An “Information Ratio” for Poker?

[m2smith2]

Much of poker theory revolves around making positive EV plays. Anyone who has played with TTH has run tests for EV. But, if you look deeper you’ll also see the volatility that comes with many positive EV plays.

In investment management, there’s a concept called “information ratio.” Basically, you take the return premium (alpha, or for poker EV) of (say) your mutual fund over an index, and divide that by the volatility of that alpha. For those with a statistics background (most I would imagine) it’s akin to a T-stat not adjusted for degrees of freedom.

I must admit that one thing got me thinking about this – a recent spiral. If I had to put my finger on one factor it would be missing many draws over an extended period. Now, the old dogs will say “that’s poker,” and it’s certainly true. But, does it have to be?

I think the old rule of thumb is 100 big bets to withstand the natural volatility of poker. A rounder recently told me he thinks it’s actually 200. So, most pros manage their volatility with the size of their bankroll, which is fine if you have unlimited resources.

Economist John Maynard Keynes famously said “Markets can remain irrational longer than you can remain solvent.” Clearly, one way to manage this is follow the max-EV rule, and control your volatility by the level of game you’re playing. This is the exact thing many on-line players don’t do.

However, what if you think that your particular game is better suited for a limit that’s higher than your bankroll would suggest at 100 big bets? (Let’s assume this isn’t ego-driven, but rather that you don’t want to play with overly loose people for smaller money, or people with cheep Internet connections, or whatever.)

I don’t know the answer, but I think it’s possible. One problem with the analogy I used is this: (in the parlance of statistics) information ratio is important because you are estimating an uncertain alpha from a sample, and gaining confidence in its sustainability with the information ratio. While a hand EV isn’t truly a “population” figure, it’s far closer.

Unlike having (say) five years of monthly data for an investment portfolio, you can run 1,000,000 simulations with five different card codes and get a fairly tight EV range estimate. So, while IR attempts to learn if alpha is “real,” we know when a certain positive EV play is “real.” The question remains whether or not it’s worth the volatility over the “long-term” relative to your bankroll.

Again, I know you can manage this by playing a game in proportion to your bankroll. But factoring in the volatility of EV can have other benefits – like “psychic” benefits. That is, a lot of people (I’d dare say most) play worse when they’re in a tailspin. Many people recommend tightening up when you’re losing. Ironically, that’s another way of saying reduce your volatility! Why not reduce it BEFORE you go into a tailspin? If you play better when you don’t have big drawdowns, then managing volatility is, itself, a “positive EV play.”

[BarronVangorToth]

I'm forgetting precisely who I read this story by (I think it was Doyle Brunson) but it coincides with what you're talking about.

Let's say that a flip of a coin is 50/50 and that it isn't rigged in any way -- it's truly A or B.

Now, you guess A or B.

If you're right, I'll give you $10

If you're wrong, you give me $9

EVERYONE will take this proposition and play it for as long as possible.

However, extend the stakes.

$100 vs. $90.... Maybe I lost a few people that will only play, I don't know, $.05 / $.10 poker. The rest of us are right there.

now

$1000 vs. $900

I lost a number of more people.

$10,000 vs. $9,000

etc etc.

Doyle Brunson (I'm fairly certain now) said something to the effect of a situation where the bet came down to risking LITERALLY everything somebody had (let's say the total net worth of everything, down to clothing, furniture, everything) was $1,000,000 vs. something a lot more ... $5,000,000.

No matter what the secondary amount was, I wouldn't risk every nickel and item I own (leaving myself with nothing but the clothes on my back) for a 5:1 shot, just because being left homeless would be, well, a pain in the butt (sure, I could live with friends, borrow from family -- but all of this is such a huge set-back, that it wouldn't be worth it).

But I'd do the $1,000 vs. $900 every day of the week for as long as you wanted.

Sometimes the "right" play is beyond one's means. Say you see the $2,000 / $4,000 game looks a bit soft -- it's RIGHT to sit down ... but I'm not taking out a second mortgage for the, whatever, $200K I'd want to have to sit down (and, yes, I know that would be too little).

Right isn't always right.

Great post, though, much to think about.


Barron Vangor Toth
www.BarronVangorToth.com

[Monty Cantsin]

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I think the old rule of thumb is 100 big bets to withstand the natural volatility of poker. A rounder recently told me he thinks it’s actually 200.

[/ QUOTE ]

Around these parts the standard answer to the bankroll requirement is 300 BB.

[ QUOTE ]
So, most pros manage their volatility with the size of their bankroll, which is fine if you have unlimited resources.

[/ QUOTE ]

Huh? How do you get from needing X times the BB to needing unlimited resources?

If you are sufficiently bankrolled there is no reason to avoid plays that you know are +EV just because they have high variance. Often, less-than-expert players (like me) avoid marginal +EV / high variance situations because they aren't confident enough about their ability to correctly negotiate them - but this is a different issue.

Consistently giving up EV in order to minimize risk is a well established form of bad poker. Isn't this what "rocks" do?

As far as the pyshic benefits of low variance, you're much, much better off working on your mental stamina to deal with the normal swings of the game than you are trying to adjust your game to minimize these swings.

Personally, I think learning how to maximize your EV in a high-risk situation is one of the greatest challenges and pleasures that poker has to offer - it may even be the essential quality of the game. I can't imagine cultivating a style of play that sought to avoid such situations.

/mc

[Cerril]

I've said a lot in my home games that I consciously aim to come in 'second'. Routinely there are two highly aggressive players in our games, and routinely they both take a larger share of the table than I do over time. So I guess technically I'm coming in third (but maybe second, if you factor in those few times that I take the table). Thing is, on any single night one will tend to be the big winner, and one a big loser. I lose my $20 now and then but nineteen out of twenty I win the second most.

I don't play quite so tight in table games, but my goal is a positive EV without going for that last little edge. And that's more or less what you're talking about. Let's say for the sake of argument that you're a player who can reliably make 1BB/hr in a game playing your best (let's call it online so it's more likely to be that or greater).

If you're given a choice between getting every edge and keeping that 1BB/hr or even maybe a little more, say 1.2BB, or of playing a little tighter, avoiding situations that come up rarely where you either end up a huge winner or second best, but sacrificing some winnings and leaving yourself a .6BB/hr player. Well most people would find that silly, and it's certainly 'bad poker' to give up half your winnings to safeguard potential losses.

On the other hand, there are some real reasons and some good ones either way. If you're an amateur or semi-amateur who plays without a bankroll, or is in the process of building one with some hard earned cash, it might be worth sacrificing the chance of losing it all (and presumably having a slower rate of growth from 0) to maintain a steady rate (that's what I'm doing at the moment. My stake was only a little more than 30BB when I started, it's up to around 200 now but I've also changed limits so that it's really only around 120BB).

Another reason you suggested might work too. If your only options for softish games are at 1/2 and 5/10, then you might take the 5/10 but play a little more conservatively to get a higher hourly even with a substantially lower +EV%.

The key, though, is never to give up so many of those marginal situations that you end up a loser over time. -that- is the rock's mistake and the mistake that will always be bad poker. If you can't afford to risk any of your money, there's no reason to start playing.

In the end there's no sound reason for a true pro, or a well-invested player to give up some +EV for lower volatility. The bankroll size is there for a reason, and the calculations (300BB is the number I'd heard before coming here too) are based around precisely those massive swings. Even pros though will say that sometimes you may need to swallow your pride and move down in limits if your bankroll drops too far, to avoid exactly this dilemma.

[Dan Mezick]

Excellent post and you are really on to something. I've been an advocate for adapting the available literature on portfolio theory and trading psychology to poker, and this posts hits home.

The poker session is a decent metaphor for position size you take per trade. Position size is an important trading decision because it delays your ruin when you do not have an edge and actually makes you money when you have a small but exploitable edge.

To large a position size can manifest an overall loss over many trades in an otherwise winning approach. IN other words, position size is a major critical success factor. To large a PS and you lose, even when you have an edge.

For example in trading if you limit any single trade's risk exposure to 2% of your bankroll, as most trading pros will do (most saying 2% is WAY too big, by-the-way,) then ... when you have an edge, you are allowing enough samples, (trades) to tease the money out of the edge. If you have no no edge or -EV in your procedures, with small PS you lose more slowly. This allows you to evaluate and 'get away from' a losing procedure.

There is much more to position sizing but that's the general concept. My main point is, looking at the poker session as a trade, and 'sizing it' accordingly, never risking more than 2% of your bankroll... appears correct if you believe the trading literature and apply it to poker.

The stakes in the game you choose for your session has everything to do with sizing your risk in this session, against your bankroll.

For example if you follow the 30-bet stop-loss rule in your 10-20 session (another trading concept related to risk definition) your TOTAL risk for this session is $600. If you are looking to not risk more than 2% of your bankroll per session, $600 is 2% of an implied $3000 bankroll.

This goes back to the psychology of it all. If you factor in bankroll size, selection of stakes (for your session) and a "stop loss" rule (for example 30 big bets) then you have defined your risk.

And that knowledge of your risk (defined) for THIS session can be the "inner edge" that makes your just slightly +EV plays really become profitable.

Just the fact you have employed a rigorous methodology to define your risk per session is going to help your game within a **key** component of your poker mindset.

Your risk of ruin is close to zero-- what will knowing that do for your game?

[chipclod]

Thanks all for such interesting and informative posts.

A thought dawned on me reading through this thread and I was wondering if it is applicable. Essentially, I was thinking that the general mentality of early round tournament play really conforms to m2smith2's contained volatility ideas involved with his "information ratio" analolgy.

Despite a very high EV potential; a big hand at your first table has a much more profound down side if it fails. Thus, it seems this general "IR" understanding permeates most play in a very not yet quantified way. I think.

[m2smith2]

The tourney construct is certainly true, as 2+2 preaches. The classic example is your AA hand when you "know" someone has KK - 4-to-1 is not even enough of an advantage if you think you have an edge overall in the tourney (as an aside, it's humorous how often I've seen this on-line recently in table tournaments within the first few hands, but I haven't seen the AA lose yet. But the Kings just can’t get away).

I think early in the tourney you just have to follow that rule, but amateurs have used this in the WSOP. Sklansky once wrote about a simplistic strategy he taught to the daughter of a casino owner that basically involved putting all-in pressure on pros. Tournament strategy also dictates that you should gamble more when overmatched, so the recent approach of many amateurs is completely logical.

Once you start to get close to the money, I think some quantification is finally possible. My guess is it involves the same type of math that you would use when valuing a potential deal (they still have those somewhere – off the WPT – right?). Then you could recast from EV terms to chip terms based on the expected advantage for a particular play, and also grade that based on what it does for your chances. So, when you’re short-stacked a lower probability play with an AI and a caller in front could be worth more (even though the chances of winning this showdown are lower than heads-up) because you can triple-up and go from, say, one round of blinds to three.

Anyway, I still wonder if there’s some merit to an IR in ring games. After all, tournament strategy is based on the fact that if you “go broke you’re gone.” That can be true when playing in games that aren’t 1% (or a half percent or whatever) of your bankroll.

And FWIW, one final point on that – not making the same EV play every time also can mix up your game. For example, betting that four flush every time. Do it from late position and you might be opening yourself to a check-raise, and the “free card” play is so well known you can’t rely on it working. If you catch on the turn your opponent might actually think that the card didn’t help since you didn’t bet on the come like you usually do. And when that turn pairs their ace and you’re holding the suited king, it’s a joyous feeling...

[Monty Cantsin]

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Anyway, I still wonder if there’s some merit to an IR in ring games.

[/ QUOTE ]

I hate to say it, but to me this whole thing sounds like a very complex justification for playing tight/weak developed in reaction to a nasty downswing.

Consistently opting out of +EV/high variance plays could lead to a general attitude of risk avoidance that will severely hurt your overall game.

Sometimes the fortune cookie gets it right: scared money don't make money.

Your 300 BB bankroll is your net. You don't also need a parachute and a bungie cord and a jetpack.


[ QUOTE ]
And FWIW, one final point on that – not making the same EV play every time also can mix up your game.

[/ QUOTE ]

Mixing up your game is something you do to maximize EV, if you happen to make lower risk plays in order to mix up your play that is purely incidental.

/mc

[chipclod]

I tend to agree with much of the sentiment behind your posts here Monty.

Mixing up your play is a means designed to help you make more money by trying to not allow your competitors to get a handle on you. I would have to say mixing your play can be much more a psychological ploy then one related to EV.

In a very simplistic example ...
Limping in with 8,3 off in early position will not be profitable in the long run; however if there are no raises, and the flop shows an eight and three .... no one in their right mind is gonna gauge your hand correctly.
This of course could throw them off gauging you correctly for a while even as you play very fundamentally afterward.

I think there is merit in m2smith2's notion, even if, as you seem to imply, it's founded on reducing the gamble. In a way, all the books and ideas regarding what has become the fundamentals of poker are based on reducing the gamble.

The striving for a way to contextualize this EV stuff in regard to stack, (or money, or reality) has not been crystalized yet ... is at least intuitively understood as valuable by anyone with finite funds.

I think a viable fundamental could be gained.

[Dan Mezick]

Avoiding marginally positive +EV situations in a ring game is playing a weak-tight style.

The 300BB rule is a ratio rule. This rule helps define total session risk but without the stop-loss (30 bet rule) that risk definition is not complete.

Once the total risk-defintion for the session is complete you can pick your spots within the session to go aggressive on marginally +EV situations. You have 30 big bets to play with before you get 'stopped out'.

The point is, if you completely define session risk you can just swing away, using your judgement to pick the proper spots.

Using the30 bet rule you can open up your game maybe 2 or 3 times and take swings at marginally EV+ situations.

Most players probably can't do that consistently in a completely relaxed way without some kind of session-based stop-loss.