The Truth about the dangers of playing under rolled.

This article aims to express just why, in a theoretical sense, you can't play poker under rolled. It's for people at all levels of the game who don't know/havn't read this stuff, and I really hope to be explicit. There are also points that even some of the more experienced posters may not have been aware of.

In the article I state some of the foundations of decision theory but have tried to make it as none mathematical as possible. You will need to know what $EV is and how to work it out but thats it.

A game of decisions

I have said this before but now I really must be explicit. Poker is a game of decisions. Totally obvious to some, perhaps not to others. Every time it is our turn to act we must make a decision: fold, call, raise, how much to raise, and so on. How do we make our decisions?

Based on our cards, reads (of player and situation) and the betting patterns of other players we work out a rough probability for us winning the hand (or improving to win the hand) for each decision we could make. Then we look at the $$ we win if we do win the hand given we made a certain decision, and multiply it by that probability to find our expected value of that decision. We choose what to do based on the decision with the highest expected value.

The above sums up basic decision theory. Sure we might not get our probabilities exact (or even remotely correct), but we make our best judgements and choose the corresponding correct decision. I call it the correct decision because that is exactly what it is. There can be no ambiguity once you have your probabilities estimated and the possible outcomes defined, there can be only one correct decision. (we ignore the possibility of indifference between two decisions with the same expected value as choosing one of these and no other is still "correct").

So as poker players the skill is all about reading the game correctly to get as close to those probabilities as we can. Sure I don't mean we sit at the table and work them out in our head, but we do an equivalent personal judgement that probably doesnt include the figures.

So that's poker, a game of decisions. Easy no? Well not quite. The theory is not quite correct.

Utility over preferences

Ask yourself this: If i offered you a gamble where I toss a coin and give you $100 if it lands heads, would you pay me $40 to play?. My answer to this is of course yes. What about $400 for $1000? My answer is no because I can't afford to lose $400. What about $4000 for $10000? But the decision theory says a clear yes in each case!!

This is because absolute value of money is not the only thing we lose. Money buys things, changes life styles, makes sure you have somewhere to eat/sleep, pays for education and buys you into the next game. We have to have enough to do all those things. We don't want our quality of life to diminish as a consequence of a decision.

And so we come to utility. Utility is a measure of how much you like a consequence. So your utility for winning lots of money is high and your utility for losing everything is low. the lowest. Now, and here's the rub, everyones utility is different. Ask Phil Ivey what his utility is for $1000 (the big blind in some of his games) and it will be different to mine (half my bankroll). That much seems obvious.

So how do we estimate our utilities for consequences of poker decisions?

Well almost certainly you can't unless you're a very experienced statistician or working with one. So how can we make good poker decisions? The only way to be able to make coherent poker decisions (for most mortals) is to make sure your utility for the different consequences of the game is are the same as the value of the money you stand to win and lose. I.e. you are indifferent between gaining $x for certain or winning $2x with probability 1/2. Whatever x is.

Now there is always such an x for all of us. If you have $200 in your wallet and I offer you such a gamble for $1 you would'nt mind taking it (unless you needed the whole $200 for something specific). The other universally true thing, is that x is always much less than all of the money we have.

So let me say it clearly: In order to make poker decisions via maximised $EV YOU must be indifferent over gambles with the same $EV.

The Danger of Playing Under rolled

I said YOU in that last sentence because preferrences are always personal, they are different for everyone. Maximising $EV is what all the books and what people on this forum always advocate for making the best decision. But they are wrong. You have to maximise your expected utility and make the decision best for you!

Now this brings me neatly to the Danger of playing under rolled. If under rolled, the money you are betting and making decisions with means something to you. You would rather keep $x that take a 50/50 shot at $2x, for some amount x that you're actually gambling with. Which means that your utility for the money you are playing with is not the same as it's absolute value. Which means that many decisions that maximise $EV don't maximise expected utility for you. That makes them wrong!

So the danger of playing under rolled is that many of the decisions you will make at the table and that book writers and players on this forum would advise you to make WILL BE WRONG. And they'll be wrong for you only.

Consequences

"So my decisions are wrong. Big Deal! what does that mean?"

It means you're losing. You're giving away what you don't really want to give. If you continue to make the wrong decisions for yourself, you are not getting what you want. The rewards don't outweigh the risk and eventually, unless you stop, you'll go broke. Why take gambles you expect to lose? Utility is a measure of your personal preference and choosing things you prefer less over things you really want is absolutely ridiculous as I'm sure you'll agree.

If you do wish to play under rolled, you must understand that the correct decision for any situation you face will often be different from the correct EV decision, and that decision is TOTALLY PERSONAL. How can people on this site advise you without knowing how your preferences are scaled? The problem is that you won't know really either, so unless you guess right, you'll make bad decisions.

What is a proper bank roll then?

A proper bank roll allows you to play at the stakes you wish to play so that your utility for any amount bet in that game is precisiely the $$ value of that bet. Which is to say that for any $x you wish to bet you are indifferent between keeping $x or taking a 50/50 shot at $2x. That's it.

A proper bankroll is necessarily then different for each stake and for each player. There are amounts suggested everywhere as general guidelines. These are based on the sizes of the swings you expect to see in that game but all are designed so that you don't worry about losing a buyin or three. If you do worry about it, you are not properly rolled and are making bad decisions for yourself.

Once you have a proper bankroll, advice posted here and in books is all correct again!

Conclusions

Playing correctly under rolled is very difficult.
You will likely make bad decisions left right and centre.
You will lose opportunities at the table to make money because your preference for keeping what you have is higher.
You thus become exploitable. You should fold to bigger bets more often, which if spotted leaves you open to being pushed out of more than your fair share of pots.
Your risks are greater than the possible rewards.
No hand advice on this site or any other applies to you.

I hope this has been informative for you. Some of the language may seem complicated and you may not have quite understood what a utility was, but I hope you at least take away the message about playing under rolled and why you shouldnt do it.

For the more experienced posters, if you didnt know some of this stuff I hope you found my outline to decision theory and the mathematical explantation behind the insanity of playing under rolled interesting. I'd also like to re-enforce the point that, when someone is under rolled and asks for advice, the right decision depends entirely on him and his attitudes and preferences. You can only help with the probability side and not with the decision.

I'll write another article in a similar vain on the subject of playing over rolled quite soon.

GingerWizard

very good post.

The paragraph about utilities reminds me of the prospect-theory. It´s point is an asymmetric function of utilities of equal values, which means, that people tend to rate the (negative) utility of losing a certain amount greater than winning the same amount. U can imagine a function utility(ev), with different gradients for winnings and losses.
Applied to BR manangement we can say, that the more we play above our roll the greater the difference of the gradients.

I´ve had a couple of drinks and can´t express all my thoughts right now, for further info´s u might read here
http://en.wikipedia.org/wiki/Prospect_theory

I like this post a lot. Great timing too. It's making me reevaluate my recent (tonight) move from 10NL to 25NL.

Right now I'm 25 buy-ins deep which I feel pretty good about. I'll keep an eye out if I start getting too nitty, maybe I'll move back down to build more.

Great post as always man. So your BR is up to $2,000 - that's nice!

I'd be interested in hearing your thoughts on playing over-rolled as I suspect that's my problem right now.

Playing over rolled is coming. Thinking I shoudlnt have posted this article in Beginners cos it won't get noticed enough. Maybe NL strategies?

i think one of beginners biggest mistakes is playing overrolled. they waste so much time.
they're good enough to beat $100NL, but they're not going to playing it until they have a $5k BR (50 buyins). this seems ridiculous to me. players are killing the lower limits but they don't take a shot at the higher stakes. they waste so much time.
i think for players should take a shot at a higher level when they reach 20 buyins. if the lose 4 buyins then move down again and grind it back up. too much time is wasted by being overcautious.
the article on being overrolled should be interesting.

nice article btw.

I am overrolled for $100 NL BUT I WOULD LOSE LOTS OF MONEY AT 200NL. Why does no-one on this site ever acknowledge that sometimes, people just aren't good enough to move up?

Originally Posted by biondino

I am overrolled for $100 NL BUT I WOULD LOSE LOTS OF MONEY AT 200NL. Why does no-one on this site ever acknowledge that sometimes, people just aren't good enough to move up?

biondino. i've read your posts. you give some good advice.
i play $400NL and have taken shots at $600NL.
i remember a couple of months ago, you were playing higher stakes than me.
i think you underrate yourself and you should take a shot at $200NL. i think you are good enough. you may even be a better player than me and i play 4x your stakes.
commit $800 to playing $200NL and play a bit slower and carefully. look to take money off the donks. if you lose, then grind it out again. if you win then great! just keep grinding it up.

the players at $200NL really aren't that good and there are so many donks lieing around. try to avoid the better players (the full buyin players) and try to make a profit from the donks.
what's your VPIP% and PFR? and what site(s) do you play at?

Thanks for your confidence in me, but a) I'm really not that good and b) I am struggling with that prospect theory stuff enough at $100NL - I honestly don't think I could take the variance at $200. Losing a four figure sum, even if I'm rolled for it, would just devastate me. I'd certainly play scared.

I have played mainly at Crypto sites, with the occasional hand at Stars and Party (I play SNGs and the occasional MTT mainly at the latter two). My stats are between 20/13 and 24/16, depending on how the table is playing. This is at 6max. Post-flop, I bet too often on the river, and am too weak in the face of bets and raises. I rely too much on HUDs and not enough on genuine reads.

Originally Posted by biondino

Thanks for your confidence in me, but a) I'm really not that good and b) I am struggling with that prospect theory stuff enough at $100NL - I honestly don't think I could take the variance at $200. Losing a four figure sum, even if I'm rolled for it, would just devastate me. I'd certainly play scared.

I have played mainly at Crypto sites, with the occasional hand at Stars and Party (I play SNGs and the occasional MTT mainly at the latter two). My stats are between 20/13 and 24/16, depending on how the table is playing. This is at 6max. Post-flop, I bet too often on the river, and am too weak in the face of bets and raises. I rely too much on HUDs and not enough on genuine reads.

are you destroying $100NL?
if your BR is $6k+ you need to take a shot at $200NL. have you ever taken a shot in the past?
put aside 2 buyins for $200NL. look for tables with short stack donks and take there money by just playing tight solid poker. if you win then start playing more and more $200NL. if you end up winning $1k and then losing $1k that's how it goes, but you prepare yourself for it now and if you do lose a $1k then don't get too annoyed about it. remember that you won that money at $200NL too and you haven't made an overall loss.

everyone is scared to move up, but you're never going to make a million playing poker, by never taking a shot at a higher level.
if you can get through 3000 hands at $200NL breakeven you should be ready to start winning. you'll be comfortable with the game and i promise you $200NL really isn't as tough as it seems. i used to think $100NL was so tough, but now i'm playing $400NL and i feel like the game is way too easy.

I think prace is right, regarding both, moving up more agressive and biondino´s skills. We have certain members at FTR, who frequently post advices/opinion´s with an "wow, I have so much to learn"-effect to me and biondino is definetely one of those.

I recently switched back to full rings, b/c I just suck shorthanded, moved up to 100NL with 19 BI and am now frequently taking shots at 200NL with a 3.5k roll atm. I´m aware, that I´m on a heater right now, but there´s nothing wrong with taking a shot when tables are good. Nit it up a bit, avoid confrontations with the regs, focus on the donks and profit.

Thanks XTR, I honestly don't think I am that skilled but I'm not a complete fish and perhaps I am at my most perceptive when trying to advise others. Notice that most of my advice is on the beginner's forum, though

are you destroying $100NL?

Oh god no. I might not even be over 1ptbb/100. My moneyz were made at £25nl for the most part, which of course is financially equivalent to $50nl.

Your never gona be good enough to move up, if you never move up. Losing when moving up is a right of passage. Think of it as paying dues. Theres no reson to belive that there is any drastic skill increse from one level to the next. As a matter of fact its not the leel at all, its the players at that level. If barry G daniel and mike matasuw where all playing 1-2NL it would be a tougher game then whatever 5-10 nl was running. Watch the players, rail them. Learn who the regulars aree and how they play. Post questions and hands. I truly believe anyone with an IQ over 90 could beat 1k NL with the right attitude and disipline.

Above that online i have no idea. 2K NL live and up most players are very good at reading players and thats where there edge lyes. Theres only so much math.

As ive said in previous posts we play poker because we believe we have an EDGE. What that edge is is dependant on you. Gain an edge, exploit the exploitable. You cant tell me everyone plays perfect poker at 600NL.

The post on playing over rolled will come when enough people have read and understand this one. It's a little deeper than it looks, but once you really get it, then you'll understand my thoughts on playing over rolled much better.

For now all ill say is that I believe it dangerous to advise people to move up without giving good enough reasons for why.

Originally Posted by biondino

are you destroying $100NL?

Oh god no. I might not even be over 1ptbb/100. My moneyz were made at £25nl for the most part, which of course is financially equivalent to $50nl.

ok. i agree you shouldn't move up if you're only barely beating $100NL.

i found this post searching google:
http://www.pokertips.org/forums/showthread.php?t=43881

i find it surprising that 2ptBB/100hands is the max you can earn at $1kNL. it must be a really really tough game.
according to this you need at least 4ptbb/100hands to move up from $100NL to $200NL. i didn't read the article. i just skimmed thru it. is it a good post?

i read this in the comments of that post:

1 PTBB/100 at 5/10 is $20/100. 3 PTBB/100 at 2/4 is $24/100. Where did these numbers come from? Also, no offense, but are you qualified to tell someone when they should move from 1/2 to 2/4?

something must be wrong with his post. why play $1kNL if you can make more at $400NL? lol

Over rolled version written

i'll be looking forward to reading that.

i finally read this post today, but i'm not 100% satisfied with it.

i have a lot of friends that will play out of their roll. they don't even have a bankroll. whenever they get some money together they might put it on a game of poker. they will sometimes play for £100 which is way out of their BR's and sometimes they'll play for £10 (which is also out of their BR's since they really don't have one).

but when they play for £10, they definitely will not be worried about losing it. they'll even be happy to take a £40 coin-flip if they can win £100. they will making the correct $EV decision.

the reason for them to not play in a £100 cash game though, is not because they will make -EV decisions, but because of variance.

it's like in rounders, matt damon is skilled enough to play in the big game and will make correct EV decisions, but the reason he shouldn't is because of variance and he could lose his entire roll on a bad beat.

i don't see this mentioned in your post though. maybe i'm misunderstanding something though.

FINALLY! Someone asked me that question!

This is one of the nuances I feel is not obvious, but let me help.

Your friends want to play poker at that stakes and don't mind going broke. Now with variance such that you have a great risk of ruin, most BR builders have a very low utility for playing. But if going bust doesnt worry you at all, and therefore doesnt affect your utilities then sure the maximum $EV play is right.

Of course This situation is completely rare. Hardly anyone is not bothered about possibly going bust. And so we come to the crucial point.

If they are normal humans who really dont want to lose their roll then playing a games with a "significant" risk of ruin is a bad Idea for the following reason:

The decision maximising $EV is often or even usually not the correct decision

E.g. You have your whole roll on one table. Your opponent goes all in with AK and shows you it and you have TT. If fully rolled, this is a call all day all night. But a 45% chance of ruin is, for most mortals totally unacceptable and the utilities will reflect this making it a correct fold.

So: If your maximising EV, you are making bad decisions. Making bad decisions costs money.