More questions

Phil Gordon interviews Howard Lederer about the apparent death of the Reid bill on ESPN Radio here.

At about the 21:30 mark, Gordon asks Lederer when he first became aware that a 15-month blackout period would be part of the bill. Lederer says, casually, "A couple of months ago." Aha! This would seem to confirm that (1) Reid had this thing cooking for a while, and (2) prior to the election he had tipped off some insiders about what was coming.

This may be the answer to the question I asked last month: "What am I missing?" Reid had been an opponent of online gaming, so it made no sense to me that in the closing days of the election we suddenly heard from Lederer, Andy Bloch, and Barry Greenstein that Reid would be a champion for online poker.

But, of course, this answer (assuming my inferences are correct here) just leads to more questions. First among them is why Reid kept this under wraps. He apparently recruited poker insiders to speak up for him in an effort to win votes of poker players. So why not publicly announce what he was planning to do?

Second, I'm still completely baffled by the actions of the Poker Players Alliance. One would assume that if Lederer knew about Reid's intentions prior to the election, then so did the PPA. But when the Reid bill was announced, the PPA sure as hell looked like it was caught completely off-guard, with its first public statement being utterly devoid of any indication of support for the proposal. Today the PPA did a press release wagging its finger at Congress for not passing the legislation. Uh, well, if this bill was such an obvious win for poker, why was your first statement on it so carefully neutral? And I still continue to wonder what then happened in the subsequent 24 hours to change that bland "we dunno about this thing" attitude into salute-the-flag enthusiasm? Something very strange was going on behind the scenes there, and they're simply not being candid about it. Hey, PPA: Candor is a prerequisite for trustworthiness. Your credibility is awfully low here.

Yet another question is the overall timing. The UIGEA passed in 2006. What took Reid so long to decide to do something for poker? He gave himself very few opportunities for passage, waiting until so late in the congressional session. Was the idea for the bill a last-minute thing when he realized that he was polling behind Sharron Angle, and he became desperate to attract more votes? If so, how strong is his commitment, now that he is safe for another six years?

As an aside, you can make a fun game out of counting how many times Lederer says "y'know" during this podcast. Caution: Do NOT make this a drinking game.

Folding K-K

I was struck by the juxtaposition and similarity of two things I've read within the last 24 hours from completely different sources.

First was this from Doyle Brunson's blog, October 22, 2008:

The Bellagio tournament is the greatest! There is no dinner break and
you can be home in bed by 10:00 pm if you choose. It is really good if you
are a little long in the tooth. I had a decent 1st day and am sitting with
$95,000 in chips. I could have had 50,000 more but I threw away 2 kings
preflop. I was convinced the other player had two aces and couldn’t
believe when he showed two jacks after I passed. That is the fifth time I
have passed two kings preflop in tournaments. I think this was the first
time I’ve been wrong. Oh well, who knows, he might have caught a jack and
really crippled me.

Then I was reading Matt Lessinger's column in the November 5, 2008, issue of Card Player magazine. He writes:

The point I am making is that going all in preflop with K-K against A-A is
clearly an acceptable way to lose a tournament. There are some rare instances
when you can get away from K-K preflop, perhaps very early in a major
tournament, but not often. For what it's worth, I've folded K-K preflop three
times in 12 years, and each time I was correct, but that demonstrates how rare
you can expect to do it. If you start looking for too many situations to fold K-K
preflop, not only will you end up folding it as the best hand too often, but you
will be adopting a mindset that virtually guarantees terrible tournament
results.

One of the best K-K laydown stories comes from Phil Gordon. In his Little Green Book, he describes in great detail the considerations that led him to fold K-K at the final table of the World Series of Poker Main Event. It's such a good story that I scanned it in above. (It's too long to type, and if it's within the "fair use" copyright exception to type it in--as I believe it is--it should also be OK to scan it in.) Go read.

And here's one more Main Event K-K laydown story, this one from 1992, as told in All In: The (Almost) Entirely True Story of the World Series of Poker, by Jonathan Grotenstein and Storms Reback, p. 170:

As was becoming increasingly common, the most exciting poker of the entire
tournament was played when there were seven players left, all desperately hoping
to make it to the final televised table, which only had room for six. Hamid
Dastmalchi, a longtime professional who moved from his native Iran to San Diego
when he was seventeen, was the chip leader. Dealt pocket kings, he raised before
the flop, only to be reraised by Mike Alsaadi, a professional from Las Vegas,
who pushed all of his chips into the middle.

Hamid stared across the table at his opponent. Most players, especially
those blessed with the chip lead, would call such a bet without thinking twice.
Pocket kings, after all, are the second most powerful hand in Texas hold'em.
Hamid, however, thought back to a comment Mike had made earlier about how badly he wanted to make it to final day. And Mike wasn't just reraising, he was
reraising the chip leader, who was more than likely to call his bet.

"What do you think I've got?" Mike asked him.

"I know you've got two aces," Hamid replied as he threw his two kings into
the muck.

It was an incredible laydown, one that only the top professionals are
capable of making. Confirming the brilliance of the move, Mike showed his two
aces to the crowd.

How many times have I folded K-K before the flop? Zero. How many times should I have done so? Two. That's because in both situations I had enough information to reach the right conclusion from (1) the pattern of raising and reraising, (2) the demeanor of my opponent, (3) the knowledge that he or she had been playing tight and solid, (4) the knowledge that these opponents both knew the same about me, and therefore wouldn't be making a move on me after I was showing such strength.

In one case, at the Orleans, I lost about $200. The one that really sticks in my craw, though, was at the Golden Nugget. I was sitting on about $600 at the time, and was literally about to stand up and go get a couple of chip racks to cash out my bounty when I saw the kings, and the only player at the table who had me covered was the one who had the aces. I don't remember for sure how the raising went, but he was the one that moved all-in first, a big overbet to the $100 or so that had been my previous raise. I had such confidence that he would not do that with anything except aces that I could and should have written off the $100 and saved myself $500. But I didn't, and when I lost all of that in one fell swoop--the most I've ever lost in a single hand--it was as close as I've ever come to throwing up on a poker table.

In both of those cases, I can clearly remember thinking that there is no way that this particular person would be doing this with any hand except exactly A-A. And my rationale for calling in both cases went no deeper than "I can't fold K-K preflop."

(Note that these were both cash games. I play very few tournaments, and can't remember any tournament situation where folding K-K before the flop would have been reasonable.)

To be clear, there have been plenty of times when I've had kings and knew that I might be up against aces, but the situations were such that calling or pushing (depending on whose turn it was) was still reasonable. That's because of one of us having a relatively short stack, or facing a pretty loose/aggressive opponent who would push lesser hands, or whatever. In those cases, although I haven't kept careful track, my impression is that I'm about 50/50 in the long run--roughly half the time seeing the aces, but the other half seeing queens or A-K or occasionally even jacks. One time it was the other two kings. Those situations don't bother me, because calling or shoving was still the right move under the specific circumstances. They didn't feature the compelling, resounding, tidal wave of you're-in-trouble information that I had with the two instances in which I believe I could and should have folded.

But I've learned from those mistakes, I think. I've thought about them a lot, naturally, and tried to sear into my memory the overwhelming sense I had of confidence that I was behind. My hope is that the next time I get that same sickening realization that A-A is the only hand this particular opponent could have in this situation, I'll have the fortitude to act on that conviction and push my lovely but second-best cards back to the dealer.

Whether I succeed or fail at doing that difficult thing the next time the occasion arises, I shall dutifully report it here.

Three in a row???

Two weeks ago, when ESPN messed up on its weekly "Poker Fact," I thought it would be a one-time thing. They surprised me the next week by doing it again. I would not have believed they could hit the trifecta, but they somehow managed.

This week they say, "When holding any pocket pair, the probability of flopping a set is 11.76%."

Wrong.

The usual way of running this calculation, which is apparently how ESPN's people went about it, is to calculate the probability of the flop not having another of the rank in question. There are 50 cards left, so the probability of the first card of the flop not completing one's set is 48/50. If that happens, then the probability of the second card of the flop also not completing one's set is 47/49. If you have gotten that far without a set, then the probability of the third card of the flop still not completing one's set is 46/48. Multiple those three together (because all must be true simultaneously), and the probability of the flop not bringing a third card to one's pocket pair is 0.882449. Subtract that from 1.000000 (because the flop must either contain another of the rank in question or not), and you get 0.117551, or about 11.76%.

The problem, though, is that four of a kind is not a "set," and the calculation above does not exclude flopping quads. Given that you start with a pocket pair, the probability of flopping quads is 0.2449%, if I've done my math right.* (And if I haven't, please let me know in the comments so I can fix it.)

Therefore, the probability of flopping a set but not quads is 11.7551% - 0.2449%, or about 11.51%. What the ESPN graphic was showing was not the probability of flopping a set, but instead the probability of flopping either a set of four of a kind, starting with a pair in the hole. They are not the same thing.

Be sure to tune in next week for the next exciting installment of "How Many Ways Can ESPN Get the Math Wrong?"

By the way, when starting to write this post, I pulled out Phil Gordon's Little Green Book, which has a handy section of common poker probabilities. It's my usual first place to look for quick answers. But I see that he has it wrong here. On p. 271, he says that if one starts with a pocket pair, the probability of flopping a set is 10.80%, and the probability of flopping quads is 0.20%. Wrong on both points.



*We're specifying that the flop must contain two exact cards. There are therefore 48 cards left in the deck to fill that third spot on the flop. We don't care about the order, so that's effectively 48 different flops that will work. We already know that there are 19,600 possible flops, once we've accounted for the fact that our two hole cards can't be in the flop. 48/19,600 = 0.00244898, or 0.244898%.



Addendum

I just knew I'd mess something up. Every time I've tried doing a math post in the middle of the night (note the time stamp on it), I make a mistake. As one commenter pointed out, I failed to account for full houses. If flopping quads can't be counted toward flopping a "set," neither can flopping a full house. I even noticed Phil Gordon's book separating that out, but then my sleep-deprived brain dismissed it as irrelevant. (I thought so because what flashed through my mind was the pocket pair plus three of a kind on the flop, which I dismissed as not flopping a set.) Clearly it is not.

So what is the probability of flopping a full house if one starts with a pocket pair? Well, that means a flop containing a third of our pair's rank, plus another pair. Hidden among the 50 remaining cards are 12 full ranks. There are 6 different pairs that you can pull from a group of four: C(4,2) = 6. That means that there are 6 x 12 = 72 different pairs that can hit our flop. Each of those might occur with either of the two remaining cards that would make our three of a kind, for a total of 144 flops that meet our specifications for a full house. 144/19,600 = 0.007347, or 0.7347%.

We subtract that from the previously calculated 0.115102 and end up with 0.107755, or about 10.78% for the final probability of flopping a set.

So, to summarize--given a pocket pair, the probability of flops is as follows:

Set: 10.78%. (That's 1 in 9.28 times, or 8.28:1 odds against.)
Full house: 0.73%. (That's 1 in 137 times, or 136:1 odds against.)
Quads: 0.24%. (That's 1 in 417 times, or 416:1 odds against.)

Set or full house or quads (which is what ESPN's graphic was actually about): 11.76%. (That's 1 in 8.50 times, or 7.50:1 odds against.)

(Note that "full house" here refers only to pair in the hand, third of that rank on the flop, plus a pair of a different rank on the flop. You can also flop a full house with a pocket pair and flop of three of the same rank. But since this possibility does not include the third card to the rank of one's pair, it does not enter into the calculation here. For completeness, though: There are 12 full ranks left in the deck. Each rank has three different combinations that can make up a single-ranked flop, because C(4,3) = 4. So there are 12 x 4 = 48 possible flops that would be three of a kind on the board. 48/19,600 = 0.00244898, or 0.24%. By strange coincidence, this is the same probability as flopping quads, starting with a pocket pair.)

Phil Gordon gives these numbers as 10.80%, 0.70%, 0.20%, and 11.80%, respectively. This is a little peculiar, in that he appears to have done the math correctly, then rounded off to the nearest 0.1%, then later decided to make it look more precise and added in an extra 0 digit at the end. That last step is the part that isn't right. If he had left the numbers as 10.8%, 0.7%, 0.2%, and 11.8%, he would have been fine. My apologies for incorrectly faulting his set calculation in the original post. It appears that his only error was in rounding, then "unrounding" by adding zeros.

Strangest "Poker After Dark" ever

Last night's episode of "Poker After Dark" was the strangest ever. It had little to do with the poker. The whole thing was dominated by a weird prop bet that started as a seemingly trivial bit of small talk.

Phil Gordon said to Howard Lederer, "I saw your mom playing poker at the Mirage yesterday." Lederer doesn't believe it. And it eventually turns into a $1000 bet. Gordon is so convincing that Robert Williamson takes $1000 of the action, too.

Before the bet is actually placed, though, Gordon's story changes several times, and gets embellished. First he decides that it was at the Venetian, not the Mirage, and it might have been two days ago, rather than yesterday. And maybe she wasn't actually playing poker, but was just in the poker room.

Then there's a big question about whether it was Lederer's mother or stepmother. Both Gordon and Lederer state that Gordon has definitely met both of them, and should be able to recognize either one and tell them apart. But Gordon is confused for a while. Apparently at some unknown time in the past there was a karaoke contest at which Lederer's mother was a judge, and she voted against Gordon. Gordon at first says that this is the woman he talked to yesterday. Then later he says, no, not that one, the other one--so presumably Lederer's stepmother.

Whichever one it supposedly was, Lederer isn't buying it. His mother hates casinos, and won't even go to a movie theater inside of one, so the idea that she was casually playing poker (she doesn't play poker, either) in the Mirage or the Venetian is just out of the question, even though she does live in Las Vegas. Lederer's stepmother does play poker, but Lederer was pretty sure that she was then in San Diego (she does not live in Vegas; I assume, though it wasn't stated, that she lives in New England, where I believe Howard's father still lives and teaches English), and that she would never hit town without calling him. On the strength of those presumptions, he's willing to bet that whoever it was that Gordon saw and spoke to, it was neither his mother nor his stepmother.

But Gordon isn't backing down. In fact, his story gets more specific, which is what draws Williamson into the bet. Gordon says that not only did he recognize the woman in question, but that she asked him if he recognized her. He said, "Yeah, you're Howard's mom," and she confirmed that. Gordon is so certain of all of this that he says he would bet up to $20,000 on it. When others at the table express interest in the bet, he is so confident that he tells them that if Howard will cover their bets, "Back the truck up!" He had temporarily forgotten Lederer's stepmother's name, but when Lederer mentions "Simone," he adds extra emphasis--yes, that's definitely who it was.

Well, after a lot of back and forth (and this is a greatly condensed version of all that took place), they make the bets, somebody gets a cell phone, and Lederer places the call to his stepmother. (They never call his mother; apparently Gordon accepts that it was not she.) She is in Florida (I think that's what she said) and has been for a few days. She has not been in Las Vegas recently. Lederer is careful not to lead the witness; he simply asks her where she is now and how long she has been there, without telling her the back story or that there is money on the line. Gordon speaks briefly to her, too, ruling out the possibility that Lederer is faking the conversation.

He pays up, but remains apparently completely baffled at how he could have it wrong. He suggests that maybe Lederer has set the whole thing up, coaching Simone in advance to deny having been in Vegas. (This seems unlikely. Not only do I not think that Lederer would stoop to that kind of rank dishonesty, but it just seems too looney a thing to set up in the hopes that it would somehow lead to a prop bet.) Williamson seems to believe that Lederer and Gordon conspired to make the whole thing up just to take Williamson's money, which they will secretly split later. (Unlikely, I think, for similar reasons.)

This is a really bizarre situation. I'm impressed that Lederer would have such reliance on his knowledge of the two women in question (particularly his stepmother, who does play casino poker; he was therefore relying solely on the presumption that she would not come to town without calling him) as to disbelieve an incredibly earnest and highly convincing Gordon. Gordon, in fact, was so convincing that Ali Nejad said that if Lederer accepted the bet, it could only be because he hated money. Gordon had me convinced, too. I thought that Lederer was going to get a surprise on the other end of the phone. (I wasn't sure enough that I would have put $1000 down on it, though, especially because of how Gordon's story changed in significant details along the way.)

So what could possibly have occurred in Phil Gordon's life that had him 100% certain that he had had a conversation with Lederer's stepmother the day before, yet be wrong about it? That's the core of the mystery for me. I hopped over to the http://www.twoplustwo.com/ "televised poker" forum to see if there was speculation about this. A reasonably plausible suggestion was made by somebody calling himself "badatmath": "It was probably some lady that had met Phil in a poker tournament or something and when he said "yeah, you're Howard's mom!" she didn't hear what he said, thought he was joking, or just went along with it for some reason."

That does seem to be just about the only possibility that makes sense. Of course, it also requires that she coincidentally happened to resemble Lederer's stepmother, or that Gordon had a brain lapse as to what Lederer's stepmother looks like. Nobody during the show nor online has openly suggested this, but a healthy dose of alcohol in Gordon's system at the time might also be part of the answer. That would also help explain his uncertainty as to which casino this happened in, what day it occurred, which of Lederer's relatives it was, whether she was actually playing poker or just hanging around the room, etc.

Phil Gordon hasn't had any well-known nickname before now. At the close of the episode, the fill-in voice-over commentator said that Gordon, now with some egg on his face, could become known as Phil "Back The Truck Up" Gordon.

All in all, it was a weird but fascinating glimpse into human psychology generally--i.e., how we can trick ourselves so easily, and be much more certain of things that we really ought to be--and, more specifically, into the lives of professional gamblers, and how easily they turn ordinary interpersonal interactions and conversations into betting opportunities. No matter how long I stay in this racket, I can't imagine ever becoming such a gambler at heart that I would act that way. Maybe I still just value money way too much....


Addendum, May 25, 2008

It's actually even a little weirder than I reported above. I'm watching the "Director's Cut" show, where they recap the week's events. In replay, it's clear that I slightly misremembered what Gordon said in his story of the encounter. Rather than him being the one to affirmatively suggest to the woman that she was Howard's mom, he actually says that she offered this: "You remember me. I'm Howard's mom." If he's accurate about that, it effectively eliminates the suggestion discussed above about Gordon saying such a thing and it being unheard or misunderstood or shrugged off by the woman he was talking to. Of course, memory is tricky, and perhaps it did happen as suggested above, and in Gordon's memory he has accidentally inverted who made the identification. (In the twoplustwo thread on this, somebody transcribed part of the discussion, and very specifically quotes Gordon as saying that he's the one who suggested the identification. But just moments ago I saw a replay of another part in which he says that the woman is the one who affirmatively identified herself, so apparently he told it both ways, a detail that I didn't catch the first time around.)

In the post-game interview, however, Gordon remain adamant about who he spoke to. He is mystified about the whole thing, says it's the strangest thing that has even happened to him, and he is headed over to the Venetian to investigate. Perhaps he is hoping to find other people that know Lederer's stepmother and will verify that she was there.

This all transpired several months ago, so I wonder what he uncovered. Gordon has a blog, but he has only posted on it twice in the last year and a half, and there's nothing there. I submitted a question about this through his web site, but I'm not really expecting a response.

Poker gems, #116

Phil Gordon, in this Q&A session on the Freakonomics blog. For the pointer, thanks to Ted at Red Bull and Poker, who in turn got it from uber-blogger Iggy. There are several nuggets here that would ordinarily mean separate posts, but rather than repeat all of this intro stuff, I'm going to break my usual pattern and compile them all into one.


I have a simple theory: change 10 river cards in any poker player’s tournament career and I would bet that they would be a losing tournament player for their career.

I think my game selection skills are just about as good as anyone in the game.
If there aren’t a few guys that are just giving their money away, I don’t play.

[W]hat we do at the poker table isn’t very different than what investment professionals do — we just get our results every two minutes instead of every few months or years.

I’ve never worn sunglasses at the table and I think it looks completely stupid and is unnecessary.

If I had to guess, I would say about 50 percent of the “name pros” you see on television on a regular basis have a negative net worth.

Poker gems, #85

Phil Gordon, as quoted at http://www.pokerblog.com/watching-phil.html, when he was having a bad tournament day (photo from the same source):

I forgot my number one rule of poker. Don't bluff if they're gonna call.