Great video Pygmy.

One minor note. You didn't explicitly mention this, though it's implicit in the professional bankroll requirement, is that the risk of being a losing player bankroll-wise increases significantly once you start to take out living expenses. (It's implicit in that it's in the equation for pro bankroll. So it's not like you ignore it, but just that I think it's worth mentioning explicitly.) If one constantly withdraws near the amount of historic winrate, it's pretty much certain that you're going to go broke, or at least have to go down in limits. Which might not be an option if you're a professional. After moving down, you're expectation decreases and you need to build up your bankroll in order to move back up.

By the way, The Mathematics of Poker has good discussion on sort of advanced concepts of bankroll management and risk of ruin if anyone wants to know more.

holy crap. awesome vid PH! Thanks

Equations

The format I'll use is as follows:
Description of the cell data (cell location)
Explanation of equation in words
The exact syntax that needs to be entered into Excel in quotes

The cell references will assume you've followed the form I've laid out and will make all entries into column B (since column A has the headings). If you formatted the data differently (like a horizontal layout) you'll need to adjust accordingly.

Uncertainty in big bets per one hundred hands (cell B5)
Standard deviation in big bets per one hundred hands divided by the square root of the number of hands divided by one hundred
"=B4/SQRT(B2/100)"

68% Confidence Interval Lower Bound (cell B6)
Win rate minus uncertainty in big bets per one hundred hands
"=B3-B5"

68% Confidence Interval Upper Bound (cell B7)
Win rate plus uncertainty in big bets per one hundred hands
"=B3+B5"

95% Confidence Interval Lower Bound (cell B8)
Win rate minus two times the uncertainty in big bets per one hundred hands
"=B3-2*B5"

95% Confidence Interval Upper Bound (cell B9)
Win rate plus two times the uncertainty in big bets per one hundred hands
"=B3+2*B5"

99% Confidence Interval Lower Bound (cell B10)
Win rate minus three times the uncertainty in big bets per one hundred hands
"=B3-3*B5"

99% Confidence Interval Upper Bound (cell B11)
Win rate plus three times the uncertainty in big bets per one hundred hands
"=B3+3*B5"

Recreational Bankroll (cell B14)
Negative natural log of risk of ruin times the standard deviation in big bets per one hundred hands squared divided by two times the win rate in big bets per one hundred hands times the big bet
"=-LN(B13)*B4^2/(2*B3)*B12"
N.B. The negative sign at the beginning of the equation. You can make the carrot by pressing SHIFT+6.

Total Budget (on the Budget tab, cell B13)
Sum of all expenses
"=SUM(B2:B12)"

Monthly Nut (cell B15)
All expenses in a month for the professional player
"=Budget!B13"

Professional Bankroll (cell B17)
This one really doesn't make any sense in words, especially because you need to have parentheses in the correct locations to ensure that order of operations is carried out as you want it, but this is about it: negative natural log of risk of ruin times the standard deviation in big bets per one hundred hands squared divided by two times the win rate in big bets per one hundred hands minus the monthly nut divided by the big bet divided by the number of hands per month divided by one hundred times the big bet
"=-LN(B13)*B4^2/(2*(B3-B15/B12/(B16/100)))*B12"

Living Reserve (cell B18)
Monthly nut times six
"=B15*6"

Starting Pro Bankroll (cell B19)
Required professional bankroll amount plus a six month living reserve
"=B17+B18"

For the Live Player

Note that I changed much of the cell formatting. Almost everything on this tab is formatted to be currency with two decimal places showing. Also note that the Big Bet row is removed, meaning the cell reference locations are slightly different at the bottom of the sheet. Most of the formulas are the same, except for as follows:

Uncertainty in dollars per hour (cell B5)
Standard deviation in dollars per hour divided by the square root of the number of hours
"=B4/SQRT(B2)"

Recreational Bankroll (cell B13)
Negative natural log of risk of ruin times the standard deviation in dollars per hour squared divided by two times the win rate in dollars per hour
"=-LN(B12)*B4^2/(2*B3)"
N.B. the slightly different cell locations.

Professional Bankroll (cell B16)
This one makes a little more sense in words, but not much. Also you still really need to watch that your parentheses are correct. It is: negative natural log of risk of ruin times the standard deviation in dollars per hour squared divided by two times the win rate in dollars per hour minus the monthly nut divided by the number of hours per month
"=-LN(B12)*B4^2/(2*(B3-B14/B15))"
N.B. again, slightly different cell locations.

That was a lot to type up, so if anyone spots an error in any of the equations please let me know.

does multitabling really change anything ?
that should be covered by a lower winrate or am i wrong ?

SD for LHE is as you say appr 17.5 or so.. For NLHE its prob about 50.. Dont you have to take this into consideration?

And another thing..If you belive you are a 3BB/100 winning player at 100nl, playing 25000 hands a month with a SD of 50, and you have 1000$ a month for expences then you need a 7500$ bankroll for 100nl?Is that because you always wanna increase your bankroll while playing?

Hmmm,

No edit function here...

FYI, the "Game" cell is B2

Sugar Nut

And another thing..If you belive you are a 3BB/100 winning player at 100nl, playing 25000 hands a month with a SD of 50, and you have 1000$ a month for expences then you need a 7500$ bankroll for 100nl?Is that because you always wanna increase your bankroll while playing?

The bankroll doesn't have any resiliency for swings if you take most of your winnings out. Another thing is that if you estimate having 3BB/100 winrate and in actuality you have a 2BB/100 winrate and if you cash-out 2BB/100 monthly, then your bankroll doesn't have resiliency for swings at all and you will eventually deplete your whole bankroll (unless you move down in limits etc).

Hey Sugar Nut, your formula looks correct and I got the same result using your data. I'm not really sure why this is yet. I'm going to try breaking the equation down a little bit. I really hope I didn't make a syntactical error in this video as that'd be pretty bad.

I'd guess it's the fact that he's taking more out of his bankroll than his monthly expecation and this does some funny stuff to the equation.

SD for LHE is as you say appr 17.5 or so.. For NLHE its prob about 50.. Dont you have to take this into consideration?

The spreadsheet does take this into account. Just fill in your std dev in BB/100 for the corresponding cell and you're good to go.

Or did I misunderstand your question?

Okay Sugar Nut, I think I've solved the problem here. The part of the formula (from your spreadsheet, NOT mine) I want to look at is:

"C4-C16/C13/(C17/100)"

In words this is your win rate minus the nut divided by the big bet (big blind*2 since you play NL) divided by hands per month divided by 100.

The problem is that nut/big bet/hands/100 = 6.25, which is a larger number than your win rate of 4.7. That negative number propagates through the rest of the formula, which is why you have a negative result for bankroll requirement. This of course doesn't mean you need no money to play that game professionally, it rather means you CANNOT play that game professionally given the stakes, your win rate, and the monthly nut you input.

For the Excel geek who really wants to solve this problem I would recommend re-writing the bankroll formula to include an IF statement. Going back to my sheets format, cell B17 might read something like:

"=IF(B15/B12/(B16/100)>B3,"lol not a pro",-LN(B13)*B4^2/(2*(B3-B15/B12/(B16/100)))*B12)"

Edited to add: so jajvirta is right again. And faster than me. :) Your win rate just isn't high enough to support that monthly nut (if you were a pro that is).

The spreadsheet does take this into account. Just fill in your std dev in BB/100 for the corresponding cell and you're good to go.

Or did I misunderstand your question?

jajvirta - I think he's saying I didn't recommend an appropriate SD for a NL player and we both recognize it'll be different then the 17-18 I recommended for the LHE player.

I get the bankroll for NL is correct, but is 350 enough for 100L?

Awesome vid tyvm for sharing this.

Looking foward to some clarification for NLHE if there needs to be any.

"...324$ for L..."
"...is 350 enough for 100L?"

NL = No Limit
L = Limit ;)

THats pretty obv though durka beacause your nut will often be closer to your actual earnings pr. month..
How many hands did you type in as an expected hands/month?

Holdem manager doesn´t show Standard deviation, what is a good approximate for me playing 2-4$ with the stats 23/20/3,7 and mostly at 5-max. Hard to tell maybe but give me something.

Hard to tell if you don't specify the game you're playing. But I guess one can assume from the stats that it's NL so I'd say something in the order of 50BB per 100 standard deviation.

Sugar Nut - does everything make sense now? I didn't hear back from you. Sorry if I offended you - I wasn't trying to make fun of the fact that you're not a pro. I'm not either and at the stakes you play I'm sure you make more than I do in a month. I was just having some fun - sorry if it came out the wrong way.

Jake123 - If you're playing limit I would suggest you use 17-18 BB/100. If you're playing NL I would suggest 50 BB/100 unless you get better advice from a NL player. I don't use HEM but I'm surprised that it doesn't show SD. If you searched pretty thoroughly and couldn't find it I'd suggest you write HEM support as they definitely should show it and I understand that the HEM team is very good about responding to these sorts of things and updating their product.

Really intresting video i was wondering what stats i would need to make an sng 1 any ideas?

Number of hands would be Number of tourneys
Win rate would be ROI
SD in BB/100???
Uncertanity in BB/100???

pkr_brat, I just wanted to let you know that I'm working on this and that I did see your post and am not ignoring it. I'm not a tournament player so I'm not very familiar with the stuff that goes into it. I'm going to do some research and see if I can get you some answers.

THats pretty obv though durka beacause your nut will often be closer to your actual earnings pr. month..
How many hands did you type in as an expected hands/month?

I know it's obvious, but it's not clear (without doing the numbers) how it affects BR calculations.

I put in 50k hands, which is reasonable.

No offence taken pygmy, I'm just going through some tough real life times right now and am not online every day.

Seems to make sense, thank you.

I do unserstand and love humour, don't worry about that pygmy,

Sugar Nut

Assuming 5ptbb/100 WR, you'd have to play 25k hands to make your nut and you'd have absurd swings because your effective WR is zero. So, in order to have any chance to beat the variance fairy, you'd have to be putting in a minimum of 40k hands/month, IMO at 100NL with a 2500 nut and a WR between 4-5.

Also, it seems unclear that for the spreadsheet, those values are PTBB/100 right?

I do not take rakeback and bonuses into account in this spreadsheet. That's because they don't matter in terms of determining whether or not you are a winning player (i.e. I would consider a break even or small loser who makes money on rakeback and bonuses to be a 'profitable' player, but not a winner). They also then don't matter in terms of figuring out if you're beating a limit and should move up (assuming you use the metric I proposed - that you be 99% certain you are winning at your current limit).

I don't agree with this at all. I find it a bit arbitrary to draw the line on the rake-reduced and rakeback-added winrates. The ultimate goal is to make money and it really doesn't matter whether it's from "pure" win or rakeback. Rakeback just means that the effective rake isn't exactly what is announced on the site's rake structure. Different sites have different rake + rakeback systems and for the player, the only thing that really matters is the net result.

To give more concrete example let's think of a player A playing FL 2/4 on Ongame network and player B playing the same game on PokerStars. Both have the same raw winrate of say 4.5BB/100. Player A has a 50% rakeback deal, but what'll show up on Poker Tracker is 0.5BB/100 winrate (if it has converged), because Ongame takes roughly 4BB/100 rake. Player B, however, has 2.5BB/100 winrate on Poker Tracker as PokerStars take roughly 2BB/100 rake. So they both have a net winrate of 2.5BB/100.

So they have the same raw result, they net the same result (other one partly through rakeback), but what shows up without rakeback is radically different number. I don't see this should make any difference for determing whether one's "winner" or whether one can move up in limits.

I have mixed thoughts on how to factor in RB. I think it DOES matter in your example because the person w/ RB isn't beating the game very well without it.

But, really, what's the difference? Both are playing the same game, effective 2BB/100 rake with the same absolute and net winrate.

So, it would be a bad idea for him to move up vs the non-RB player since it seems unclear whether he can actually beat the game.

If you define "beating the game" as beating the gross rake, then this makes some sense, but it doesn't make any sense to make such a definition. :-)

PS. Maybe this discussion should be moved to its own thread or something. I'm not sure if this is relevant to the discussion about the video anymore.

I think this conversation is definitely still relevant to the thread. As I mentioned in the video a few times, people should be aware that I'm just presenting one way of looking at win rate, moving up, etc. There are different perspectives and I'm always glad that jajvirta presents his.

I will say that I disagree on this point though - I think rakeback and bonuses should be excluded when we talk about someone beating the game. I realize the semantics are starting to be a problem here, so I mean, 'beating the game' to mean the same thing as when I said, 'a winning player' in my previous post. That is, someone with a 0.0 BB/100 win rate (w/o rb and bonuses) is NOT a winning player. I think you're talking about whether or not a person is 'a profitable player.'

I think this is an important distinction because players with a lower win rate will have larger swings. Your hypothetical 0.5 BB/100 winner who makes an extra 2 BB/100 in rakeback and bonuses will have larger swings then the 2.5 BB/100 winner.

Let's say both players get exactly the same card, situations, and opponents and that they run cold for a while. At first I'd expect them to both dip below their normal win rate by about the same amount. But note that the rakeback player is now losing at the tables, while the winner is still in the black. I think the rakeback player is much more likely to exacerbate the bad run and end up losing more than the other player.

Also, is it really run to just grind a bunch of hands in order to break even? I know people do it, but I guess I just don't really understand why.

Heh, I see that this discussion isn't going anywhere anymore, and I'm fine with that, but I just wanted to say that I guess it boils down to me thinking that the "rakeback winner" isn't grinding in order to break even. But I'll leave it at that and hope that both viewpoints have been presented here somewhat objectively. I guess both views have their merits.

Well, the people I'm referring to play 10 tables 12hrs/day and are MAYBE 1-2ptbb/100 winners, but since they get 1.5ptbb/100 in rb and basically play 10k hands/day, they're making good $$. But, BORING!

ShLiM, it's no bother. And this will be easy to fix. When I said enter the big blind*2 in cell B12, I didn't literally mean, enter "big blind*2" in the cell. Rather, I meant enter the value, depending on the limit you are playing.

For 50NL enter 1 ($0.50 big blind * 2 = $1).
For 100NL enter 2 ($1 big blind * 2 = $2).

And so on...

You won't need to enter an equal sign, the dollar sign, or anything else fancy. Just "1" (or "2" or whatever the case may be - leave off the quotes too).

Let me know if you need any other help.

pkr_brat, I just wanted to let you know that I'm working on this and that I did see your post and am not ignoring it. I'm not a tournament player so I'm not very familiar with the stuff that goes into it. I'm going to do some research and see if I can get you some answers.

Thanks for trying