Mrs. Lederer suggested that I should join her for the Imperial Palace Sunday night mixed game last night. I hadn't seen her yet on this trip to Vegas, so I agreed.
One remarkable hand was making the nuts in badugi. The goal is to get one card of each suit, and have them be as low as possible. I started with A-3-4 in three different suits, plus one useless card. I needed a low spade to make a strong hand. I invoked my new-found powers of card-calling, focusing specifically on the deuce of spades. I slid my dud card to the dealer, and he gave me in return...the deuce of spades! It's the first time I've ever made the best possible hand in this game.
The other remarkable hand was in ace-to-five triple draw. I started with four clubs, traded in my mismatch, did my mental voodoo to get myself the ace of clubs, and bingo!
That all by itself wouldn't be so remarkable, but Mrs. L. ended up drawing the king-high club flush. Between us, our ten cards consisted of ten of the 13 clubs in the deck:
I don't even know how to go about calculating the odds of that happening, but they must be pretty long. I'm amazed that she somehow knew not to raise on the last street (when she finally made her hand), and lost only one more bet there.
The only other even remotely interesting thing that happened was that when she went up to her room to get a sweatshirt (it was cold in the poker room), I swiped three stacks of $1 chips from her and hid them in my lap. I wanted to see how long it would take her to notice. The problem was that she took her sweet time about getting back, making some other stops along the way, so I ended up with about 15 minutes of paranoia that the surveillance people had seen me do that and security would be showing up any second to confront me about my theft. Fortunately, that didn't happen. And it only took her about five seconds to notice that she had been looted, so I didn't even get much fun out of my juvenile little prank.
Everybody has heard of dogs playing poker, but apes? Apparently they have some characteristics that would be useful to the game, according to two news stories of recent research that I saw today.
In the first, scientists found that all four species of the great apes are capable of making sophisticated risk/reward decisions. When presented with a choice between a small piece of banana with a known location or taking a chance on lifting one of several cups in the hope of finding a larger piece, the apes make their decisions based on the probability of success and the discrepancy between the size of the small and large piece. The larger the hidden piece, the more risk they are willing to take to find it. Sounds like calculating pot odds to me.
In the second, researchers found that chimps in the wild take into account whether the other chimps already know about a danger before deciding whether to sound a vocal alarm. Awareness of other players' states of knowledge is a critical poker skill. Was that guy here when I bluffed in this situation 30 minutes ago? If so, was he paying attention, and will he recognize that this hand is very much like that one? It seems that chimps have at least the rudimentary ability to process this kind of information.
In both of these traits, I'd have to say that they exceed the capacity of at least some human poker player, who display zero ability to perform such complex tasks.
A political blog post I was reading today (here, in case anyone is interested) quoted something by Honest Abe about gamblers. It interested me enough to track down the original, which, thanks to Google, is almost ridiculously easy these days.
It comes from his speech to the Young Men's Lyceum of Springfield, Illinois, January 27, 1838, which can be found here. Lincoln is warning of the dangers of the increasing arbitrariness of mob violence in retribution for alleged crimes.
In the Mississippi case they first commenced by hanging the regular gamblers — a set of men certainly not following for a livelihood a very useful or very honest occupation, but one which, so far from being forbidden by the laws, was actually licensed by an act of the Legislature passed but a single year before.... Abstractly considered, the hanging of the gamblers at Vicksburg was of but little consequence. They constitute a portion of population that is worse than useless in any community; and their death...is never matter of reasonable regret with any one. If they were annually swept from the stage of existence by the plague or smallpox, honest men would perhaps be much profited by the operation.
Gee, thanks, Abe! Appreciate the compliment! Care to know what I think of members of your professions, i.e., lawyers and politicians?
I just stumbled upon a new (at least I think it's new) show on the Discovery channel. It's called "Best in the Business." They design competitions specific to the skills of any given profession or occupation. So far I've seen their segments on excavator operators, grocery baggers, oyster shuckers, and blacksmiths. The program is hosted by Ben Bailey, best known as the driver-questioner on "Cash Cab."
It seems obvious to me that they could put together a competition for poker dealers. Some sort of crazy card-pitching contest. Fastest to accurately count a table full of poker chips. That kind of thing.
You can find instructions for submitting a demo video here:
I'm sure if they get enough submissions from poker dealers with interesting personalities and flashy skills, they'll consider putting together a segment showcasing the best.
As the guy across the table reluctantly called the four-bet all-in from the rock who he knew probably had aces or kings, he muttered, "This is the most overrated hand in poker." I was in Seat 1 next to the dealer, and said, "Sounds like ace-king to me." Dealer said, "Yep." And it was as we all thought: His A-K to her K-K, neither improving.
My very next hand I had 7-2 offsuit, and was about to flash it to the dealer and say, "No, THIS is the most overrated hand in poker." But right then he was busy telling somebody something, so the moment passed. I still wanted to do it, however, so I began summoning up my willpower to make myself get another 7-2 offsuit on the next hand. I concentrated. I focused my third eye. I channeled my chi through my shakras. I beamed my Kirlian aura at the electrical energy surging through the auto-shuffler to direct its activities. I remembered "The Secret" and let only positive 7-2 thoughts flow through me. I prayed to fourteen different major religions' dieties. I sent my spirit animal (it's a porcupine) on a vision quest to fetch me a 7-2. I called on the Ghosts of Christmas Past, Present, and Future. I scribbled 7-2 on a piece of paper, quickly burned it, and scattered its ashes to the four winds. I gotta tell you, all this woo-woo stuff is hard work!
Drumroll, please. The hand ended, the dealer pulled the next deck out of the shuffler, I got my two cards, checked them, and there it was. I had done it. I had successfully willed myself a second consecutive 7-2 offsuit. And there was with the angels a multitude of the heavenly host praising the poker gods.
As the cards I had called into my possession headed to the muck, I flashed them to the dealer and delivered my line. It was a dud. Seat 10 had already called, so I had to be sure he didn't see, which means that I'm not sure the dealer saw or was even paying attention to either the cards or what I was saying.
But it doesn't matter. It was a lame joke to begin with. What matters is that I have proven that I have learned how to harness the unseen forces of the universe to bring me whatever cards I want on demand.
Now I must remember to use my powers only for good, never for evil.
Today I finally had some time to sort through the rest of the hundreds of pictures I took during my recent week there with Cardgrrl. Though I had a wonderful time, the photographic record of it is pretty paltry, once you narrow it down to the shots that look halfway competent.
One afternoon we spent at the New Mexico Museum of Natural History and Science. Like the zoo, this surprised me for being a well-done place, given the small population it serves. What I especially liked about it was that they tried wherever possible to illustrate the principle or time period under consideration by using New Mexico specimens, whether geologic strata or fossils or whatever. There's lots of stuff there besides dinosaurs, but nothing cooler. I mean, how could anything be cooler than dinosaurs, right? So the only interesting pictures are of....
I've already mentioned our day at the zoo. After taking a lot of time with the gorilla photos Saturday, today I sorted through the remaining shots and found only a handful that even show decently what was being photographed, and trashed the rest. None of them will have the editors of National Geographic frantically searching for my phone number to offer me a job.
That same evening, we strolled through the adjacent Botanic Garden for its annual "River of Lights" exhibit. They have hundreds of arrangements of Christmas lights like the ones that follow. All very pretty, but extremely hard to photograph well.
As I mentioned last week, Cardgrrl and I spent an afternoon at the Albuquerque Zoo, which is surprisingly large and nice for such a small city. (Albuquerque proper is about 500,000 people, with a metropolitan area of only about 900,000.) I think we lingered at the gorilla exhibit for nearly an hour, mesmerized by these amazing animals.
I highly recommend visiting Cardgrrl's photo essay on the experience. Her words and photos do much better at capturing the feeling than mine will. Her final photo, in particular, just slayed me when I first saw it; the distant shot is a worth-a-thousand-words indictment of putting these animals into pens on the other side of the world from their rightful homes. This particular enclosure is among the nicer ones, as zoos go, but it's still a prison built for our purposes, not theirs, its inmates wholly innocent of any crime.
I found myself spending most of my gorilla-watching time trying to decipher their emotions. I don't think it's easy. Consider this female.
Is she feeling sad?
Confrontational?
Contemplative?
Annoyed?
These shots were taken with only a few seconds elapsing between them, so it's unlikely that she was actually going through that range of emotions in so short a time, even though those labels are what get immediately conveyed to me by the images. I don't think our experience correlating human faces and emotions serves us well to interpret other species, even one as closely related as these primates.
I'll bet, however, that they have no such difficulty reading each other. Why else would they have such expressive faces, if not to communicate to other members of their tribes? The next pictures are of this troop's dominant male. Look at how his face changes, again over the course of just a matter of seconds in this series:
The entire dimensions of his face undergo transformation. Lots of other mammals have some range of facial expressions, but offhand I can't think of any non-primates that invest this much in making their faces so enormously flexible. It takes a lot of muscles and bony attachments--plus the neural wiring and brain mapping--to generate this variation. From an evolutionary perspective, that expenditure can only be justified if such communication is tremendously important to their survival. I wish I were in on the code.
I think both Cardgrrl and I were most taken with one female who tended to sit off by herself, not interacting much with the rest of the group. I know I took more pictures of her than any of her friends. I think I felt some sympathy with her, knowing well what it's like to be sitting alone in the corner of the playground while everybody else is interacting easily. Maybe she's on the outs socially. Maybe she's in some sort of pain. Maybe she was just having a bad day. Again, though we're naturally quick to interpret body language and facial appearance by experiences with our own kind, I doubt that the correlation to the apparent equivalents in gorillas is as close as we tend to assume. But what do I know?
Another of the band's females was obviously in late-stage pregnancy. If I saw this expression and posture in a woman of equivalently impending delivery, I'd probably be inclined to think she was contemplating the birth of her child, perhaps wondering what kind of personality he or she would develop.
But I confess that I have no idea to what extent a gravid gorilla's brain is capable of understanding what is happening to her, or what is about to happen, which in turn makes me interpret what I'm seeing with much more curiosity than certainty.
Here is a final olio of gorilla snapshots for you to ponder over. What are they thinking and/or feeling? Were I in their situation, it would be nothing but "How can I get out of here?" until I finally gave in to the futility of such efforts and surrendered myself to my fate, at which time my escape anxiety would be replaced with a crushing and unending sense of helplessness. Is that what these magnificent creatures are feeling? I don't pretend to know. But if the answer is yes, shame on us for inflicting that on them.
Addendum
I originally wasn't going to include this video, because it's already in Cardgrrl's post, but I just can't resist. I've watched it several times and love it too much to leave it out.
The babies are adorable, obviously, but I'm most impressed by the silverback. You don't need any imagination to see the immense power of his musculature. He could toss around the NFL's biggest linebacker like a rag doll. But it's entirely contained and restrained, like a Ferrari engine at idle. He gently nudges his child away from the man at one point, then just sits and watches, like a patient dad tending his children at the playground. Maybe the little ones are so relaxed and bold in their exploring because they know they've got the biggest bad-ass in the jungle behind them, ready to rip apart anything or anyone that might threaten them. When it's time to move on, he just gives a little "follow me" grunt and saunters off. Amazing film.
Actually, it's not usually much of a question for me. It's rare that I feel an intention to be mean* in what I write. When I do, I'd like to believe that I leave no room for a reader to doubt my feelings about the subject at hand. For example, when I have written about cheating and cheaters in poker, or Richard Marcus plagiarizing poker bloggers, or Phil Hellmuth's embarrassing ego and antics, or several other topics that get my dander up, I do my best to deploy my limited rhetorical talents in a way that gets readers to share my disgust and/or outrage. If anybody running their eyes over those posts fails to grasp that I despise the people or actions that are in my crosshairs, then I have failed very, very badly. After all, when I check the thesaurus to make sure that I have exhausted every synonym of "stupid" or "wretched" or "evil" or "contemptible," I certainly hope that the point has been made.
But far more often, even when I'm criticizing and/or disagreeing with something or somebody, I feel no malice; I simply think that something that was said or done was wrong, and wish to explain why I think that. I have previously compared my sense of mission in such instances to that of the robot "Nomad" in an old Star Trek episode: to find and eradicate error. (As the currently popular joke puts it, "Somebody is wrong on the Internet!") My goal is to convey information, not to condemn in any moral or personal sense, nor to arouse any negative emotion in a reader. If I'm not feeling outrage, I don't have any motivation to trigger it in my readers.
Just before I left for a week's vacation with Cardgrrl, I wrote a post responding to something Very Josie had written about counting outs and estimating probabilities in poker. My intention was to set the record straight, not to be insulting or condemnatory--or, to return to the central word in today's post title, to be mean.
Shortly after publishing that post, I read an article in a poker magazine that made exactly the same mistake as Josie had, and so I whipped out a post about it just a couple of hours before I was to be leaving for the airport for my week away. Even though the error was the same, I was much harsher on the magazine columnist, for several reasons: He was writing for publication, which, in my mind, requires more care than a personal blog. He presumably has at least one editor, who should have noticed the problem. He describes himself as a poker teacher or coach, and says that he emphasizes the importance of math to his students. Finally, he took a rather haughty tone toward those who don't see basic poker math as being important. To have such a fundamental error of understanding of poker math under those circumstances strikes me as a far worse sin than having the same misconception as a recreational player, and my language reflected my sense of indignation and condemnation.**
I think that the sarcasm, the snarkiness, the sense of meanness in the latter post is self-evident. But I also think that the absence of such qualities in the first post is equally self-evident. In fact, I reread it just now and still don't see it as mean-spirited.
It was, therefore, quite a surprise and mystery to me when I started getting complaints about how I had been, well, mean to Josie. Commenters used words such as "painful," "harsh," and "crime of courtesy." Josie told me she felt I had been--here's that word again--mean, and that I had ridiculed her. She said she had received a number of emails sympathizing with how she had been "wronged." Even Cardgrrl mentioned that she was surprised Josie was still talking to me.
It's hard to describe how confused this makes me feel. How could I write something that to me felt completely neutral and dispassionate, lacking any of the markers that I deliberately include when I want to be mean, yet have it apparently come across to so many people as being vicious?
It's true that I didn't pad my criticism with softeners, such as starting with compliments then gently bringing up the points of disagreement, or qualifiers like "maybe" and "I think," nor did I hold open the possibility of this being a matter on which reasonable people might disagree, with language along the lines of "my opinion is..." or "I see it differently." I just said, in essence, here's what's wrong and here's what's right.
I don't see that as being mean. I neither felt nor intended readers to feel anything negative about the person who made the mistakes. I even started the post with an admission that I've made a whole bunch of mathematical errors in my posts--and I might as well expand that to having made all kinds of errors, not just mathematical ones. My readers point these out to me, sometimes gently, sometimes harshly. When I see that I've been wrong, my usual response is to acknowledge it, either in a comment or an addendum to the post or a whole new post revisiting the subject. I don't see this process--either having my mistakes pointed out or issuing some form of mea culpa and correction--as any big deal; it's just the way I've been taught that one should communicate in public forums.
One might certainly take issue with whether I should ever inject meanness into posts, even when I think the targets deserve being blasted with both barrels. I remember when I was a teenager and had one of my first letters to the editor published in the local newspaper. I was slamming somebody who had written about the evidence for UFOs, which I thought was ridiculous, and my language left no doubt about my feelings. My father, upon reading it, didn't commend me for my superior facts and reasoning, as I had thought he would. Instead, his reaction was, "You could have made your point just as well without being insulting." So if I were to be charged with being rhetorically heavy-handed sometimes when it isn't necessary, I'm afraid I would have to plead guilty to a very long roster of offenses.
But that's an aside, and fundamentally a different issue. What I'm talking about here is being perceived as having been mean when I had no such intention. That, too, is hardly unprecented, I'll admit. I have many times ruffled feathers when that wasn't my goal. It happens much more often in written communications than in person, perhaps because I'm at least averagely able to sense from nonverbal cues that something is amiss when I'm face to face, and can right away try to figure out where the message went wrong. In writing, though, I don't get the feedback telling me that I've accidentally stepped on a toe until the damage is done.
I'm sorry that I injured Josie's feelings and ticked off some of her friends. It was not my intention to either hurt or ridicule. I didn't even realize that my words could be read that way, since hurt and ridicule were not in my mind when I wrote. It should be clear from my previous posts that I genuinely like Josie (see, e.g., here and here and here and here and here). She's smart and funny and fun to be around. I hope that she will continue to consider me her friend, in spite of my failings and missteps.
*The word mean has several possible definitions, even when dealing with it solely as an adjective. I'm using it herein to broadly refer to the set of concepts in Definition 5b and 5c here, i.e., "characterized by petty selfishness or malice," "causing trouble or bother; vexatious."
**The second post also mentioned Josie in passing. The juxtaposition of seeing the same error in two places so close in time made me wonder if they were connected--specifically, I wondered whether Josie had read the poker magazine article, and that is why she had the same misunderstanding as its author. This speculation on my part annoyed her even more than my first post had. She commented, "Really? Now you think I'm plagarizing a dumb magazine article?" Not at all. Had I thought that the connection was suspicious of being conduct that I would find unethical, I would have said so explicitly (as I did when I wrote that I thought Josie acted more unethically than she was aware of when she agreed to soft-play a friend). For example, when I discovered that somebody had flagrantly plagiarized a friend's published column, I called the violator a "low-life scumbag" and a "scummy thief." That's not even remotely what I thought about the connection here. Even if I had known for sure that there was a cause-and-effect relationship, I would not have labeled it plagiarism. Learning for the first time some widely recognized concept and then restating it in one's own words without specific attribution is not, in my mind, plagiarism. If I assert that a flush beats a straight, I don't need to footnote where I first learned that. I also don't remember with confidence where I first learned the "rule of 4" shortcut that was the subject of both posts under discussion here. Maybe Phil Gordon in his commentary on "Celebrity Poker Showdown," but I'm not sure. It doesn't matter. The more widely known something is, the less need there is to point to any particular source when discussing it. Josie says that she never read the article in question, and I believe her. But even if she had, and even if that had been where she first learned that rule of thumb, I would have thought nothing wrong with not bothering to mention that fact when she decided to post about it.
Cardgrrl and I spent yesterday afternoon wandering through one of the three main trails of the Petroglyph National Monument, just outside Albuquerque. See her observations here.
I uploaded a bunch of photos of the glyphs we saw here. (As the sun became very low, its color tricked the white balance on my stupid camera. The rocks are not actually blue. They are, in fact, mostly black, some dark brown.) Note that in a few spots some moron has come along and decided that these ancient pieces of art would make good targets for shooting at.
I haven't been following Twitter much during this trip, but back in the hotel room for the night, I looked to see if I had any mentions or direct messages, and boy did I! Everybody who knows me, it seems, was trying to make sure I knew about a hand played at the Epic Poker main event today, in which Joe Tehan's Mighty Deuce-Four knocked out both Faraz Jaka with A-A and Vanessa Rousso with Q-Q, three-way all-in pre-flop.
Read the details here (don't miss the Twitter messages from the principals at the end of the story) and here. The three of them talk about the hand on camera here.
My only gripe with the coverage is how some people refer to Tehan's move as a "bluff." How can moving all-in with the most powerful hand in poker be considered a bluff?
Day 4 of a week-long trip to Albuquerque to see Cardgrrl and her family. Today was zoo day. We spent a long, long time watching a group of six gorillas. They are endlessly fascinating creatures.
Open the picture in a new window to see it full size. I think it turned out well, for being a cheap point-and-shoot camera on maximal zoom in dodgy light.
Just minutes after writing the "Math is hard" post last night, I was leafing through the December issue of Ante Up magazine and spotted a column by Antonio Pinzari titled "Going further with math" (page 59). In it he recounts how he has learned the importance of knowing the basic math of poker, and how he drums it into his students.
Then we come to this paragraph:
Again let's go further with two suited cards preflop. You've overcome the 89 percent and flopped two of the same suit, what are the chances of making the flush by the river? Using the Rule of 4 x 2 (if you don't know what that is I suggest you find out fast) you have about a 35 percent chance of making the flush on the turn and an 18 percent chance if you missed the turn card by making a flush on the river.
I'll give him a pass on the awkward sentence construction, but I will not give him a pass on the bad math--not in a column in which he boasts about how important it is to know the numbers and in which he claims to be teaching this math to his poker students. I sure as hell wouldn't hire as a poker coach somebody who claims to know what he's talking about but obviously doesn't.
There are 13 cards in each suit. If I have two of a suit in my hand and there are two more of them on the flop, that's four, leaving nine unaccounted for. There are 47 unseen cards, so the probability that the turn card the dealer puts on the board will complete my flush is 9/47, or about 19.1%. Not 35%, Mr. Pinzari, O Great and Wise Coach of Poker Math. (The second part of his assertion is closer to correct. If I missed on the turn, the probability of spiking a flush on the river is 9/46, or 19.6%. Why is it slightly higher on the river than on the turn? Because the deck is now a little bit more depleted of cards of the other suits.)
I wonder how Mr. Pinzari thinks it is possible that the chance of a flush card hitting on the turn is twice as high as the chance of it hitting on the river. Is there something magical about that particular spot on the board--the one between the flop and the river--that magnetically attracts cards that will complete a flush?
The similarity between Josie's errors and Mr. Pinzari's is striking. Did she read this article, I wonder, and get misled by it?
Let's go on.
Here is a huge number Lee [Childs, in the October issue] didn't cover: 60 percent of all flops contain two suited cards.
BZZZZZZZZZZ! Wrong again.
This is stated without reference to what cards one is holding, so let's run the numbers that way. I.e., we'll just take three cards at random from a full deck of 52, ignoring what might have been dealt to any players. The easiest way to calculate the probability of getting two of one suit and one of a different suit is actually to sneak up on it the back way. It's easier to work out the probability of getting all one suit and of getting three different suits. Then we subtract those values from 100%, and what is left is the probability of getting two suits, since the only possibilities are one, two, or three suits.
We start with figuring the probability of the flop consisting of all one suit. It doesn't matter what the first card is. Let's say it's a club (or "crub," just for my friend Eric, who absolutely loves it when I use that word). The probability that the second card will also be a club is 12/51, because there are 12 clubs left among 51 cards. If that happens, then the probability that the third card will also be a club is 11/50, because there are 11 clubs left among 50 cards. The combined probability is thus 12/51 x 11/50, or 5.1%.
Now we figure out the probability of getting three different suits. Again, it doesn't matter what the first card is. Let's say it's a club again. What is the probability that the next card is something other than a club? Well, there are 51 cards left in the deck, of which 12 are clubs and 39 are non-clubs, so the probability is 39/51. For the river, we have 50 cards left, of which 12 are clubs, and 12 are whatever the suit of the second card was, leaving 26 that can complete our rainbow flop. Thus the combined probability is 39/51 x 26/50, or 39.8%.
So now we know the probability of a flop containing just one suit (5.1%) and of it containing three different suits (39.8%). The only other way a flop can come is with two suits--two cards from one suit and one card from another. That probability must therefore be 100% - 5.1% - 39.8%, which works out to 55.1%, not 60%, as Mr. Math Genius Pinzari claims.
What if we alter things a bit by assuming that we start with two of a suit in my hand? Again I'll use clubs as my example. We use similar logic, but it's made messier because now we have to do the arithmetic separately for each suit, since the probability of clubs hitting the flop is lower than for the other three suits (there being two fewer of them available in the remaining deck). I just filled a sheet of scrap paper with my numbers, and I'll spare you the details, but I work it out to be a probability of 11.0% to flop exactly two clubs, and 14.7% each to flop exactly two diamonds, hearts, or spades. Combining those last three is 44.1%, for a grand total of 11.0 + 44.1 = 54.1% to flop two of any suit, starting with two suited cards in one's hand. In other words, that assumption still doesn't get us to the 60% that Mr. Pinzari asserts. In fact, it's a little bit lower than our first calculation.
Sorry, Mr. Pinzari, but you get an F for a column in which you boast about knowing poker math while showing that you really don't understand it at all.
Lord knows I've made more than any blogger's share of mathematical mistakes in the course of five years of writing about poker. I kind of doubt, however, that I've ever made as many in one post as my pal Very Josie did earlier today.
Here's her first example:
I’m holding a KQ of spades. The flop comes ace of spades, 10 of hearts and 2 of spades. I have a nut flush draw and an inside straight draw. What are the odds that I hit one of these great hands? Hmmm…First thing to do is to count how many cards are out there that will complete my hand. 4 spades are showing, so there are 9 left that will give me a flush; 9. There are 4 jacks in this deck that will give me a straight; 4. Nine plus four is thirteen. Surely you don’t need to be an accountant to figure that out.
It appears that being an accountant is not enough to get it figured out correctly. The jack of spades is being counted twice here--once as a spade and once as a jack. The number of cards that will complete either a flush or a straight is 12, not 13 (as Josie acknowledged after a commenter pointed this out).
There are 13 cards that will give me a big and most likely winning hand. To determine the odds of hitting one of these cards on the turn you take your 13 outs and multiply that by four. 13 times 4 is 52. I have a 52% chance of hitting my winning hand on the turn. If I do not get my card on the turn, it’s time to calculate the odds of hitting it on the river. You take those same 13 outs and this time multiply them by 2. 13 times 2 is 26. I have a 26% chance of hitting my hand on the river.
No, no, no. The "rule of four" gives you the approximate probability that you will hit one of these cards on either the turn or the river. Look at it this way: Each card constitutes about 2% of the deck, so the probability that the next card the dealer shows is, say, the eight of hearts is about 2%. If there are 12 favorable cards whose position is unknown to us (i.e., they might be in the stub of the deck in the dealer's hand, might have been dealt to an opponent, or might be among the burn cards), there is a roughly 2 x 12 = 24% chance that one of them will appear as the turn card on the board. There is another roughly 24% chance that one of them will appear on the river. Combined, that yields about a 48% chance of hitting one on either the turn or river.
A commenter calling himself "Four Hands" correctly made this same point on Josie's blog:
the Multiply by 4 is to calculate the odds of hitting on the turn _OR_ the river. It important for calculating whether or not to go all-in on the flop, but it not accurate if you're calling for a single card, or comparing pot-odds unless you're going to be all-in.
The odds of hitting on the turn are the _same_ as hitting on the river, well, slightly different because you've seen one card, but close enough that the approximation is usually fine.
To which Josie responding, puzzlingly:
NO 4 HANDS! I think you're saying the odds between the turn card and river are pretty much the same, except for that one measly card. i disagree because after the flop you have two chances to hit your hand, yet after the turn you have 1 chance, which is 50% less chance of hitting your hand.
see what i'm saying?
Josie has confused here two different quantities. One is the probability of hitting one of the desired cards on the turn. The other is the combined probability of doing so on either the turn or river. They are both potentially useful numbers, but they are completely different. If your decision is simply whether to call a bet on the flop in order to see the turn card, then the 2 multiplier is your approximation, because you don't yet know if your opponent will bet again on the turn, nor how much he might bet. On the other hand, if one or both of you will be all in on the flop, then you're getting both the turn and river, and you'll be interested in the combined probability that a desired card will hit either spot. "Four Hands" had it exactly right.
Josie's post said that she is twice as likely to hit one of her outs on the turn as on the river. A moment's reflection should reveal that that is an absurd conclusion.
Her next example:
I have J-J, which is definitely okay. The flop is 4-4-8 rainbow (all different suits). I have an over pair and I’ll come out betting here. The question is, what are the odds of improving my great hand. Any jack or four will give me a full house, and there are two jacks and two fours left. I have 4 outs. Four times four is 16. I have a 16% chance of hitting a full house on the turn and since four times two is eight, I have an 8% chance of hitting that full house on the river.
The problem here is more conceptual than mathematical. When I'm in a situation like this, the probability of improving my two pair to a full house is the last thing on my mind. The far more important question is whether I have a better hand than my opponent right now. If he called me pre-flop with Q-Q or K-K, I'm in deep doo-doo--so deep that even making a full house by another 4 hitting the board won't get me out of it. On the other hand, if he called me with 10-10 or 9-9, he's the one that's deep in the doo-doo. The probability of me catching another jack is so low that it's not worth basing any decisions on. It's true that a 4 improves my hand, but it improves the other guy's hand equally, so it's not really a meaningful consideration. If he already has a 4 or 8-8, I'm toast, and only a jack will change that, not another 4.
Another problem with the language here is the use of the term "out." Outs are defined as cards that will improve a currently losing hand to a winning one. If you're already ahead, it's nonsensical to count your outs, or even to speak of having them; it's the other guy that has to be looking for outs. So when Josie says that she has "4 outs," it means that she either thinks she's behind here or doesn't understand the whole concept of outs. And, again, even if it's the former, the number of outs is actually just two, because the remaining two 4s don't move her from being behind to being ahead. Only the jacks can do that. Having a full house is still a losing proposition if the other guy has a bigger one.
But fundamentally this situation does not pose a mathematical problem. It's a hand-reading problem. I have to figure out whether I'm winning or losing. Most of the time it's a favorable flop for me; I was ahead with the jacks before the flop and remain so after the flop. But once in a while an opponent will have smooth-called pre with a bigger pair, or got very lucky with either 8-8 or a 4 in his hand. My primary tasks are (1) to extract the most value from my opponent if he has a pocket pair smaller than mine (which is just about the only thing he could have with which he might pay me off), or (2) spend as little as possible to determine that my hand is second-best on those occasions that he has 8-8 or a 4.
Josie's final example:
We’re playing with the two and three of hearts. The flop is 4 of spades, 5 of hearts and Q of clubs. Right now I have an open ended straight draw and there are 8 cards in the deck that will give me a straight. After the flop I take the number of cards out there that will help me (8) and multiply that by 4 to get 32. There’s a 32% chance I will hit my straight on the turn.
This is wrong, for the reasons given in the first example. It's closer to 16%. To be exact, there are 47 unseen cards, and 8 of them make the straight, so it's 8/47, or 0.170, or 17.0%.
Alas, the turn is a king of hearts. In addition to my open ended straight draw, I also have a flush draw. Now there are 15 cards in the deck that I want. If one of them hits on the river, I’ll have either a straight or a flush. 15x2=30. I now have a 30% chance to hit one of my hands.
That's about right. It usually works out to actually be about 2% more than the rule of thumb predicts. Here, for example, there are now 46 unseen cards. 15/46 = 0.326, or 32.6%. But the difference between the quick estimate of 30% and the actual value of 32.6% will essentially never matter to a poker decision. Either way, you're next going to translate it into odds (about 2:1) for purposes of determining whether a call is worthwhile.
Each tells the story of a single bet--on a horse race, a boxing match, blackjack, a chess match, along with reflections on life as revealed in the game in question. I like the author's writing style and hope that there will be more in this series.
It's rodeo time. The National Finals Rodeo is one of the biggest events of the year, and the entire tourism industry goes cowboy for the first two weeks of December. As I walked to Binion's, I passed two examples of that fact.
First, the bands hired for the free outdoor concerts play, as it was phrased in the great movie, "The Blues Brothers," both kinds of music--country and western. In this case, it was Christmas music with a hard-to-miss country beat.
Even if that's not a sufficiently explicit tip o' the ten-gallon hat to the season's visitors, I don't think you can deny that mechanical bullriding is right up their alley:
The marathon is over. For reasons that I can't understand, this year they moved it from morning to evening, which was far more disruptive to the city's tourism business. I had no interest in fighting traffic getting to or from any of the Strip poker rooms. I figured I would just walk over to Binion's and play there. Incidentally, the race route this year went down the street behind my apartment building. This was near mile marker 20 for the marathoners and 7 for the halfers.
I talked to Cardgrrl for a while before heading out. This was around the time that the race was beginning for the half-marathon runners, which included several of the poker bloggers finishing up their annual winter Vegas get-together. Of the runners, the one I know best is Brad Willis, a.k.a. @_Otis_, a.k.a. the purveyor of Rapid Eye Reality. Though we're far from being what anybody would call close friends, we've chatted many times and had dinners a couple of times. He's smart, funny, interesting, and, if you ask me, the overall best writer the poker world has working in it these days. He has earned my respect and admiration.
Because of knowing that, Cardgrrl asked me if I was going to watch for him passing by in this, his first half-marathon. No, I said, and explained my reasons: It's cold, I don't know when he'll be in this vicinity, I don't have any Gatorade kind of stuff to offer him, he's not expecting to see me and won't care whether or not I'm there, etc. All of which she dismissed with barely disguised disapproval.
I was unmoved by her opinion at first. But it started eating at me after the conversation ended. Some small remnant of an actual human conscience still survives inside of me, despite my best efforts to bludgeon it to death, and it started talking to me, along approximately these lines: "Brad has been nothing but kind, decent, open, complimentary, and inviting to you. His father died a week ago, and he had to cut short a trip to China to go home for the funeral. After initially planning to cancel the Vegas trip, he listened to friends and family who encouraged him to go through with his plans for this race, for which he has been diligently training for the last several months. And you can't be bothered to walk THIRTY FUCKING YARDS past your door to give him a shout-out and a thumbs-up?"
So there was that.
There was another factor. One of the surprising things about being in a relationship with Cardgrrl is that something about her makes me willing to try new things. That may not sound remarkable, but I have long been the kind of guy who knows what I like and don't like, set in my ways, with neither need nor interest in stepping outside that comfort zone. She is the opposite. She craves new experiences. So my initial willingness to try new things was primarily an accommodation to her, an attempt to achieve compromise. But doing these things has turned out favorably a high enough percentage of the time that there has been some spillover into decisions I make even when she's not involved. I won't claim that there's been a sea change in what choices I make in foods and activities, but there is a definite degree to which I will now choose something different from my default simply because it's new, and that's an element that was completely absent from my personality as recently as three years ago.
On the long list of things I've never done are "watch a marathon" and "cheer for a friend who's running in a marathon." So despite my initial dismissal, I started thinking that maybe I should take the opportunity to add them to my life experiences.
The combination of those two factors caused me to change my mind, and instead of heading straight for Binion's, I instead went to the street to see if I could spot Brad as he dashed by. (I would have been happy to shout and wave at any of the other poker-blogger runners, too, but they are all people I have either never met or have met so briefly that, while I would recognize them across a poker table, my chance of picking them out in a race situation like this was virtually nill.)
My first problem was crossing the street, since most of the runners were on the far side. It took a while before there was just enough of a break that I could dash across without making anybody swerve around me. I felt like a squirrel running across a freeway, lucky not to have been squished under a tire.
The next problem was spotting the person I was looking for. This I had not anticipated. I know Brad's face, but not with the deep, subconscious recognition that we develop for our most intimate circles, where the brain recognizes the well-known face from any angle, with any light, under any circumstances, in a fraction of a second, from just the corner of one's eye. Here I was faced with a sea of faces, all bobbing up and down, moving rapidly towards me, in the dark. I would guess that an average of about ten people were passing by my vantage point every second. Brad had no idea that I would be out there, so the task of recognition and rapidly reacting was all on me. Due to the light conditions and density of bodies, there would be no way to spot somebody a long way off.
It was strangely fatiguing, mentally. It was also visually disorienting, like when you scroll a long document on the computer screen for 20 or 30 seconds straight, and when you stop it feels like your eyeballs keep moving. I found myself feeling true vertigo after a minute or so of scanning this wall of moving faces, and I would have to look away at something stationary for a few seconds.
I don't know how well this video clip conveys the problem, but it at least shows you how fast people are going by. Warning: this may be the most boring four minutes in YouTube history.
After a while, I started hearing race officials, embedded in the crowd on bicycles, shouting reminders to the runners that the half-marathon folks were to stay to the right. I, of course, was on the left. Damn. That meant I had to be like Moses and part the Red Sea again, because I could really only effectively scan the faces in the half of the street closest to me. But by now the race was even denser than before, as we were towards the mid-pack. I waited for five minutes for a break, without one appearing. I realized that was not going to work. I devised an alternate strategy: If you can't beat 'em, join 'em. So I stepped into the street and began running my first marathon, moving over a little at a time as spaces appeared to my right, as if trying to change lanes to catch a freeway exit. It worked, though the half-block of running was enough to fulfill my personal quota of exercise for about a year.
I hung out on the other side of the street under a lamppost for quite a while--longer than I thought, as it turned out. I estimated I had been out there for 45 minutes, but when I was finally too cold (it was about 45 degrees out, and my blood is a lot thinner than it used to be after five years without real winters) and dizzy to continue, and as the runners were starting to thin out, I came back in and learned that it had actually been almost 90 minutes.
I never spotted Brad. It's possible that I was already too late when I got outside if he was faster than I was guessing. I don't think I missed him by leaving too early, judging by when he sent a Tweet announcing that he had reached the finish line. But by far the most likely scenario is that he ran right past me without either of us realizing it. Oh well. I gave it my best effort.
As with the majority of newly-tried things, I ended up glad I had done it. It was an interesting view of a slice of American life that is completely foreign and unknown to me. I saw people in gorgeously tip-top physical condition, but also a few of obvious morbid obesity, who I have to assume were making an impressive attempt to make radical changes in their lives. Costumes abounded, from gorilla suits to Elvis to showgirls to Star Trek uniforms to cross-dressers. I saw a ton of t-shirts and banners proclaiming one cause or another that was motivating the run. My favorite of that genre was the palpable pride behind one that said, "Cheer for my amazing wife Mary doing her first marathon!"
I saw two gentlemen who were at least in their 70s and more likely in their 80s. Both were struggling and moving slowly, appearing to be in considerable pain, but determinedly moving forward. I saw two pairs of parents carrying small children, 1- or 2-year-olds. I saw people missing a limb.
I was intrigued when I began to notice how overwhelmingly white the field was. People of color were severely underrepresented in this race. I would guess that persons of African descent constituted less than two percent of the runners. I had been unaware how disproportionately running is not an activity of equal appeal to all races in this country.
Predictably, I saw a lot of people in obvious pain, having to force themselves onward. Others carried on elaborate conversations with friends, of which I got to hear a lot of very short snippets. They seemed to be feeling neither agony nor ecstasy. Some eyed me with what I interpreted as a hostile "What are you looking at?" attitude (though admittedly their faces were probably mostly objectively blank, with me just projecting onto them what I would be thinking if our roles were reversed). But what most surprised me was how many of these runners smiled, waved, and said hi to this random stranger leaning on a lamppost. They appeared to be basking in the glow of pleasure from the whole experience, and eager to share their ebullience with others. I don't feel that way towards strangers in my best and most relaxed moods; it's incomprehensible to me how one could feel it in the midst of such a grueling, torturous workout.
Around the corner from my building was this guy playing his saxophone. As far as I could tell, he was not officially part of the race experience, not paid to be the entertainment, not with anybody else, not selling anything. He just set up his amplifier and played along with it for the sheer joy of enhancing the experience of the runners. (As you can see, this was well after the main part of the race was over, with just the walking stragglers remaining.)
I still consider myself far on the left end of the misanthrope/social butterfly spectrum. Still, people are as endlessly fascinating as they are maddening and annoying. It was an interesting experience to study so many of them for such incredibly short periods of time, like opening 20,000 novels just long enough to read one word from each of them. I recommend trying it sometime.
I will remember WPBT 2011 as the year that several of the poker bloggers literally went runner-runner.
It's a little hard to say this, because I'm not used to it yet, but I suppose that I'm a professional poker player. I moved to Vegas intending to get a job as a poker dealer, but while waiting to get hired, I spent the days playing poker instead of dealing it, and soon found that I was able to keep the bills paid. So I've just kept on doing it. I play Hold'em exclusively, usually no-limit, and most commonly $1-2 or $1-3, with occasional forays into $2-5 territory. I play tournaments on-line once in a while, but for some reason that I haven't entirely figured out, I'm much more successful playing at casinos than on the Internet, and much better at cash games than tournaments.
You can contact me via email: it's rakewell1 at yahoo dotdotdot com.
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