Is eliminating players from tournaments worthwhile?

• Mike Caro   Exit

This article first appeared in Card Player magazine.

If you were asked to name things that comprise the universe, which ones would go at the very top of your list? Tough question, right? Everything is part of our universe, whether it’s a physical object or an emotion. Galaxies are part of the universe. So are black holes and peanuts, toothpicks and battleships. So are feelings of anger and of contentment.

Gee, the more I think about it, the more I realize how many choices you have. There must be more than a hundred. When itemizing all the things that make up the universe, it’s hard to decide what you might list first. But if you’re like most typical Americans, one thing almost surely will be among the first five things that occur to you. What is it? OK, I’ll tell you, if you really want the answer, but you’re going to feel really stupid for having to ask.

Near the top of almost everyone’s list of things that comprise the universe is this: Strategy for poker tournaments. Don’t feel bad – I know you meant to say that. Everyone has a mental block now and then. Anyway, just the other day, I was thinking about this important piece of the universe. And it occurred to me that there exists a popular tournament concept that’s completely wrong!

A terrible tournament concept.
The incorrect concept is: You should almost always seek to eliminate opponents in a percentage-payoff tournament. The thinking is that the more players you can get rid of, the closer you are to the money. After all, if prize money will go to only the top eight finishers, then if you can eliminate all but eight players right this second, then guess what? You’re in the money!

For this reason, most serious players believe that it’s worth a sacrifice to eliminate an opponent. And, actually, that’s theoretically correct. But what players don’t seem to realize is that often the sacrifice they should be willing to make is a very small one. In fact, the adjustments you can correctly make in an attempt to knock a player out of a tournament in the early stages are so insignificant that they should rarely affect your decision. That’s important, and I’m going to repeat it: Early in a tournament, you should seldom change your strategy in an attempt to eliminate an opponent. Let’s straighten out the misconception once and for all.

Not long ago, I’m in a seven-card stud tournament and, by the second round, one player – I’ll call him Tim, because that’s what everyone else calls him – has experienced such misfortune that he commands less than $200 worth of his original $1,000 in tournament chips. I have somewhere around $600 remaining. The betting limits are currently $40 through 4th Street and $80 after that. Tim finds himself heads-up against me at the river. The pot is small. At this point, he has $150 in front of him and decides to make an $80 wager.

The opponent, an extremely knowledgeable player with a charming disposition – OK, it was me – thinks and decides to call. On the showdown the bettor has a pair of kings and I have tens-up.

Some second guessing.
Immediately, the woman to my right starts complaining nonstop, "How could you let him survive? Why didn’t you raise and put him all in? He’s going to come back and beat you. You could have knocked him out of the tournament!"

And the dealer says, trying to lighten the tension, "Maybe they’re friends." I know, you think that was an inappropriate remark for a dealer to make. Some players would have gone ballistic hearing those words, but I never let things dealers say annoy me. They have tough jobs and once in a while things tumble from their lips that don’t sound right. Happens to all of us.

I just reply, matching the dealer smile for smile, "Well, Tim does look like he’d make a good friend. Maybe he’ll be nice and not bluff me in the future. Favor for favor, if you know what I mean."

My attempt at friendly sarcasm wasn’t satisfying the woman on my right. "You had an obligation to knock him out of the tournament. It’s not fair to the other players when you play soft."

Of course, I hadn’t played soft at all. In fact, I had almost not called the bet. If I hadn’t, then the player would have had hundreds of dollars more in tournament chips, rather than the $70 I had left him with. Had I raised in an attempt to knock him out, I would have risked almost a full $80 bet ($10 short) in a situation that barely justified a call. Looking back I figured that I would have lost three out of four times had I made a similar call forever.

If I assume that my opponent would have always called and my handicapping is correct, that means that for every four raise attempts, I would lose $70 three times and win $70 (eliminating the opponent) once. That translates to a loss of $140 every four attempts or $35 per attempt. What this means is that I would need to sacrifice $35 on average if I made an attempt to eliminate this opponent. Of course, there are other factors to consider: The raise might cause Tim to fold a better hand and Tim might not call the raise, among others. But let’s just assume Tim is always going to call my raise and that I’m a 3-to-1 underdog. That way, we can simplify and accept the $35 projected cost as valid in order for me to make my point.

So, let me ask you a question: Would it have been worth $35 to me to attempt to knock Tim out of the tournament? Remember, that is the cost of the attempt, not the cost of eliminating him. By my prediction (although he would have lost, as it turned out) I would have won only a quarter of the time.

The woman to my right certainly must think it was worth $35, because she continues her critique, "You wrote that you should always do everything possible to eliminate people, and then you have the chance and you don’t do it."

"I see your point," I respond as politely as possible. "But you might have me confused with someone else. I don’t remember ever writing that."

The truth about eliminating opponents.
The truth is, you should seldom make this type of raise with anything but a major advantage, especially if it will cost you a significant portion of your stacks. Even if you have a great deal of chips and your opponent has only a few, it is not incumbent upon you to put that player all-in in hopes of eliminating him. Also, it is not required that you make a "courtesy" call when you have a large stack and your opponent puts himself all-in for a pittance. The later it is in the tournament, the more beneficial it is for you to eliminate opponents. Early in a tournament with, say, 201 players remaining, there is very little value in taking the worst of it in an attempt to knock out an opponent.

You need to ask yourself this question: How much will this sacrifice cost me? Let’s say it’s $35 in tournament chips, as in the previous example. Then ask yourself how much you will gain from eliminating an opponent. Wait! This is tricky. In simple (but not precisely accurate) terms, you will actually gain on average about 1/200th of the value that eliminating this player will have to the entire field of competitors. In other words, whatever eliminating this player adds to the expectations of all players, you – being only one of 200 then remaining players – will profit only the same as everyone else will. So, here’s how it appears: If it’s costing you $35 in chips, then the value of eliminating this player right now needs to be at least $7,000 (200 times $35). But, wait! Since I’m only going to succeed in eliminating Tim once in four similar raises, the value of eliminating him needs to be four times as large as my sacrifice. That means, the value to the entire field of players of eliminating Tim right now needs to be $28,000 in tournament chips. You read it right.

You might see this better if you think of it as costing $140 to eliminate Tim. That’s because on average, it will take four similar tries, each costing $35 in sacrificial money, to get him out. Since 1/200th of $28,000 is $140, and that should just about balance your books.

If you’re beginning to suspect that the value of eliminating Tim cannot possibly approach $28,000 in a tournament that has roughly $100,000 in total chips, I’m glad. You are seeing how silly this sacrifice-to-eliminate opponents advice can be in early stages of a tournament.

Now it becomes clear why the advice to always try to knock out opponents is bad. Most players sacrifice too greatly in their attempt to send opponents home early. The logic I’ve just presented is not quite pure, though. Small stacks often benefit more than large ones when an opponent is eliminated. This is easy to see at the final table, because small stacks move up in money position when they might otherwise have been eliminated.

One of the best things that can happen to all remaining players is for two opponents with huge stacks to collide and one be eliminated. You then face the same number of opposing chips, but you have fewer opponents to contend with. Contrary to the opinions of some, this does not make it harder for you to win a tournament. Your chances of winning first place are about the same with $10,000 vs. two players each with $45,000 as vs. one player with $90,000. In each case – ignoring other minor factors which I’ve discussed elsewhere – your chance of winning are about 10 percent. That’s because you have 10 percent of the chips. Of course, your chance of taking second place are much improved against the single opponent – in fact your chances are absolute. That’s why you want big stacks to go to war. It’s also why – when you have a lot of chips – you do not want to go to war with another big stack.

Won’t you feel silly if they beat you?
The big argument players give for wanting to eliminate an opponent is: "They might come back and beat you." So what? They also might come back to beat somebody else. Besides, they’re more likely to beat you if you call and lose, because then they have more chips to build from and to attack you with. Why is it so much more tragic if a person you might have eliminated comes back to beat you then if someone else knocks you out of a tournament? When you’re out, you’re out.

There is no logic to the popular eliminate-players-at-all-costs advice. The only factor that matters is whether sacrificing your normally profitable strategy in an effort to eliminate an opponent will add or subtract from your expected payoff.

In the late stages of a tournament, where fewer players share large benefits when a player is eliminated, it’s often worth making some sacrifice. In the early stages, it isn’t. That’s the simple truth. You may not like the sound of it, and it may run contrary to everything you’ve heard before. But it is the truth, nonetheless.