given in the Gambling Theory book.

As for my numbers, I'm using 1 big bet per hour (which I think is doable at $20-$40 but too high for most $40-$80 games and 9 big bets for the hourly standard deviation. This gives a required bankroll of 182 big bets. Then this should be increased a little to account for things like you don't have the exact same win rate and standard deviation every time you play. (This is equivalent from a statistical point of view of reducing the sample size by a little bit.) Thus 200 big bets (or perhaps a little more) should be enough for a safe bankroll using this criterion.

Notice your $9,000 downswing is 225 big bets so you're not far off my numbers.

A couple of quick points. Two errors I see from many of today's players is that they open too loosely from early position and three bet too loosely. This will add plays that lower your expectation a little but will increase your standard deviation by a lot. Lowering your expectation will increase your required bankroll (in this case a little) and increasing your standard deviation will increase your required bankroll (in this case a lot).

Also, as a aside, it seems like I'm reading many posts like yours recently where the poster seems to be unaware of the formula above and where it comes from and how it's derived. All of this has been around for many years.

Best wishes,
Mason

Bingo. Thanks. Mason, play around w this for a bit and you'll see what I'm talking about re theory. Much of what you say is absolutely correct especially about people's self inter personal assessments. But a tiny bankroll just isn't sufficient for even the best non tilting winning player.

Rodeo, is agree w what you're saying there and would add that you should also be willing to drop to 20 if you lost half ish of that 300bb roll. That would be a very doable number.

9bb/ hr is way low on the variance side imo. That pretty much sums up where the disagreement lies.

Mason, I use 14 BB/hour which I think is pretty standard for full ring, if anything it could be higher given all the times you will be playing closer to 6 max.

You are 50-75x more likely to bust your roll with a 14 Bb standard deviation than 9

Most people I know who diligently keep track of their stats have/use 11-13BB for full ring standard deviation.

In addition to this, in SoCal the $21/hr rake eats up .25BB/hr from your winrate compared to $10 rake in Vegas for the $20/40.

These two elements combined explain what appears to be a factor of 3-4x between what we consider a proper bankroll.

Hi Jon:

I'm actually a little under 9 big bets an hour and while not the same subject, if you're at 14 my guess is that your hand reading ability can still improve as you keep playing.

But if 14 is your sd, then your numbers are right.

Best wishes,
Mason