CardSharp

I want to like Mike Caro. I really do. Every discipline needs it’s mad genius, and the man certainly has the hair for the job. But I can’t deny his Poker Player column is making a encore appearance on “Nonsense Debunked”. That’s not a good thing. This week’s nonsense is about tournament bubble play. Here’s the setup in Caro’s own words from the Oct. 1 2007 ‘Poker Player’:

You’re at the final table in a proportional-payoff tournament. Three players remain. First place pays $100,000, 2nd place pays $50,000, and 3rd place pays $25,000. You’re in the big blind holding QcQs. 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 started with $95,000. the player in the dealer position moves all in and the small blind calls. Now what?

You should immediately fold!…

This is a perfectly legitimate question, but Caro’s answer is incorrect in two different senses: it contains mathematical & strategy errors and is motivated by bad poker thinking. The strategy errors get off to a roll as follows:

While it depends on the traits of your opponents, a good guess would be that you’d win 40 percent of the time and each opponents would win 30% of the time.

This is just plain wrong on so many levels. First of all, there’s no possible way you can assign hands to the villains to make the equities 40-30-30. Or even close. In fact 40-40-20 is about as close as you can get. Try it on pokerstove if you don’t believe me. Even if you consider caro’s statement an average over what the villains might have, it’s probably not accurate. This tournament is short stacked – M of between 6 and 7. Everyone should be near-desperate, and at the very least, the guy on the button in steal position is not necessarily sitting on a premium hand. And QQ is at least a 2:1 favorite against a range of hands he would play in that situation – it could be as high as 4:1 if he’d steal with anything there. But of course we’re facing 2 villains, and the second villain has indicated that he has something decent by calling. Not necessarily that much – he’s calling a guy who may well be on the steal. But he probably has a decent hand. Here’s the interesting thing: even if you assign SB a range of TT+,AK hero still has more than 40% of the equity against both of them. If you add in hands like AQ, it’s much more than 40%. So Caro’s “good guess” is in fact not particularly good at all. The only question is whether it’s a little pessimistic or a lot pessimistic.

However, Mike’s error there maybe not that significant to the overal logic. The next error is not small at all.

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 2nd and 3rd place money – $37,500.

Uh, what the hell? That’s totally wrong. If you win, you get $100,000. If you lose, you still have $15,000 in chips left and one of the two villains is eliminated (since they have equal stacks). So you’re always guaranteed at least 2nd and $50,000 no matter what happens. This mistake of course snowballs through the rest of the column and leads Caro to the wrong conclusion at the end.

Now, I realize Mike Caro just made a mathematical error here. It could happen to anyone. But it’s no coincidence that he made this particular error. For some reason it’s become a fad in poker strategy circles to try to come up with reasons to fold big hands on short stacks in tournaments. Almost all those justifications are in fact based in both conceptual and mathematical errors as this one is. I guess it makes people feel smart if they can give a reason to fold a huge hand. But this trend is totally wrong conceptually. When you get a big hand on a short stack in a tournament, the correct play is almost always to thank the poker gods and push your stack in. By and large players are too afraid of elimination and hence too passive in the late stages of tournaments, and this intellectual fad just reinforces that bad play.

I’ve emailed Mike and given him a chance to respond if he’s so inclined. I’ll publish his response verbatim if he does.

Update: Mike has responded

Hi, Wayne –

Thanks for pointing out the error. Others have already brought it to my
attention, too.

I’ve illustrated the same concept in columns and books over the years, using
statistics that (hopefully) worked. The chip counts I chose for my Poker
Player column didn’t work. The intent, made obvious by the accompanying
text, was to choose figures so that the decision-maker would be out of the
tournament if he called and lost. As you correctly say, using the figures I
provided, calling and losing would still leave $15,000.

It’s simply a bad example. I’ll correct it in a coming column.

I guess where I disagree with you is on the concept itself. It’s clear to me
that there are many times when you should fold toward the end of a
proportional-payoff tournament and hope opponents eliminate each other. It’s
pretty easy to come up with real-world examples. Well, I take that back –
apparently it’s not easy for ME to come up with examples.

While I’m proud of my 30-year record for conceptual accuracy, I’m sure you
could make a career out of finding glitches or ambiguity in my published
words on poker. I always feel honored when others point out mistakes. Keep
up the great work and vigilance.

Straight Flushes,
Mike Caro

I still think my basic conceptual point is sound.  I’m going to email Mike back about this, and I’ll probably have more to say in the future.