2 Questions for Fossilman (long and theoretical)

[Ian]

This post addresses the issue of optimal macro strategy in today’s large field tournaments. Conventional wisdom is to play tighter in tournaments because you can’t reach into your pocket after going broke and because of the survival value of chips in terms of payoff structures (e.g. bubble situation, you are second smallest stack with 1% of the chips and the last position pays 3% of the total prize pool). The stated exception, of course, being that the big stack should play looser to take advantage of the survival orientation of the other players and also because he is getting a free ride on the survival premium himself. Sklansky in Tournament Poker says you should both practice this survival-driven strategy yourself and be prepared to take advantage of the other players’ survival bias by using what he terms the “Gap Strategy” – i.e. being looser with openers than you would in a cash game, but tighter with non-opening calls and raises.

I have significant doubts about the efficacy of this “tighter is better” strategy. These doubts are based both upon empirical evidence and theory. The empirical evidence is summarized by Jesse May in his May 7 report from the WSOP. http://www.thegoodgamblingguide.co.uk/columns/jessemay/latest.htm
In short, Jesse argues that a fearless, super-aggressive, even seemingly reckless style of play seems to be winning the day in the large field tournaments: witness Hansen, Moneymaker, Ivey, Flack, and so on. Jesse does not have the technical ability to analyze this beyond making the observation that conventional wisdom on winning poker does not appear to be holding up in these tournaments.

The reason I am addressing this to Fossilman in particular is that my understanding is that we share a background in high level finance (me more on the academic side, him in the real world of trading) and that I believe certain areas of modern finance theory holds some value in analyzing the situation. I won’t try to explain here the science of valuing real-time options, embedded options, etc. Suffice it to say that variance plays a key role in the equations. And contrary to conventional poker-world wisdom, modern finance theory tells us that the optimal tournament strategy is to crank up the variance much beyond what would be optimal in a cash game. The reason for this is the steep payout structures. Typically, you must finish in the top ten percent to receive any payout, and in the top 1% is where most of the prize pool resides. (If you think of this in cash game equivalents, what style of player at a 10-handed table is most likely to have the biggest stack after any particular session. Hint: it’s not likely to be the player with the highest EV style. Interestingly, Sklansky acknowledges this fact in Tournament Poker when he describes how the big stacks after the first round are likely to be poor players, but he doesn’t recognize the pertinence of this to what the optimal style of tourney play should be for skilled players).

I have considered these ideas somewhat proprietary and have not shared them in a public forum before. The reason I am doing so now is that I think this year will be my last WSOP, and the reason is that as the fields get larger, so to does the optimum level of variance in my play. But with 2,000 runners likely for the Big One this year, increasing the variance by that much takes much of the hand-to-hand tactical decisions out of play (or to be more precise, reduces their relevance) and makes the whole thing feel much more like a lottery. So, my questions for Fossilman are:

1. Am I correct that optimal play in large field tourneys calls for a much higher variance style than for cash play?; and
2. Do the larger fields create such a “lottery effect” that it takes away from the joy of the game for a skilled player, even as it increases his EV (increases his EV at least to the extent he recognizes the variance premium).

I’ll take my answers off the air /images/graemlins/grin.gif

[cferejohn]

Terms (just in case someone doesn't understand what the heck I'm talking about):

chipEV - Your expected value in chips. If some particular move will, in the long term, net you more chips than it will lose you, it is +chipEV.

cashEV - Your expected value in cash. It is possible (though rare in a tiered payout tournament) for a move to be +chipEV but -cashEV or vice versa. In a winner take all tournament chipEV exactly equals chipEV (there are a number of proofs of this scattered about books and the web).

Fossilman will no doubt say this much more eloquently, but I think the answer here is that the right thing to do for 95% of the tournament (or maybe more) is to make +chipEV plays, without worrying about getting busted.

The mistake most players make in tournaments is to worry about survival way way too far from the bubble (indeed, sometimes it influences their decisions from hand 1), and even very near the bubble, unless it is a supersattelite, reducing the chipEV of your play is probably sacrificing quite a bit of cashEV for the sake of survival.

Given that some fairly large (imho) number of players are making this mistake, the chipEV of being aggressive goes up, since players may be folding hands they might otherwise call or raise with because they are concerned about survival.

To concretize this, I am sure there are players who would lay down top pair vs. what they *knew* (somehow) was a flush draw if the decision was for all their chips, because they "don't want to risk being busted." Similarly, every once in a while around here, someone asks the question "would you call for all your chips with AA in the first hand of the WSOP?" and incredibly people answer "no". This is exactly the sort of thing that makes the aggressive players so very effective (if you *knew* someone would not call for all their chips with *anything* in the early going, going all-in against them with any 2 cards would, by defnition, be +EV).

I should say that I've never played in a WSOP event. These observations are based on playing (and beating) online tournaments in the $30-$200 buyin range. However, it seems extremely likely that if players make this mistake in a $50 tournament while there is another $50 tournament starting in 2 hours, they probably make this mistake *much much* more often in a WSOP event that comes once a year, especially if they are a sattelite winner who is taking their one shot at glory (which is probably a sizable majority of the field at this point).

Now, there are worse things to be in poker than over-tight, and these sorts of players are probably going to last longer than the complete maniacs (that is to say, the maniacs who don't take their opponent's tendencies into account, which Flack, Ivey, Hansen, et al *certainly* do). In fact, probably a couple of them will catch *such* good cards (even these guys aren't going to go laying down a flopped set or the like, and some of them are going to hit them) that they will get into the money or even the final table (Young Pak's final table play last year seemed to indicate that he was in this category).

However, the fact that the players who seem to make multiple final tables in big-money tournaments seem to have similar styles, if not demeanors, seems to imply that there is something to that style.

To sum this up using an incredibly cliched sports anology, you aren't going to win by trying not to lose.

[Myrtle]

Why would you ask these questions in a public forum and then ask for a reply in private?

[cferejohn]

I don't think that's what he meant by the 'off the air' comment Myrtle. He was just making a cute call-in radio reference...

[Myrtle]

ahhh....perhaps?

I was not being a wise guy with my post.....Was just curious.

FYI, Greg is a patent attorney.

[eastbay]

I think Fossilman would say something like "I'd rather stake a maniac than a rock" here. And you're right, it'd be a lot more eloquent and succinct.

FWIW, I have a little hobby of simulating poker-like games and tournaments with computer programs. If I've learned anything from the exercises, it's that optimal strategy is far looser and more aggressive than conventional wisdom or intuition seems to dictate.

So yeah, I think the general idea is right. c.f. Hoyt Corkins. We'll see if he holds up over time.

eastbay

[M.B.E.]

Cferejohn, excellent post (as usual).

Here is a theoretical thought-experiment related to this issue. Suppose, in the middle of the second day of a multi-day NLHE tournament, all the remaining players are equally skilled, and the average stack size is 20000. The tournament has a typical laddered payout structure. You are playing a hand heads up and you have your opponent covered. Exactly 10000 went into the pot preflop, and now on the flop your opponent pushes in for 5000. You have exactly 20000 remaining in your stack at this point.

Now if CEV were your only concern, you would fold if and only if your opponent is more than a 3:1 favourite against you (since your pot odds are 3:1).

So, just to drive home this point, if you fold then your stack will be exactly average. If you call and lose then your stack will be 75% of average; if you call and win then your stack will be 175% of average.

Now suppose further that you have a very accurate idea of how your opponent plays, and you can do the Bayesian math in your head to put him on a range of hands with a precise probability distribution. You then calculate the probability that on this flop, the probability that his hand will win against what you hold is precisely 75%, with the probability of him losing 25% and 0 chance of a tie. In other words, he is exactly a 3:1 favourite so if maximizing CEV were your only objective, you'd be indifferent between calling and folding.

Okay, maybe I've made this more complicated than I had to, but too late now. Here's the question: What play maximizes your $EV for this tournament:

(a) call,

(b) fold,

(c) it makes no difference; your $EV is exactly the same either way.

I think the answer is (a), largely for the reasons alluded to by Ian. However, it wouldn't surprise me too much if someone convinced me the answer is (c).

[Greg (FossilMan)]

Well, I know nothing about financial theory, modern or ancient. So I'm not much help there.

However, as a generality, I agree that the players with the higher variance style certainly do better, as judged by appearances, than their very-tight brethren. Now, if given the choice of who to back, I will back the highly skilled poker player, loose or tight, over the relatively unskilled but hyper-aggressive player. Skill is still better than naked aggression.

The best players are very aggressive much of the time, but their aggression is backed up by very good reads and judgment. Phil Ivey is a great example of this. He can bluff you with nothing, but he seldom does so when his opponent has a really big hand, because he's good at sensing that strength, and getting out of the way. He makes mistakes, but many fewer than the maniac at your local room.

As for the lottery effect, I don't see it. It appears to me that when more players enter a tourney, all of those extra players are from the pool of weaker players. That is, the extra 500 players in a 800 player field (as compared to a 300 player field) are mostly the weakest of the field. Thus, even though it is much harder to WIN such a tourney, it is much easier to cash (as long as they still pay 10% or so of the field). And it is much easier to accumulate chips early. I guess I'm just a bully, because I prefer to beat up on weak players rather than butt heads with tough players.

Later, Greg Raymer (FossilMan)

[Ian]

Yes, I think this is exactly right. But why not make it even simpler and more dramatic:

You are Ivey, Lederer, Seidel or some other well above average skilled player. Second day of WSOP championship, 1000 of original 2000 players remain, 180 places paid ($25,000 for 150-180, $3 million for first), you have exactly average stack of 20,000 and hold AKo in big blind. Folded to small blind who has you covered, flashes his 44 to you and moves all-in. Conventional wisdom and intuition says this is not even a close decision -- the super-skilled player should pass up a coin-flip hand for all his chips and wait for a better opportunity. I agree that it is not a close decision -- it is, in fact, an easy call. By substantially increasing your tournamanet variance in an EV neutral hand situation, you are actually increasing your tournament EV. To borrow a Wall Street term of art, you are "buying beta" at a zero EV cost in chip terms. An easy decision, and one that most players won't make. In fact, I suspect the top players who would make the right call here -- a Gus Hansen, a Layne Flack, etc. -- do so more for psychological reasons than because they actually understand the math.

[Ian J]

I see where you're going with this, but aren't the majority of players like Hansen, Flack, Ivey, etc. playing in such a manner that has to do with getting their opponent to fold, rather than calling off all their chips. I don't think that this is close, I'd fold every time, but if the SB flashes 44 and a guy like Hansen has 33 for instance, if the 44 makes a 5xBB raise, Hansen or Ivey may then decide to move in on him. I think that is the essence of what these hyper aggressive players are doing, not so much just calling off their chips in coin flip situations.

[eastbay]

[ QUOTE ]
To borrow a Wall Street term of art, you are "buying beta" at a zero EV cost in chip terms. An easy decision, and one that most players won't make.

[/ QUOTE ]

Well, you're just making an assertion here using an undefined term. Can't you do a little better than that?

eastbay

[FlyWf]

Here's a slightly better example, IMO. The big blind shows the table his AKo before betting, and everyone folds around to 44 in the SB, who should go allin. Sklansky says avoid sub-60% percent winning chances if losing knocks you out, but IMO Ian is correct and Sklansky is wrong in the usual tiered payout system.

My last two tourneys were similar buyins, but one had 27 people and the other 500(actually this one had a slightly larger buyin). I finished 1st in the small one and 10th in the big one and made significantly more money beating 26 people than I did beating 490.

The only time you should care about the bubble is when you are broke and need that money, in which case you shouldn't be playing poker with it. If the difference between 1st and 4th is larger than the difference between 4th and dead last, you shouldn't fold JJ when shortstacked on the bubble to an allin because you want to make 150% your buyin.

[Whitey]

I'm not so sure your "easy call" is correct here.

I think it is more dependant on the blind level,the players at the table,how passive/aggressive the table is.

Even Gus Hansen or Layne Flack may well choose to fold in this spot if they believe they can pick up pots irrelelevant of what cards they are getting.

Why risk all your chips on a coin flip when you can consistantly pick up pots with any two cards by bullying your weaker opponents? This is exactly the type of stategy that makes Hansen such a good player and by calling in a coin flip situation his skill is taken away from him.

However if the blind level is at a point where any raise is committing a large portion of his stack then calling becomes correct.

[Expunge]

[ QUOTE ]
Yes, I think this is exactly right. But why not make it even simpler and more dramatic:

You are Ivey, Lederer, Seidel or some other well above average skilled player. Second day of WSOP championship, 1000 of original 2000 players remain, 180 places paid ($25,000 for 150-180, $3 million for first), you have exactly average stack of 20,000 and hold AKo in big blind. Folded to small blind who has you covered, flashes his 44 to you and moves all-in. Conventional wisdom and intuition says this is not even a close decision -- the super-skilled player should pass up a coin-flip hand for all his chips and wait for a better opportunity. I agree that it is not a close decision -- it is, in fact, an easy call. By substantially increasing your tournamanet variance in an EV neutral hand situation, you are actually increasing your tournament EV. To borrow a Wall Street term of art, you are "buying beta" at a zero EV cost in chip terms. An easy decision, and one that most players won't make. In fact, I suspect the top players who would make the right call here -- a Gus Hansen, a Layne Flack, etc. -- do so more for psychological reasons than because they actually understand the math.

[/ QUOTE ]

Aggression <> calling. Aggression = betting.

[cferejohn]

[ QUOTE ]
You are Ivey, Lederer, Seidel or some other well above average skilled player. Second day of WSOP championship, 1000 of original 2000 players remain, 180 places paid ($25,000 for 150-180, $3 million for first), you have exactly average stack of 20,000 and hold AKo in big blind. Folded to small blind who has you covered, flashes his 44 to you and moves all-in. Conventional wisdom and intuition says this is not even a close decision -- the super-skilled player should pass up a coin-flip hand for all his chips and wait for a better opportunity. I agree that it is not a close decision -- it is, in fact, an easy call. By substantially increasing your tournamanet variance in an EV neutral hand situation, you are actually increasing your tournament EV. To borrow a Wall Street term of art, you are "buying beta" at a zero EV cost in chip terms. An easy decision, and one that most players won't make. In fact, I suspect the top players who would make the right call here -- a Gus Hansen, a Layne Flack, etc. -- do so more for psychological reasons than because they actually understand the math.

[/ QUOTE ]

I don't know the financial theory stuff, but I don't agree with this. I would definitely bypass a high-variance/0 EV bet in a tournament. If I think I am better than the field (and not to be immodest, but in the $50-$200 online tournaments I play, that's pretty much always), <x> number of chips is worth slightly more to me than it is to the average remaining player, so calling for all my chips on a 0 EV proposition, odds-wise is, in fact, slightly negative.

Now, I know that Hansen specifically is well known to be happy to call with a 'coin flip' after being re-raised all-in, but in these situations, there is almost always a substantial enough amount of money in the pot that he is getting considerably more than 1:1 on his call, making the call definitively correct (assuming that his read of a 'coinflip' is correct). I doubt he would call in this situation if there was very little or no money in the pot to begin with.

[M.B.E.]

[ QUOTE ]
If I think I am better than the field (and not to be immodest, but in the $50-$200 online tournaments I play, that's pretty much always), <x> number of chips is worth slightly more to me than it is to the average remaining player, so calling for all my chips on a 0 EV proposition, odds-wise is, in fact, slightly negative.

[/ QUOTE ]
Cferejohn -- this statement is clearly correct, but what if it's just a small portion of your chips on a 0 CEV proposition (or even perhaps slightly negative). How would you answer the hypothetical I posed earlier in this thread?

[cferejohn]

[ QUOTE ]

Here is a theoretical thought-experiment related to this issue. Suppose, in the middle of the second day of a multi-day NLHE tournament, all the remaining players are equally skilled, and the average stack size is 20000. The tournament has a typical laddered payout structure. You are playing a hand heads up and you have your opponent covered. Exactly 10000 went into the pot preflop, and now on the flop your opponent pushes in for 5000. You have exactly 20000 remaining in your stack at this point.

Now if CEV were your only concern, you would fold if and only if your opponent is more than a 3:1 favourite against you (since your pot odds are 3:1).

So, just to drive home this point, if you fold then your stack will be exactly average. If you call and lose then your stack will be 75% of average; if you call and win then your stack will be 175% of average.

<yada yada yada; you exactly have odds>

Okay, maybe I've made this more complicated than I had to, but too late now. Here's the question: What play maximizes your $EV for this tournament:

(a) call,

(b) fold,

(c) it makes no difference; your $EV is exactly the same either way.


[/ QUOTE ]

I'm not much of a statistician (I can read and understand them, but statistical proofs aren't really up my alley), but I would suspect the answer is close enough to (c) that it doesn't really matter and we're back to considering whether you are better than the field. At least, that's how I play. The idea that increasing variance essentially for the sake of variance increases your EV seems intuitively wrong to me, but I don't have a proof (or even some random blathering with numbers) to offer.

If you do this often enough against observent opponents, they may pick up on it and make steals/thin value bets less often (i.e. they might not push with A5 if they know you will call with A6 and 33). I suppose *that* could be +EV, but in the online environment, I'm not seeing the same players often enough to feel like such a corner case image play has much value. Maybe if I was a pro coming up against the same players over and over I would feel differently...

I suppose there is an amount small enough that I would call knowing I was ~0 EV, but it would really be as a result of my usually suppressed table sherriff who comes out when there is a chance to bust someone at the risk of a miniscule portion of my stack, rather than any knowledge of advanced financial theory.

Once you get to the point of the tournament where you are close enough to the money that CEV and $EV start to diverge noticably, than the answer depends on your stack and your control of the table. If you have a big stack and you feel like you can bully the table around on the bubble, fold. If you are a medium stack and feel like you are getting pushed around because of the bubble, call. I know, I know, that wasn't the question...

[Doctaprofit]

I read this post and a light bulb went off in my head as far as my tournament play goes... im playing far to similarly to the way i play limit which probably explains a lot of my sub par results... excellent post, thank you.

[Ian]

Sounds like a good strategy Greg. Why don't you try it at this year's WSOP and see what happens?

[NoTalent]

[ QUOTE ]
Sounds like a good strategy Greg. Why don't you try it at this year's WSOP and see what happens?

[/ QUOTE ]

You really think it would work? /images/graemlins/grin.gif
GL Greg! /images/graemlins/spade.gif

[ceczar]

[ QUOTE ]
You are Ivey, Lederer, Seidel or some other well above average skilled player. Second day of WSOP championship, 1000 of original 2000 players remain, 180 places paid ($25,000 for 150-180, $3 million for first), you have exactly average stack of 20,000 and hold AKo in big blind. Folded to small blind who has you covered, flashes his 44 to you and moves all-in. Conventional wisdom and intuition says this is not even a close decision -- the super-skilled player should pass up a coin-flip hand for all his chips and wait for a better opportunity. I agree that it is not a close decision -- it is, in fact, an easy call. By substantially increasing your tournamanet variance in an EV neutral hand situation, you are actually increasing your tournament EV. To borrow a Wall Street term of art, you are "buying beta" at a zero EV cost in chip terms.

[/ QUOTE ]

Ian,
You're really an academic in high finance?
You are badly misusing the financial analogy. A tournament situation is far more like a knock-out option than a traditional option.
A knock-out option is an option that ceases to exist when the price of the underlying reaches a certain level.
Not that this adds anything to the understanding of tournaments, but when you use the proper finance analogy, it is easy to see why you are probably giving up a lot of EV with this call.
An option has some "time-value" that's directly related to the volatility (variance), but only if having twice the chips at that stage of the tournament more than doubles your EV$ will this be a plus-EV call, since you're taking an almost even money bet to lose all the EV of staying alive. I'm sure there are situations when this works out to be correct, but in the early stage of the tournament as a world-class player, i find that hard to believe.
It's clearly not as simple as adding volatility with no cost to EV.

[paland]

[ QUOTE ]
As for the lottery effect, I don't see it. It appears to me that when more players enter a tourney, all of those extra players are from the pool of weaker players. That is, the extra 500 players in a 800 player field (as compared to a 300 player field) are mostly the weakest of the field. Thus, even though it is much harder to WIN such a tourney, it is much easier to cash (as long as they still pay 10% or so of the field). And it is much easier to accumulate chips early. I guess I'm just a bully, because I prefer to beat up on weak players rather than butt heads with tough players.

Later, Greg Raymer (FossilMan)

[/ QUOTE ]

Well greg, looks like you can butt heads with tough players as well as weak players.
Congrats on what is probably the finest display of poker ever up to this point.

[trillig]

Howdy!

My nutshell answer is:

Adapting to the environment is best... whatever it is at that particular table, this includes players, money management, and clock management.

I am not claiming to be a big time pro, but I have been in at least 300 tournaments, most online and have survived to top 25% 5x more than I went out in the first 25%, so I have to feel my way is at least GOOD, and my play varies with conditions... but if I am not capable of my A-game then I am in trouble right off the bat and typically one blunder is death, I try to avoid that... just admitting that I am not 100% is sometimes hard and ego gets in the way occasionally and so does NOT having played in 3 days and 'I need to make some $...' attitude prevails.

Serious poker is constantly working out the kinks and adjusting... IMHO!

As always, YMMV!

-Bri