That incredibly silly subject...

[AleoMagus]

Yes, money management...

In my little hiatus from the poker world, I have been giving some thought to this subject and I though I'd post a few of my opinions.

I see a great deal of posts on this forum about sng bankroll requirements. Some of you say as few as 10 buy ins is sufficient, some of you say 30 or more. In the past I myself have stated responses similar to this.

More and more though, I just think it doesn't make much sense answering. The reason I say this is becasue probably 99.9% of all who are asking what they need have jobs. Those who are asking and don't have jobs should probably not be playing poker because if they don't know the answer they aren't gonna survive off of poker for long. If you have a job, who cares how many buy-ins you have?

In fact, even if you don't have a job, who really cares? I know of many succesful gamblers who notoriously 'overbet' their bankroll. They get broke along the way sometimes but many are still sucessful in the long run.

The point is - If you are a winner, and getting your money in with the best of it - you will win in the long run anyways. If you get broke along the way a few times, that's your preference. Some can deal with that, some can't. Some will be psychologically affected by getting broke, but some won't be fazed at all.

On the flip side - If you are a loser, you should maybe not be playing in the first place. If you are a loser trying to improve, bankroll requirements really only dictate how many tourneys you can play in (to get better before you go broke).

So, If you have a job and can reload with every paycheck (for a while until you finally get a return anyways) then who cares how many buy-ins you have. If you feel like playing $200 sngs then play $200 sngs. If you can only afford one every two weeks then so be it. If you lose, you will be playing no poker for two weeks. If you are a winning player though, you will not lose forever.

I believe that Ken Uston had this approach to Blackjack. He was (arguably) one of the very best counters ever but he claims he almost always bet with high risk of ruin compared to what many experts recommended. He was comfortable with this level of risk and ultimately he knew he would come out ahead.

I think if you have a job, and you are a winner then all you neeed is enough to keep you in the game till the next paycheck. For some that might mean 5 buy-ins. For some, it might be as high as 30.

Lets face it, no bankroll will keep you in the game forever anyways. There will always be a risk of ruin. How high this risk of ruin is is a personal preference. I believe that a player who is a winner and who makes the money ~50% of the time needs only about 11 Buy-ins to have a 5% risk of ruin in the long run. That may be wrong but I know I read it sometime on this site (take that for what it is worth)

Yes, I suppose going broke might mean that you miss future betting opportunities until you get back in the game. That can definitely have a cost, but so can playing below your level. Now, I realize that is a dangerous thing to say here because most bad players make the opposite mistake and don't need encouragement to move up in stakes. Still, I suspect many a veteran grinder wishes that they had taken more chances along the way.

I also suspect that many a world champion decided 'Hey, I don't have the money to play this game, but damn it... I can beat these guys'.

Truth be told, I think the best idea is somewhere in between (for me anyways). I think a good bankroll is a good idea, but I also think that the occasional big jump in limits can only improve your game and will ultimately reap great rewards. I once suggested a plan where a player allows themself a big tourney at certain bankroll growth points. I still think this is a good idea. The bankroll may still be insufficient to play that higher level on a sustained basis (with low risk of ruin anyways) but that lone tourney (or ring game) will still utimately return it's positive expectation if there is one. You will still stay afloat because you will only be playing that tourney as an occasional change from a regular schedule of smaller buy-ins and you will still make money because eventually, if you are good enough to beat the bigger game, you will.

If psychological factors are a big deal to your play, then maybe bankroll is very important, but if your game is very solid no matter what you bankroll looks like then it might not matter as much. I know nobody is immune to getting rattled but some are better than others, and some can play even better when it is their last 100 dollars on the line.

Any Thoughts?
Brad S

[Guy McSucker]

Hey AleoMagus,

I think part of what you're saying is something quite similar to a point made by (at least) Caro, Ciaffone and I think Malmuth: a small bankroll requires less protection than a large one.

Anyone playing $50 sit'n'gos and below should, I hope, be able to replace a 20 buyin bankroll relatively easily, even if it all disappears in a bad run. At any rate, you should be able to replace half of it: enough to get you playing again. As the stakes go up, it becomes less and less likely that you will readily replace your playing capital if you lose it, so it makes sense to take bankroll requirements and risk of ruin very seriously.

Most high stakes poker players do not take the risks seriously enough, I think, hence the maxim that all pros go broke at least once. I simply fail to see how a "professional" can live with the idea of earning nothing for months on end and having no job at the end of it, which is what happens if you go broke; so I think these guys should take risk of ruin more seriously than they do.

Guy.

[DrPhysic]

AleoMagus & Guy,

There is a story from golf. Lee Trevino was asked by a reporter during a major tournament, "How do you deal with the pressure?"

Trevino answered "Heck, this is no pressure. Pressure is playing $100 Nassau at the country club on Saturday morning with 3 guys you don't know, and $10 in your pocket."

I think all great gamblers have some similar story. And some run risk of ruin more often than others. Or maybe the great gamblers are just the ones that learned to win much more often than they lost.

The thought that floats through is that size of bankroll vs buyin is far more important to those of us who will never play at that level, because we do worry about risk of ruin.

Doc

[AleoMagus]

[ QUOTE ]
Lets face it, no bankroll will keep you in the game forever anyways. There will always be a risk of ruin. How high this risk of ruin is is a personal preference. I believe that a player who is a winner and who makes the money ~50% of the time needs only about 11 Buy-ins to have a 5% risk of ruin in the long run. That may be wrong but I know I read it sometime on this site (take that for what it is worth)

[/ QUOTE ]

I am pretty unsatisfied with that statement, so while I am on this subject, I'd be interested in the actual math here.

Suppose I had a ROI of around 35% in single table tourneys with SD about equal to 2nd place profits. (Note: 2nd place profits means nothing special here, I just find that it correlates pretty well to my SD at almost every level I play). More concretely put, suppose at 10+1 I make about $4/tourney and have a standard deviation of $19. I think this is a good general assumption for most winning sng players to go from.

How do I determine my Risk Of Ruin compared to starting bankroll

How much do I need for a 5% ROR?
How much do I need for a 25% ROR?
ETC...

Any comments here would be greatly appreciated

Brad S

[Guy McSucker]

I will probably mess this right up, never having studied statistics, but here goes anyway. For anyone that wants a laugh: I have a PhD in mathematics.

I believe that for a 95% confidence in statistical findings, you look within 2 standard deviations. Perhaps this only applies to normal distributions, and perhaps poker doesn't have one of those. Anyway.

If this is right, the formula for your worst expected result after n tournaments would be

n times (average win) - (standard dev) times sqrt(n) times 2

We want to find n such that this is minimum. Differentiating w.r.t. n gives:

average win - (standard dev)/(sqrt n)

This is zero when

n = (std dev/avg win) ^ 2.

which in your case is about 25.

Plugging n = 25 into the formula for worst result gives

25 times 4 - 2 times 5 times 19

which is -90.

This would mean that 8 buyins at the $10 level would give you your 5% risk of ruin.

I've done all this in my head and rounded the numbers pretty much at random, so the actual numbers may be way off; and the formulae might be bunk too.

For "almost no" risk of ruin, rework the math with three standard deviations instead of two.

Not sure how to do 25%. Some other number of standard deviations to give a 75% confidence level I suppose.

Guy.

[PrayingMantis]

Just to make it clear for me.

[ QUOTE ]
This would mean that 8 buyins at the $10 level would give you your 5% risk of ruin.

[/ QUOTE ]

In other words, if you take 100 players with avarage win of 4$ net at the 11$ SNG, and give them each a bankroll of 88$, 5 of them will bust at one point, but 95 will continue to make $$ as long as they live (if they don't cash-out?)

I think that one problem with risk-of-ruin calculations, is that *in reality* players take some of their winnings out, yes, to use the money for buying stuff and enjoy. that would make ROR calculations much more complicated, because other variables are getting into it. Tho I'm not sure which and how.

Am I making sense, Guy?

PrayingMantis

[Bozeman]

Since I was called on by name, I guess I have to respond to this thread.

I will respond in reverse chronological order.

Warning: math ahead

PM: "In other words, if you take 100 players with avarage win of 4$ net at the 11$ SNG, and give them each a bankroll of 88$, 5 of them will bust at one point, but 95 will continue to make $$ as long as they live (if they don't cash-out?)"

Yes. Except for corrections in his formula, detailed below.

The cashing out correction can be dealt with very simply: when your bankroll changes (because of a win, a loss or a cashout), your risk of ruin, from that point, changes. So, if you cash out any excess whenever bankroll is larger than B(r), you will have r probability of going broke after each cashout. Those times your BR falls below B(r) your risk of ruin, calculated at that time, will be larger.

While 1% risk of ruin doesn't sound like much, it can be significant over many opportunities for ruin, since if you play with this RoR always (never less), your risk of going broke sometime will increase linearly (~1%*NumberofSNG's/25). Playing 400 SNG's like this is more dangerous than playing with a bankroll 2/5 as big that you never touch.

Guy:
Your estimate is essentially the same one used by Mason in GTAOT. The problem is that it somewhat underestimates the RoR since it misses all the times where you go broke in < n = (std dev/avg win) ^ 2 trials but end up with finite money at n, as well as those times where you go broke after > n SnG's. Your approach yields BR=f(r)*SD^2/EV, where r is RoR, SD is one tourney standard deviation in $/sqrt(SnG), and EV is per tourney expectation (in $/SnG). The f(r) you get is Z(r)-1, where Z is the critical value: number of SD's away from the mean of a normal distribution for which a fraction r of the area is to the left, and 1-r to the right. Z(1%)=2.33, Z(5%)=1.64.

You made one mistake here, because you used the two sided Z instead of one sided. Obviously, you won't go broke if you run +2SD well. (You calculated the Z=2 result, which is 2.3% RoR, instead of the Z=1.64.)

A better result was derived by Patrick Sileo ( Risk and BR), which gives f(r)=-ln(r)/2 (for a total BR formula of B=-SD^2/(2*EV)*ln(r)). Not only is it a better estimate, but ln(r) is easier to calculate than Z(r). This gives BR numbers ~1.5-2.5 times as big, with the largest corrections coming for the largest RoR's. For 5% RoR, -ln(r)/2= 1.5, giving a 50% larger BR than Guy's erroneous estimate (the errors patially cancel).

This answer relies on the normal distribution, so there will be small errors since SnG results will vary somewhat from a normal distribution over the relatively short number required to break you with the relatively small SD of SnG's. So this eq. is better for ring games than SnG's, but errors are still probably small. One could correct for exact SnG results (%1st,2nd,3rd), but it doesn't look like it is worth the trouble.

As for your estimates, they are not too bad. Over my last 425 SnG's, I would have gone broke in one 25 SnG set if I started each with 8xBuyin:



1/17= 6%. However, I suspect that my game was suffering over some of the down times, and I know my table selection was. Just wanted to prove we are not off by orders of magnitude.

Aleo:
I think your SD and EV numbers are pretty good. At the $109 level, my SD is about $180 (2nd net - $11) since I am unfortunately not getting more 1st's than 2nd's (my EV is slightly less too).

For your #'s, B(5%)= $135, B(1%)=$208, B(25%)=$63.

For your general argument, as long as reloading to your bankroll is easy, physical bankroll requirements are not very meaningful. Psychological BR is probably more important. However, as you get to larger stakes, bankroll becomes less replaceable, so you should protect it more.

After spending almost all my bankroll on travel and expenses, I had less than $500 left. I figured there was some chance I'd go broke at $55 SnG's, but it was only a one time risk, since I was going to build my bankroll without touching it until it was much more comfortable. This worked out for me, but I probably wouldn't have done it if I didn't have any possible other sources to borrow replacement money from. In addition, the possibility, undesireable that it is, of dropping in limits will greatly reduce risk of ruin.

Craig

[DrPhysic]

Could you repeat that in English? Anybody have any Physics problems? Always stats, huh?

Excellent analysis Craig. Helpful to those of us who are relearning stats 40 years later, also.

Doc

[Al_Capone_Junior]

Bottom line...

and i say this as if my opinion were PURE FACT...

10 is NOT enough

30 is "probably" enough if you play well, and have not just deluded yourself into thinking you play well

Other than that, I like your post. Good observations.

Personally, I tend to push the envelope of the proverbial "300 big bets" a bit. I tend to play more on the lines of 150 big bets total bankroll, but not 100% of the time, and I back off pretty quick if I have a losing session of 25 big bets (at the 300 BB bankroll size) or more. I am NEVER willing to lose my entire bankroll, but I do tend to push the envelope a bit. Say I am playing with a $3,000 bankroll, well I will play 10-20, but won't lose more than $500 before I back off and drop down to 5-10. My bankroll has not broke the $12,000 mark yet, thus I have only played 20-40 a couple times, and each time I was extremely cautious, my greatest loss only being $400 at that level. My current bankroll allows me to play up to 10-20 under the conditions I have outlined. Thus the hazards of living off your poker earnings.

Caution is in order, but as I have always said...

"when in doubt, throw caution to the wind."

al

[eastbay]

[ QUOTE ]

Most high stakes poker players do not take the risks seriously enough, I think, hence the maxim that all pros go broke at least once. I simply fail to see how a "professional" can live with the idea of earning nothing for months on end and having no job at the end of it, which is what happens if you go broke; so I think these guys should take risk of ruin more seriously than they do.

Guy.


[/ QUOTE ]

From what I've read about the current state of pro poker, it's not exactly populated by the most responsible people.

See, for example:
http://www.pokerpages.com/articles/archives/dalla27.htm