Thursday, May 07, 2009

The Winner is the Loser?

Winners & LosersWas reading through the Full Tilt Poker Strategy Guide: Tournament Edition the other day. A lot that is worthwhile in there, I think.

In Howard Lederer’s chapter on limit hold’em tourneys (one of the few discussion of LHE tourneys you’ll find, actually), he brings up a concept regarding tournaments that I remember Mike Caro at one time making a lot of noise about. Kind of a curious idea (as most of Caro’s ideas are).

Early in the chapter, Lederer extols the virtues of making it to the cash -- and in fact ultimately makes simply cashing a primary goal for tourney players, kind of countering what a lot of folks will say about the importance of winning or finishing near the top where one usually finds the big money. He admits that he might have won more money in his career overall if he’d adopted a looser, more aggressive approach, but for him that was “not a style I’m comfortable playing.” This business of approaching tourneys conservatively is not the concept I want to talk about, though.

'Full Tilt Poker Strategy Guide - Tournament EditionAmid that discussion, Lederer offers the observation that when you cash in a tournament, but don’t finish first, “you have, by definition, taken advantage of the tournament structure.” Why? “Because you ended up broke -- zero chips -- but they paid you a big check anyway.”

It’s kind of an interesting point, I think -- this idea that, as Lederer goes on to say, “the winner actually is the one that pays the biggest price for the tournament structure,” because “the winner gets all the chips but does not get all the money.”

Like I say, this is an idea that I first saw Mike Caro address as what he calls a “conceptual problem” with tournaments. In Caro’s discussion, he points back to the mid-1970s when tourneys stopped being “winner-take-all” affairs and the prize pools began to be distributed among several of the top finishers, not just the winner.

The history of the World Series of Poker Main Event exemplifies this trend. For the first eight years of the WSOP (1970-1977), the winner of the Main Event won the entire prize pool. When Doyle Brunson won his second title in ’77, there were 34 entrants in the event, each of whom paid $10,000 to play. That meant Brunson’s first prize was $340,000.

However, in 1978 the WSOP began to divide up the prize pool. There were 42 entrants that year, and Bobby Baldwin won. But he only got $210,000 for winning, and the other half of the money was divided among those finishing second, third, fourth, and fifth.

Another big change in the payout schedule at the WSOP Main Event happened in 1986, the year Berry Johnston won the WSOP. There were nearly the same number of players in the Main Event in ’86 (141) as there were the previous year (140). However, in 1985 only the top nine finishers cashed, while in 1986 the top 36 players cashed (although those finishing 28th-36th got less than their buy-in back -- $7,500). So Johnston’s first prize of $570,000 was considerably less than the $700,000 Bill Smith got the year before for winning.

Mike CaroFor Caro, this change created a “conceptual problem” with tournaments insofar as the way he views it, “first place is punished and all other close finishers are rewarded.” For the Mad Genius of Poker, this makes tournaments much, much less attractive to him, and in fact becomes a reason for him not even to play them. He goes on to suggest that “in terms of strategy... if you play to win first place... you’ll probably lose money in the long run.”

Because if you win you lose. Get it?

Caro thus offers the same advice as Lederer and insists “the way to make a profit in these tournaments is to survive” -- that is, play conservatively, try to make the cash, and be satisfied with knowing that when you do cash (but do not finish first) you have taken advantage of the structure. Ever the iconoclast, Caro probably takes the whole idea a bit too far when he adds that “you should not go out of your way to win the first-place trophy, because the winner of the tournament is penalized.” (Here’s an article in which Caro explains his idea, if you’re interested.)

I’ve heard him made this argument in other contexts, and he usually insists that finishing second is really where it’s at. The guy finishing second is the one who makes the most money despite losing all of his chips.

Now I’m no mad genius. (In fact, I’ve been known to have trouble operating a cell phone.) But I think the point being made by Caro and Lederer actually depends on a particular view of the relationship between tournament chips and buy-ins -- namely, a view that essentially sees tournament chips as directly representing the money one paid to enter the tournament. Which sort of makes sense when we talk about tournaments in a theoretical way, but creates a different “conceptual problem” (I think) once we sit down and start playing the actual tournament.

For example, there’s gonna be somewhere around 5,000 players entering that $1,000 no-limit hold’em “stimulus special” tournament (Event No. 4) this year. Let’s just say exactly 5,000 enter. All players will be receiving 3,000 chips, meaning, in a sense, that every chip cost them 33.33 cents.

Of course, since some of the prize pool is going to be taken out before the first hand is dealt, you could say the players will already be getting the worst of it just by entering the tournament. According to the WSOP, 7% of the prize pool is going to be withheld for entry fees, and another 3% taken for the tourney staff. With 5,000 players, that means there is going to be 15 million chips in play. Players will have paid $5 million total, but the prize pool is going to be $4.5 million after the juice. That means every chip is technically worth exactly 30 cents, even though players paid 33.33 cents per chip to play. If we view tournament chips as the equivalent of cash, every player is going to be down $100 just for entering the tournament.

Now I’m going to guess somewhere around 9% of the field is going to cash in this event (judging from the payout schedules of similar, big field events from the 2008 WSOP). That’s 480 players. Not sure what the prize will be for first place, but last year Grant Hinkle took a little over 15% of the prize pool for winning that first no-limit hold’em event -- the one that had nearly 4,000 enter. So let’s say the winner of the $1,000 “stimulus special” gets 15% of the prize pool for winning -- that’s $675,000. That means the other $3,825,000 will go to 479 players who finish with zero chips. If we think of tournament chips as cash, well, then it does appear that 479 of the 5,000 players entering are getting a pretty good deal here.

But really, once the entry fee is paid, that $1,000 each player handed over is long gone. All that’s left are the 3,000 chips waiting at the player’s seat at the start of Day 1. And it doesn’t make a lot of sense (to me) to think any longer of those chips bearing any relationship at all to the money spent for them, because you can’t go back and cash them in. Once the tourney starts, the trick is to turn those chips into more chips, and hopefully all of the chips. That’s the only way to maximize their value from that point.

I understand Caro’s lament about tourneys moving away from the “winner-take-all” format. And I even appreciate the “conceptual problems” that result, thus making him less inclined to play tournaments. But I don’t think I’m going to buy the conclusion that the winner of a tournament is in some sense the biggest loser, even if it is the case that he or she has won all the chips but is only claiming a small portion of the prize pool.

But that’s my choice, of course. I can buy what I want -- chips, concepts -- as long as I can afford to do so.

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Blogger Gene said...

Of course if every tournament was winner-take-all far fewer people would play and, indeed, tournament poker probably wouldn't have gotten off the ground.

That said, I'd love to see the WSOP have a winner-take-all bracelet event. You hear players all the time saying they only play for first place, they only want the bracelet...let's see if there's proof in their pudding. A $10K event, the winner gets all the money, a bracelet, maybe a special trophy a la the $50K HORSE.

Oh, the players at the end might cut a deal? Fine, it's their money, it's their prerogative. But Harrah's should add a clause that if there are ANY deals made, they'll withhold the bracelet and the trophy. Those who want the money can have it, those who want glory have to play for the win. Let's put these people under tremendous pressure and see what happens!

5/07/2009 11:30 AM  
Blogger Greylocks said...

If all else is equal - i.e., the quality and number of opponents, and assuming they don't adjust their play to the payout structure - then winner-take-all payout is the highest EV for the most skillful players.

Consider a 10-player $10+$1 SnG. If your in-the-money percentages are 15/12/15, your EV in a standard 50/30/20 payout is .15*39 + .12*19 + .15*9 - .58*11 = $3.1, and your EV in a winner-take-all would be .15*89 - .85*11 = $4.

All else is not equal, however. Fish prefer deeper payouts, and players adjust their play - rightly or wrongly - to the payout structure. Those two factors alone blow Caro's argument to smithereens.

Also, from a "conceptual" standpoint, Caro was looking strictly at the EV of player who are the best at their preferred stakes level. There are second-tier players - Lederer is a good example - who just aren't going to win unless they get very lucky, but who are good enough to grind out an income nevertheless. These players are demonstrably better off playing survival poker in most payout structures.

5/07/2009 11:55 AM  
Blogger dbcooper said...

Interesting post. Love the idea of a winner take all WSOP bracelet event.

5/07/2009 12:40 PM  
Anonymous Angry_Bert said...

Hey Shamus - great post!

To me it all seems like the time to worry about "conceptual problems" is before you enter a tournament. Once you enter it is what accountants (not that I am one) would call a sunk cost - meaning you can't get the money back that you just spent. You explain this point well in your last paragraph by saying "you can’t go back and cash them in".

Also, there are other reasons that people enter a tourney - they get excited just thinking that they might win 1st place (even if it's a very slim chance), they like the limited downside risk (the price of the buy-in), etc. Economists would say they get "uility" or enjoyment just out of playing - even with a very little chance of winning.

With that in mind I think some of the other comments were on point too -> fish like fat payout structures - hence the prize pools are bigger.

I say play if you want to play! Or Don't! When I play - I like to play with Fish!

5/07/2009 3:20 PM  
Blogger F-Train said...

The problem with Lederer's concept is that "just cashing" is a losing strategy over the long haul. Consider that in most tourneys, 10% of the field cashes. So on average, you should be cashing at least 10% of the time.

Now of course if you're a better poker player than average, you might cash as much as 15% of the time. "Just cashing" without making the final table will probably pay you anywhere from 2x to 7x your buy-in. Let's say it averages at 4x (because of the weighted distribution of prize money, you will make a cash on the smaller end of the spectrum more often than the larger end). That means 85% of the time you lose x, and 15% of the time you win 4x. Which gives us this equation:

Results = .85(-x) + .15(4x)
Results = -.85x + .6x
Results = -.25x

If you don't make aggressive plays for chips, it's very difficult to make a deep run to the prize spots where most of the money is paid and over the long term will lose money without those deep finishes.

5/08/2009 1:46 PM  
Anonymous Anonymous said...

I've been toying with the idea of calculating how far you should strive to go into the money. How much money do you stand to make for how many hours of work/play? Is it worth it? With tournaments seeming to follow comparable pattern, depending on the number of players, blind structures and other factors known in advance, especially online. This is based on my observation that MTT have a fairly predictable length.

5/13/2009 4:14 AM  
Blogger TiocfaidhArLa said...

A committed Casher - I started with a BR of just $25 and have built that up over the years. I'm not particularly risk averse or disciplined. Just love the game and am taking care not to become a "gambler".

Most of my winnings have come from Tournaments, but most of my skills have been acquired in Ring games.

My first priority is always to cash and according to OPR, I have a 24% ITM rate. (The top players exhibit rates closer to the 15%). Along the way, I am always opportunistically looking for spots to take advantage with solid (not tight or nitty) poker.

Once in the money, I don't go out of my way to immediately coin flip to build a stack. In fact, ESPN Poker Edge just had an episode on the rate of exits in the WSOP when the bubble bursts. It's the same online. Sit for a few orbits and you'll be amazed how you can climb the ladder.

My Final Table rate when ITM is 54%. These figures plugged into F-Train's calculations would change things, I suspect.

Erwin, good luck with your thought processes. I too question the equation in terms of rate per hour and if I didn't Final Table with a reasonable frequency, couldn't justify Tourneys.

The truth is that I love poker and table time is both enjoyable and more experience for me. We may need to factor that aspect into the equation too :-).

Perhaps Tourneys can get a Chapter in the next release of the Psychology of Poker.

7/29/2009 2:57 AM  

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