Are slower tournaments better?

(Photo found here.)

In the March, 2010, issue of Bluff magazine, Mike Caro devotes his monthly column to a discussion of his "least popular poker opinions." Shamus discussed one of these--the four-color deck--in a recent post. On that point, I think Caro is unarguably correct that the only real reason people resist using it is that it's not what they're used to. I wish casinos would just implement the change and put up with the grumbling, because I think it would last only a few days, and then we'd all be less prone to making suit-identification errors.

But I was more intrigued by a completely different controversial opinion Caro expresses in this column:

Some players like long drawn-out tournaments that last for days. When I joined
with Foxwoods Casino to present the first World Poker Finals (which I named), I
guaranteed that all except the major events would be complete in four hours and
fifteen minutes. We held three, sometimes four, events every day! Those who say
longer events are more profitable for skillful players are wrong. There's more
profit in faster paced events, if you can play more of them, because the
increased luck factor in each short event is overwhelmed by skill when measured
over many events combined. It's an unpopular opinion, but true nonetheless.

I've read enough of Caro to know that he doesn't just pull opinions out of thin air. Unlike most of us, he tends to put a lot of thought and research into poker questions before spouting off, so I'm inclined not to brush off his assertion here lightly, even though it goes against the grain of everything I've ever heard and thought on the subject. I wish he would take a whole column to flesh out the reasoning, perhaps with some representative estimates of how a skilled player's overall EV (expected value) differs between a single long tournament and a series of shorter ones.

Suppose you were planning to devote a full day to live tournament poker, and you could choose either a single event that would last 12 hours if played all the way to the end, or three consecutive events, each of which would last four hours. Which would be a better choice, if your skill edge over the field is the same for either option? I'm not sure.

Sometimes the best way to approach a conceptual question like this is to consider the extremes. Here, for instance, we might consider a tournament in which the structure was so slow that the thing would take a year to complete, playing eight or ten hours every day. At the other extreme, we could consider a tournament that was structured so aggressively that it would be over in an hour. (You can't take this end of it too far, because when you reduce it to a single hand, it becomes purely luck. The only possible way to win is to move all in before the flop with whatever you're dealt and hope your hand improves to the best one.) Would the player doing eight or ten of these things a day for a year have a long-term EV that is higher or lower than the guy sitting all the way through the ultra-long event? Conventional wisdom seems to be that it's lower. Caro seems to be arguing that it's higher. I don't know that that's wrong, but it's not obvious to me that it's right, either.

Here's a consideration that seems to support Caro's point: There are a good number of people who make great money online playing nothing but single-table sit-and-go tournaments. Certainly the skill set for such things is somewhat different from that required for the slowest-structured multi-table tournaments, but I don't think there is any doubt that skilled players will win more money in the long run. If the pros in these games--who are no fools--knew that they would have a higher long-term EV by simply switching to longer tournament forms, it seems to me that they would.

Let me approach it another way. I'm going to bet a million dollars on roulette. I can either do it one dollar at a time a million times, or all one million in one shot. Which way has the higher EV? Well, the answer obviously is neither; they have exactly the same EV. What differs is the variance. Suppose every bet is going to be on 17. With the all-at-once method, I'll either leave down a million or up $36 million. That's pretty extreme variance. With a million separate bets, by far the most likely outcomes are those that are close to the statistically predicted loss rate, and the likelihood of deviations from that can be calculated by a binomial distribution. I.e., I'll probably finish with about 5% less than I started with. It would be virtually impossible that I would end up with the magnitude of win or loss that the one-shot approach will give me, and astronomically unlikely that I would come even close to either of those extremes. The only two variables that govern the overall EV are the total amount bet and the odds/payout (i.e., the EV) for each bet, which in this game remain constant.

My hunch is that the same is basically true for poker tournaments. That is, to go back to my first example, one's overall EV for the day is the same with three shorter tournaments as with one longer one, assuming the total amount invested is the same and one's edge over the field is the same for both. For my extreme cases, I would similarly venture a guess that the long-run EV is the same. (A caveat: I'm still not sure about this point, but it may be that if there is a considerable amount of down time between events after one busts out early then the EV drops somewhat, because when one isn't playing one isn't exploiting a skill advantage. So for theoretical purposes, one might need to assume that there is another event to go to immediately after being expelled from the shorter events. This is effectively available online, not so much in brick-and-mortar casinos.)

Interestingly, though the EV doesn't change (if I'm right), the variance does, but in a way opposite of what you might think. By the same logic that we used in the roulette example, the guy entering the shorter events will tend to end the year with a profit that closely reflects his skill advantage, while the guy playing the single, long event will probably end up with either nothing or a huge payday, neither outcome matching his edge. (I say that his payout, if he makes the money, will be huge because we have to assume that the buy-in for this event is equivalent to the sum of all the buy-ins that his hourly-event counterpart is investing in his tournaments all year long. That is, the year-long event has to be more expensive than any real-world tournament ever has been. Hence, the pay schedule will be unbelievably rich.) In other words, over the long run, the guy playing a bunch of short events will have greater predictability--lower variance--from one year to the next than the guy playing one long event every year.

My best guess, then, is that Caro isn't right to say that the EV of a bunch of shorter tournaments is higher. But I had been making an uncritical assumption that the EV would be lower, and on reflection I think that's not right, either. I think they are the same, given the constraints I've mentioned here. Still, I don't really know, and I'd be happy to hear cogent arguments for or against my tentative view.