Poker News

Mike Caro is the ‘Mad Genius’ of Poker

Before we move along in the next issue with our questions and answers, let me correct a mistake two columns ago. The concept explained in the text was valid and important-but the figures given in the question and answer didn’t compute.

Lots of readers pointed this out to me. The first was Latchmie P Soondarlal. The most vociferous was Wayne Vinson, who titled a feature article on his excellent CardSharp.org web site: “Mike Caro Inserts Foot in Keyboard.” Not the first time, either, Wayne. But since I pride myself on career accuracy, let’s reexamine the question and answer. Here is the flawed Q & A as I sent it to Poker Player.

Question 5: You’re at the final table in a proportional- payoff tournament. Three players remain. First place pays $100,000, second place pays $50,000, and third place pays $25,000. You’re in the big blind holding Qf Qs. The total chips in play amount to $300,000. Blinds are $5,000 (small) and $10,000 (your current big blind). You started the hand with $110,000 and each of your opponents began with $95,000. The player in the dealer position moves all-in and the player in the small blind calls. Now what?

You should immediately fold! If you make it a threeway scramble, it’s hard to say what your exact chances of winning the pot are. If you do claim the pot, you’ll win the tournament immediately. While it depends on the traits of the opponents, a good guess would be that you’d win 40 percent of the time and each opponent would win 30 percent of the time. That sounds like a great deal for you, but it isn’t.

Let’s do the math. If you play and win, you pocket $100,000. If you play and lose, you share half of the total $75,000 second and third place money-$37,500. If you prorate those chances, the amount of prize money you average by calling is $62,500. That’s better than $58,333-one-third of the $175,000 remaining prize pool. So, by calling, you’ll fare better than you had expected to prior to this hand.

Better still

But you can do better still by folding! If you fold, there will be just two of you competing for the remaining $150,000 in prize money. In tournament chips (which are much different than actual money), you’ll have $100,000 left, having surrendered $10,000 as the big blind. Your lone opponent will have $200,000. For simplicity, we’ll ignore the minor significance of who takes the next blind. Mathematically, your chances of winning are pretty much proportional to the total chips you control. So, you have one-third of the chips and, thus, you should expect to be crowned champion in similar cases one-third of the time.

Fine. So one-third of the $100,000 first-place money is $33,333.33 and two thirds of second-place $50,000 is also $33,333.33. This means that by folding, you’ve increased the theoretical value of your cash-out to $66,667. That’s more than $4,000 earned by folding.

In this example, you should probably play a pair of kings or aces, but not queens. There are some situations where you shouldn’t even play a pair of aces! And, of course, we could quibble about whether your pair of queens will win more or less than 40 percent of the time-and against some loose players, it’s correct to call. But that’s not the point. The point is that you should often avoid committing your chips to a pot in the final stages of a poker tournament when someone else is likely to be eliminated.

End faulty Q & A.

So, what’s wrong with that? The figures. I’ve made this same point many times in print and at seminars, using figures that worked. Those don’t. As you can see from the words, it was my intention to choose an example where you would be eliminated from the tournament if you called and lost. But actually-in the example given-you’d still have $15,000, with second place secured and 5 percent of the chips in your quest to conquer the remaining player heads-up.

If you figure those chips have a chance of winning commensurate with their tournament value, out of 20 attempts you’d still win first place once and take second place 19 times. You’d never finish third by calling, unless the two opponents happened to split the pot and you subsequently were eliminated first. Ignoring thatremote possibility, the correct math works out this way…

If you call, you win 40 percent of the time, claiming the $100,000 first prize. You lose 60 percent of the time, taking first place one out of 20 times and always getting $50,000 for second place otherwise. So, by calling and losing, your average winnings are $52,500. That means 60 percent at $52,500 and 40 percent at $100,000, which averages $71,500 by calling. Folding leaves you with $100,000 in chips (having lost your big blind). You then face a heads-up struggle against a single opponent holding $200,000 in chips.

Arguments about player ability and blind position aside, you can figure to win one-third of the time and lose two-thirds of the time. And that all figures out to a payoff expectation of $66,667-as correctly stated in the quiz.

But you make $4,833 more by calling. Because my figures were off, the answer I suggested was wrong. But, wait! The concept stands. You only need to jiggle those numbers a little to make folding the correct choice. You’ll find similar (but correct) examples of this in my books and other columns. All are extreme examples and they are simplistic in order to illustrate the point that there are very many times late in a proportional payoff tournamentwhen you should sacrifice what may seem to be a profitable call, folding instead. You do that because you’re hoping opponents will eliminate each other while you sit back and collect extra prize money.

Remember that, late in a tournament, big hands aren’t as strong as they seem when two or more opponents are already involved in the pot with a good chance that one will be eliminated.

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