"You shouldn't have bet that"

Aria tonight. I raised to $12 from early position with K-Q offsuit, got four callers. Flop came 9-10-J rainbow. How perfect is that?

I bet $25. Sadly, all three opponents folded in turn. I showed my hand while effecting an obviously fake pout about not having been called. (I think it's truly disgusting when people genuinely whine and complain that the pot they just won was too small, so I wanted it to be clear that my little tantrum was purely in jest.)

Three players simultaneously said variations on the title to this post: I should have slow-played it. I should have given them a free card so that one of them could catch up. I should have let them do the betting for me.

I didn't respond. I almost never discuss at the table how a hand was played; I think it's a terrible idea nearly all the time. I have no interest in giving other players new and different (and maybe better) ideas about how to play. Why would I?

I understand the impulse to play possum and pretend like you missed the flop when you actually have the nuts. And there are times when it's clearly the right thing to do. But I think that should not be the default play in that spot. Let's see how many reasons I can list for why a lead-out bet is defensible, and arguably even the best play.

1. I have a big hand, so I want a big pot. The most reliable way to build a big pot is to put money into it at every opportunity, hoping that somebody with a second-best hand will do the same.

2. If it checks around and fourth street is a queen or an 8, it vastly increases the chance that I will have to split the pot with somebody else, and/or that it will kill any shot at being called by somebody who flopped top pair or even two pair, because the straight will be both more obvious and more likely for somebody to be holding.

3. Waiting for the turn to bet means that I'll now have a flush draw on the board about 3/4 of the time. My decisions will then become increasingly complicated.

4. In just a short session, this was already the third time I had raised pre-flop and followed it up with a continuation bet, because I had gotten lucky and hit top pair or better each time. This meant that any players paying attention might think, "He can't have it every time," and decide to draw a line in the sand, calling or even raising with something like top pair, thinking that I most likely whiffed.

5. I know perfectly well that most recreational $1-3 NLHE players can't resist slow-playing monsters like this. Players tend to assume that others think and play the same way they do, which means that the nuts is pretty much the last hand they will think I have when I lead out looking so strong. They will put me on top pair, an overpair, a straight draw, or a pure bluff. Put another way, this is a situation in which I'm being tricky by being straightforward. If I'm lucky enough that one of them flopped two pair or a set, we play for stacks with the odds greatly in my favor, because they will not believe that I have them crushed.

6. Metagame considerations: The typical player in these games will tend to check both his complete misses and his strongest hands, which means that he's leading out betting with a fairly narrow range--mostly one-pair hands. I want to give the impression to anybody paying attention that they cannot reliably put me on a range of hands based on whether or not I c-bet, i.e., that I don't follow the pattern they have come to expect from other players. This is also the primary reason that I showed it after winning the pot (which I only rarely do). Showing a lead-out bet with the nuts means that a continuation bet with air later in the session is more likely to succeed, because opponents will remember that they can't exclude the strongest hands from my range based on the fact that I'm betting.

7. Because several of them will believe that slow-playing is clearly the superior play, they may conclude that this was a beginner's mistake and that I'm less experienced than I actually am. They may decide that I'm straightforward and not tricky, that I bet when I have a good hand and check when I don't. I hope to exploit, dash, and confound all of those expectations later in the session.

8. If I give a free card that pairs the board or puts a flush draw out there that comes in on the river, and I end up losing a big pot to some awful runner-runner combo, I'm going to kick myself down the nearest staircase for misplaying it, and I can't afford the resulting hospital bill.

9. One of Mike Caro's most frequent admonitions is to do the obvious thing. For example, here's a bit from Caro's Most Profitable Hold'em Advice, pages 119-120:

The simplest choice of strategy is usually the best. Exceptions are exceptions for a reason....

The reason I'm telling you this is, once you become skilled at hold'em, it's easy to justify doing the unusual. But the most obvious decision is usually correct. You should make occasional exceptions to keep observant opponents off-guard and to earn extra profit.

But, if you stray too often from what are the simplest and most obvious decisions, you're sure to sacrifice profit.

Of course, as this particular hand played out, it's likely that I could have made more money by checking. Had I known their exact cards--say, that I was up against a pair of deuces, a pair of threes, and a pair of fours--then I might have come to a different conclusion. Letting one of them catch a set on the turn would be about the only way to swell the pot under such circumstances.

But given the range of hands that people usually play against a raiser, and the fact that I had three opponents, there was an excellent chance that that flop hit one of them hard enough that he or she could justify a call or raise. The fact that it wasn't true this time does not dissuade me from the view that a continuation bet was the best move, all things considered.

I'll never live it down

You ever do something on an impulse that seems just silly and goofy and fun, and then about five seconds later think, "That's probably going to turn out to have been a really bad idea"?

(Photo credit--if you can call it that-- goes to PokerLawyer.)

Fitzgerald's poker room closed

See: http://www.lasvegasvegas.com/content/fitzgeralds-closes-poker-room-1326502328

Doesn't bother me. It was a pretty worthless poker room. It's closer walking distance to my apartment than even Binion's and Golden Nugget, but I played there just seven times in 5 1/2 years. I stopped in more than twice that many times, but usually found no game going. On the rare occasions that I found a game, it wasn't very good, tended to be short-handed, and tended to break up within a couple of hours.

Poker gems, #446

Bill Rini, in his blog:

How many times have you heard someone complain that they want to move up in limits where people respect their raises? Well, if you can’t beat the total fish you don’t understand the game well enough to beat people who do respect raises.

Poker is a game of adjusting to your opponent. If you’re playing against a guy who has never met two cards that he wouldn’t see a flop with or will call a big river bet just to see whether you’re bluffing, and you don’t adjust your game to exploit that, you really aren’t a very good poker player to begin with.

You can bluff into this guy all night long and complain about how everyone on 2+2 agrees with your line or pull out PokerStove and empirically demonstrate that you made the mathematically correct move, but you’re still going to end up losing pots to this guy. Not because he’s a better player than you, but because you’re employing an ineffective strategy against that type of opponent.

Google maps now includes some casino floorplans

See:

http://bit.ly/yGuUWi

How not to play kings

Stratosphere last night. After a bad start, I had clawed my way back to a little on the plus side, sitting at about $220, when I found pocket kings on the button. Four people limped, then the guy on my immediate right raised to $15. He was absolutely the tightest player at the table, and this was the first time I had seen him be the pre-flop raiser, so naturally I had to be somewhat worried that he had pocket aces. On the other hand, this raise was larger than the table average (which was $8-$10), suggesting something more like jacks or queens.

Given his table image and the raise size, I thought that I would probably be his only opponent going to the flop, even without putting in a reraise. I would normally three-bet with kings, but I had not three-bet even once so far in this session (no premium hands), which meant that doing so now would essentially be playing with my cards face up. I decided to smooth-call instead, for dual purposes: It would disguise my strength and it would allow me to see if an ace flopped and re-assess Mr. Tight's demeanor before committing a lot of chips against a player for whom aces were a large part of his range. I think that reraising will win me about $20 most of the time, and lose me the amount of the raise when he has aces, though probably not my whole stack, because this is a player against whom I could fold kings if he four-bets it.

I was horrified to see the big blind call, followed by three of the limpers, meaning that six of us were seeing a flop with the pot already swollen to about $90. To use the technical term, this situation kind of sucked.

Flop was 9-6-2 rainbow, about as dry and unfrightening as they can come. I was not worried that Mr. Tight had hit a set, though I still had to be concerned that his pocket pair was one pip bigger than mine. Everybody checked to him, and he bet $35. I considered raising, but I was still in the dark about where I stood. I decided to be cautious and see if one of the players in earlier position was preparing a check-raise. I called.

Three of them folded, but I hated seeing who did not--it was the trappiest player at the table. As a general rule, the bigger the pot, the more you want to take it down immediately rather than trying to make it even larger and risk losing everything. I think that few players who had flopped a set in this situation would do anything other than either lead-out bet or check-raise. One of the few who would be daring enough to check-call here as a trap--from out of position, against two solid opponents--was this guy. Two pair was unlikely, as I didn't think any hand that could have flopped two pair would have put in $15 pre, and there were essentially no draws, so Mr. Trappy either had a set or one pair. If one pair, it was most likely top pair with A-9 suited, possibly pocket 8s or 7s or maybe even 10s.

Fourth street was a four and a second club. Mr. Trappy checked, which didn't tell me anything. Mr. Tight also checked. This didn't tell me much, either. Certainly with A-K he might have taken one shot at the pot on the flop and then shut down. But he could easily do the same with A-A or any other big pair. My table image was solid. I had never shown down a weak hand, and had hit two flopped sets and one flopped boat on my way back to even, all of which did get shown. Mr. Tight might therefore very reasonably fear that I was the one slow-playing a monster and check even aces.

I definitely needed to bet here, both for value and for information, but I didn't think it needed to be large. I settled on $50. Mr. Trappy pondered a long time, but finally mucked, which relieved most of my concern about this hand. Now it all came down to whether Mr. Tight had aces or one of his few other possible holdings. He thought a while and then called. Again, this didn't sort out the situation much for me, except to rule out A-K. I was either one rank behind or between one and three ranks ahead (or, as an outside possibility, tied, with him holding the other two kings). His range was now almost certainly down to one of the top five pocket pairs, and I was beating three of them.

River came an offsuit queen. I mentally winced a bit, because of the obvious possibility that Mr. Tight had just gone from loser to winner. He checked, with noticeably more hesitation than he had exhibited on the turn, which further fueled my anxiety. Now to me--check or bet? I decided that there were still twice as many hands with which he might well pay off a smallish value bet (namely, jacks and tens) as there were hand with which he would call and win (just aces), so I pushed out another stack of $50. He mucked within a few seconds. I still can't say with any confidence which pair he was throwing away. It easily could have been aces, though my best guess is jacks, with tens close behind in likelihood.

The net result? I profited about $195 with pocket kings, without improving, without showing my hand, against five opponents. I find that rather remarkable. It was, of course, extremely lucky, and the whole thing could have gone horribly wrong in about a million different ways. But none of the land mines exploded where they might have, and I lived to tell the tale.

Poker gems, #445

Scott Huff and Joe Stapleton, in Bluff magazine, December, 2011, page 88, commenting on various professional poker players' decisions about where to relocate outside of the United States in order to be able to continue playing online.

Aguiar, Deeb, others -----> Mexico.

Uhhh, is it just me, or does this sound like an accident waiting to happen? In Mexico, you can get kidnapped and ransomed if you're suspected of having an abundance of unused Tower Records gift cards.

What the heck is going to happen when a country that has a pretty disproportionate gun/job ratio finds out a bunch of Vitamin D-deficient supernerds who keep massive amounts of cash on them--and who have the ability to transfer large sums of money electronically--live in that ridiculously lavish high-rise over there? You know, the only building you can see no matter where you're standing in the barrio?

Poker gems, #444

Jennifer Tilly, in Bluff magazine, December, 2011, page 76.

Sometimes I wonder if I am a compulsive gambler, and then I realize I am not. If I am losing, I quit because I hate losing. If I'm winning, I quit. I like to quit while I'm ahead.

Phil [Laak] is the exact opposite. If he is down, he refuses to get up from a table until he is unstuck. Conversely, if he is winning, he won't get up either because he is on a roll. According to Phil, there is NEVER a good reason to get up from the table.

Your not going believe this one

Did you notice a couple of problems with that headline? Of course you did. Unless, that is, you happen to be one of the people in charge of writing and proofreading headlines for Bluff magazine. To them, it would have looked perfect.

How do I know? I have evidence. The following is what one finds on page 72 of the December, 2011, issue:

Notice the subhead: "IF YOUR GOING TAKE MONEY, IT MAY AS WELL BE FROM THESE GUYS."

This will sound snarky, but I mean it entirely literally: How do you get a job writing and/or copy editing for a magazine if you don't know the difference between "your" and "you're"? Isn't there some sort of test for 6th-grade-level English competence that one has to pass before getting hired on?

Another question that will sound rhetorical, but which I ask in earnest: How many people were involved in the production of this page without any of them noticing the homophone problem and the missing word? Five? Ten? And what is wrong with all of these people? (OK, that one was just rhetorical.)

TV theme songs (no poker content)

Last night, out of nowhere, my friend Grange95 said via Twitter, "Hawaii Five-O is still greatest TV theme song *ever*." I countered with a few other possibilities, which he politely acknowledged as good, but not as good. He then suggested that we each prepare a list of our top 25 TV show theme songs and publish them on our blogs simultaneously.

I initially thought that 25 was too many and 10 was more manageable. He agreed to the lower number. But as soon as I started actually compiling my list, I realized I had made a terrible mistake. I just couldn't narrow it down that far. Grange graciously agreed to bump it back to 25 so that I wouldn't go insane endlessly second-guessing my choices.

Still, it wasn't easy. I started with a list of 40, which I assembled after consulting various online lists of the best theme songs, such as these:

http://www.rollingstone.com/music/photos/readers-poll-the-best-television-theme-songs-20110921

http://www.pastemagazine.com/blogs/lists/2008/11/the-20-best-tv-theme-songs-of-all-time.html

http://www.ranker.com/crowdranked-list/the-best-tv-theme-songs-of-all-time

http://www.artifacting.com/blog/2010/03/24/100-greatest-tv-themes/

http://music.ign.com/articles/704/704547p1.html

http://www.amazon.com/All-Time-Top-100-TV-Themes/dp/B000XUGDDA/ref=tmm_msc_title_0

So, to the inevitable question that will come up in the comments, "What about _________? Did you think about THAT?" The answer is almost certainly yes.

I was surprised that the "Cheers" theme song ended up at the top of most of the lists. I've never cared much for that one. Which just goes to show how completely subjective and personal such lists will inevitably be. (Sneak preview: No "Cheers" below.)

I approached Grange's challenge by first asking myself what makes a TV show's theme song great? I decided that it must (1) stand on its own as a piece of music, (2) make you want to watch the show that its attached to, (3) set or suggest the mood of the show, (4) be so distinctive that the viewer quickly forms a Pavlovian mental connection between the theme and the show, such that any other possible music becomes unthinkable.

I decided that those goals are more difficult to achieve if the music is instrumental, foregoing lyrics, so I awarded bonus points to that category and (rather artificially, I'll admit) made my instrumentals list into the top ten and the best ones with lyrics my second ten. (Throughout this post, I am ignoring any distinction in terminology between "theme song" and "theme music.") I then added in five more that, while not necessarily great by the criteria I established for myself, have something about them that compels inclusion in a "best of" list.

I tried to include clips of the original opening credits, but in many cases they are not available due to copyright issues, so some of the embedded clips below are of poor quality, or are some version other than what was with the show originally (e.g., a fan mashup).

So without further ado....

INSTRUMENTALS

1. "Hawaii Five-0." Yes, in the end, after a couple of re-listens, I had to concede that Grange was right all along, dammit.

2. "Star Trek: The Next Generation." The theme of the original show was pretty good, but they managed to make it ten times better and more beautiful for the show's second iteration.

3. "Peter Gunn." Even if you've never seen the show (I haven't), you'll almost certainly recognize the music, from the great Henry Mancini.

4. "Mission: Impossible."




5. "Twin Peaks."




6. "Merrie Melodies"/"Looney Tunes."




7. "Dr. Who."




8. "The Twilight Zone."




9. "The Andy Griffith Show."




10. "The Waltons."





WITH LYRICS

11. "The Sopranos." The most perfect mating ever of a pre-existing song to a new show--so perfect that most fans assume the song was written specifically for the show.




12. "The Mary Tyler Moore Show."




13."M*A*S*H." Yes, I know that it didn't have lyrics as used in the show, but everybody knew what the lyrics were, and that's important here; if the music doesn't call to mind "suicide is painless," then it doesn't really work well.




14. "Greatest American Hero." Maybe the best "feel-good" TV theme song.




15. "Ally McBeal."




16. "Rawhide."




17. "The Beverly Hillbillies." Earl Scruggs and the Foggy Mountain Boys? A shoo-in. Of all the ones in my list, this is the one that is most likely to become an earworm for me on any given day. Often just the mention of any its key words (oil, millionaire, swimming pools, movie stars) is enough to set it off. That's not so much because I love the song, but just because of how deeply it has managed to get ingrained in my engrams.




18. "The Monkees."




19. "The Addams Family." Though it deserves inclusion for its general charm and catchiness, this one could almost make the list just for the cheekiness of rhyming "scree-um" with "museum."




20. "Friends."





SPECIAL MERIT


21. "The Tonight Show with Johnny Carson." For being so iconically, inextricably linked with one man, one genre, one time slot.




22. "Jeopardy." For having become the musical embodiment of a social message in just about any context, "Time is running out."




23. "The Muppet Show." For maximal playfulness and inventiveness in always finding new twists on the theme.




24. "The Big Bang Theory." For the cleverest lyrics ever penned for a TV theme song. Seriously, incorporating Australopithicus, Pangaea, and "the autotrophs began to drool"? Genius!




25. "Gilligan's Island." For becoming the best-known TV theme show song of all time. Really—just stop anybody on the street and ask. EVERYBODY can sing along.

For the sake of completeness, here is my list of the ones that were in serious contention but didn't quite make the final cut to 25 (in no particular order):

Bonanza: http://www.youtube.com/watch?v=mjdRgBAY278

The Munsters: http://www.youtube.com/watch?v=0drJKnYg5-s

Hill Street Blues: http://www.youtube.com/watch?v=yevI8xCAKuc

Sanford and Son: http://www.youtube.com/watch?v=1WqazleR3FE

The Rockford Files: http://www.youtube.com/watch?v=d41cAOmcuxk

The Dukes of Hazzard: http://www.youtube.com/watch?v=oU6mPYFtF8E

All in the Family: http://www.youtube.com/watch?v=znrjbo9QRLk

Dallas: http://www.youtube.com/watch?v=Md2YoqPlEtU

Barney Miller: http://www.youtube.com/watch?v=ox-DmJ9H3ng

SWAT: http://www.youtube.com/watch?v=YAHvsCb-6vU

Taxi: http://www.youtube.com/watch?v=Kzhwx8aOO0A

Lost in Space: http://www.youtube.com/watch?v=YH6j63lhAAc

Mr. Ed: http://www.youtube.com/watch?v=y_PZPpWTRTU

The X-Files: http://www.youtube.com/watch?v=JDZBgHBHQT8

As a final bonus, I give you the most famous TV show theme song that actually has lyrics, though you probably thought it didn't: "The Dick Van Dyke Show":

Grange and I agreed to set the posts containing our lists to publish simultaneously, at 8:00 p.m. my time, so neither of us has seen the other's yet. You can presumably see his list here, now that the hour has arrived. The question for you, dear reader, is this: Who made the more definitive list of the top 25?

Addendum

Grange's list is here. We had only 9/25 in common. Judging these in order of their summed ranks (lowest being best), they are:

Hawaii 5-0

Mission: Impossible

Star Trek: The Next Generation

MASH

Beverly Hillbillies

Gilligan's Island

Rawhide

Addams Family

Muppet Show

The only one on his list that I had not considered is "It's a Jungle Out There," by Randy Newman, from "Monk." I love that song and that show, and I agree with him that the song serves the show perfectly. I would have included it if I had thought of it. I'm amazed that it didn't appear on any of the lists I checked (unless I just missed it).

Judging by a Twitter exchange, he admits to about the same embarrassment for including "Cheers" as I do for including "Friends"--it's a surrender to sappiness on both sides.

Oops--another milestone slipped by

Sometime recently I did my 4000th post, and didn't even notice it. This is #4015.

It's hard to sound excited about it now, since it went by like a thief in the night. But I thought I'd mention it, for the sake of completeness.

I used to think every 100th post was worth noting; now 1000 go by and it doesn't even register. Life changes.

Separated at birth?

That's Andrew "Lucky Chewy" Lichtenberger, professional poker player, top, and John Cochran, from the recent season of "Survivor," bottom.

Twins, obv.

Excellent idea of the year (so far)

A Twitter message that somebody retweeted my way last night:

Two mixer hands

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.

Apes as poker players

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.

Abraham Lincoln on gamblers

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?

Josie plays the 2-4

More evidence that the 2-4 is the most powerful hand in poker, this time from Very Josie: http://veryjosie.blogspot.com/2011/12/foxwoods-122311.html

Attention, poker dealers

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:

http://dsc.discovery.com/tv/best-in-the-business/casting-call.html

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.

The Force is strong with this one

Imperial Palace tonight.

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.

Other sights in Albuquerque

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.

Gorillas in our midst (no poker content)

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.

To be mean, or not to be mean--that is the question

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.

Petroglyph National Monument

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.

Back home tomorrow.

Hope y'all saw this

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?

Halfway through Albuquerque visit

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.

Math is hard, II

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.

Math is hard

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.

Leaving on a jet plane

Tomorrow I'm leaving for a week in Albuquerque with Cardgrrl and the part of her family that lives there.

Betting stories

I just spent a pleasant hour or so reading this small collection of gambling stories: http://www.mcsweeneys.net/columns/fading-the-vig-a-gamblers-guide-to-life

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.