Doyle Brunson is wrong

I've been reading Doyle Brunson's newest book, My 50 Most Memorable Hands. In it he tells one story illustrating how winning became harder after publishing his famous book, Super/System. Doyle has K-K, Lyle Berman has 4-4 in a pot that has been raised and re-raised before the flop. The flop comes A-9-4, rainbow.

I checked. Lyle bet and I moved in on him, a very big bet. Lyle studied his
hand a moment and then called. The turn and river cards were no help; and as
Lyle was dragging in the pot, I said in a sad voice, "Didn't you think I might
have three aces?"

Lyle stood up and screamed, "Doyle, I read your book!"

After a moment I realized what he was talking about. I say in my no-limit
hold'em section, "I never give a free card when an ace comes on the flop because
unless the board is paired, the next card can always make a straight." So Lyle
knew I didn't have three aces. We have laughed about that many times
since.

Good story, but I got hung up on this assertion: "[W]hen an ace comes on the flop...unless the board is paired, the next card can always make a straight."

At first I thought he was claiming that with an unpaired ace-high flop, a straight will always be possible with any turn card that comes. That's clearly not true. For example, the flop could be A-2-6, and if the turn card is anything other than a 3, 4, or 5, it is not possible for anybody to have a straight.

So if I were wording Doyle's assertion to be more unambiguous, I would put it like this: Assuming an unpaired board, when the flop contains an ace, there is always at least one card that could come on the turn that could make somebody a straight. For example, if the flop is A-6-9, it's not possible for anybody to have flopped a straight, but a 10 on the turn will make a straight for a player holding 7-8; an 8 will make a straight for a player holding 5-7 or 7-10, etc. I was skeptical of this at first, but I played around with a deck for a while and convinced myself that it really is true.

Then I wondered whether the same was also true when there was not an ace on the flop. Turns out that it's not--but it's almost true. If I've counted correctly, there are only four possible unpaired flops for which no turn card can make a possible straight for any player: specifically, 2-7-Q, 2-7-K, 2-8-K, and 3-8-K.

Ignoring suits, there are 66 possible unpaired flops containing an ace.* As stated above, for all 66 of those, there is at least one card that could come on the turn that makes a straight possible if a player is holding just the right down cards.

There are 220 possible unpaired flops not containing an ace.** Of those, 216 (i.e., all except for the four I listed above) share that same quality--that there is at least one card that could come on the turn that makes a straight possible if a player is holding just the right down cards.

Put another way, with an ace on the flop, it is 100% certain that an opponent holding just the right hole cards could make a straight with just the right turn card. Without an ace on the flop, it is "only" 98.2% certain (216/220 = 0.982).

In other words, I can't see any reason that Doyle makes a distinction here. It is virtually always the case that the turn card could make an opponent's straight, whether or not there is an ace on the flop.

Now, this isn't to say that one should slow-play a strong hand on an ace-high flop and risk giving an opponent a free card. As with most things in poker, it all depends on the specifics of the situation: the presence of possible flush draws, one's position, the aggressiveness of the opponent(s), one's guess as to the possible range of cards an opponent might be playing, the size of the pot, the size of the players' stacks, and a zillion other factors. But it makes no sense at all to make a blanket rule against checking the flop just because there is an ace sitting out there and one fears a possible straight being made on the turn. That always has to be a consideration (except for when you have one of the four peculiar flops I listed previously), but there is no good reason to make it the dominant, determining factor above all others.

Sorry, Doyle. You're right about a whole lot of things, and you've probably forgotten more about poker than I'll ever know, but on this one specific point you're making a distinction where there is no meaningful difference (i.e., flop with an ace versus flop without an ace). I look forward to your reply in the comments section, since I'm certain you're a daily reader. (Ha!)

Incidentally, I figured out something else along the way, which I will probably never have occasion to put into a blog post again, so I'm throwing it in here as a free added bonus. I wondered how many full boards of five unpaired community cards there were for which no straight was possible. I couldn't find any systematic, mathematical way to determine this, so I had to work it out the long, hard way, with a bunch of cards laid out on the table and pen and paper in hand. If I counted correctly, there are 31 such boards with an ace (e.g., A-2-6-9-J), and 50 without an ace (e.g., 3-5-8-J-K), for a total of 81. There are 1287 possible unpaired 5-card boards (treating all suits as the same, as I have everywhere in this post).*** So of all the full, unpaired Texas Hold'em (or Omaha, for that matter) boards, 1206/1287, or 93.7%, have a straight possible, given the right hole cards. You always wondered that, didn't you? So now you know.



*Showing my work, as endless school teachers always told me I had to do: If the second card is a K, that leaves 11 different possible ranks for the third card (2 through Q). If the second card is a Q, there are 10 different possible ranks for the third card (2 through J). And so on, down to the case in which the second card is a 3, leaving only a 2 to make an unpaired flop. By this way of counting, the second card can't be a 2, because all of those possibilities were accounted for with a higher-ranked second card. (We're not concerned with the order the cards are in here; I just arbitrarily did the counting assuming the cards came in descending order of rank.) Finally, 11+10+...+1 = 66.

**Please, please don't make me show my work on this one! I'll just shorten it up to say that there are 55 unpaired K-high flops, 45 Q-high, 36 J-high, 28 10-high, 21 9-high, 15 8-high, 10 7-high, 6 6-high, 3 5-high, and 1 4-high. The sum of those is 220. Again, the order of the cards does not matter, nor do their suits.

*** I'll approach this one somewhat differently, because I think it's easier when the numbers get this high. Again ignoring suits, the number of unpaired boards is 13 x 12 x 11 x 10 x 9 = 154,440. But that counts every different order, so it vastly overcounts what we're interested in here. Each unique set of five cards (e.g., K-J-9-5-2) can have 120 different orders, so since we don't care about the order, the number of different unpaired boards for current purposes is 154,440/120 = 1287. I felt a bit unsure that I had this right, so I actually double-checked it by adding up the possibilities the same way as the previous calculations, and got the same number, so I'm confident about it. I.e., there are 495 unpaired A-high boards, 330 K-high boards, etc., down to 5 7-high boards and 1 6-high board, adding up to 1287.

For poker rules nerds only

Yeah, I'm one of them. I think it's fun reading poker rule books and figuring out ways that the rules could be worded better, or situations that the rules don't cover. I'm a poker rules nerd.

While reading an online discussion forum, I came across a link I already like a lot: http://www.thehendonmob.com/tournament_director/articles/introduction.html It's a series of situations--some real, some hypothetical--posed to six prominent poker tournament directors, and the discussions that ensue among them about how they would apply the rules. They don't always agree, and the different viewpoints and arguments is what makes this series interesting and thought-provoking--if you like that sort of thing, that is. I realize that I'm in a minority, but I love this kind of stuff. I feel like a pig that has just sniffed out a truffle.

See? Orthography is revealing after all!

I while back I commented on a press release from Absolute Poker about allegations of a security breach allowing a player to see all of his opponents' hole cards. See http://pokergrump.blogspot.com/2007/09/getting-things-right-or-not.html. Without even examining the evidence that serious online players had amassed, I concluded from the press release that all was not well. This was because, I opined, the horrible sloppiness of the press release assuring the world that nothing untoward was going on likely signified that the claimed investigation was just as slipshod.

You can, if you wish, read how my analysis was pilloried in a forum of Absolute Poker affiliates: http://www.pokeraffiliateworld.com/forums/general-poker-affiliate-discussion/11817-what-happened-absolute-thread.html

Well, it turns out that there was indeed foul play at Absolute, in spite of the site's previous reassurance that all was well. See http://tinyurl.com/2addoj and http://wizardofodds.com/software/absolutepoker.html for details of the analysis that would leave no serious doubt, even absent the company's admission. Additionally, it appears that we do have an admission of sorts from the site: http://wickedchopspoker.blogs.com/my_weblog/2007/10/absolute-poke-2.html

Of course, it's possible that, in reality, there is no connection on any level between the sloppiness of the press release that raised my suspicions and the fact that Absolute's "investigation" (if, in fact, there was one, as they asserted), oops!, somehow failed to find the cheating. But I'd like to think that my hunch was vindicated. A company that can't even bother to proofread its official statement to the world about how there is no problem is unlikely to have actually done a careful, thorough investigation in which one can place one's trust.

So there. Nyeah, nyeah, nyeah. (That is a sticking out of the virtual tongue at my previous naysayers.)

Poker gems, #39

Gabe Kaplan, on "High Stakes Poker," Season 2, Episode 4, when asked by A. J. Benza if Jennifer Harman is the best female poker player in the world:

I think it's between her and Bea Arthur.

More on the Hilton closure

I've written previously about how much I have liked the Hilton poker room (http://pokergrump.blogspot.com/2007/07/why-i-like-hilton-poker-room-non-grumpy.html) and how bummed I was to learn it was closing (http://pokergrump.blogspot.com/2007/09/my-favorite-poker-room-is-closing.html). Well, apparently I'm not alone. Here's a nicer eulogy than I could write: http://www.vegasrex.com/2007/10/16/farewell-to-the-hilton-poker-room/ . (Thanks to smudger for pointing me to this piece.)

I must have played with this guy, given his obvious familiarity with the room, but I don't know who it is. I do recognize the cast of characters he's describing, though. And, coincidentally, Rachel was my favorite dealer there, too. (It's actually "Rachel," not "Rachael"--but she fooled me, too, by having two nametags, one with it spelled each way. I never did learn why that was....)

I went by the room at 5:00 on the last day, and there was nothing happening. I had hoped for one more game there, but it wasn't to be. I went to the Venetian instead. I later learned that a game started up around 6:00 and went until 3:00 in the morning. I missed it. Oh well. There's always another game somewhere.

You can read a bit more corporate BS from the Hilton PR team here: http://www.cardplayer.com/poker-news/article/9937/strip-poker-hilton-poker-room-closes-its-doors

I wish I had written this

http://www.washingtonpost.com/wp-dyn/content/article/2006/03/09/AR2006030902272.html

If you don't catch the reference to cheese on the floor, well, it's way too filthy to repeat here, but it was one of the funniest tantrums ever on "The Sopranos." Let's just say that Silvio gets a little grouchy when he's losing at poker--worse than the Poker Grump, even.

Poker gems, #38

Steve Badger, in 1999, after winning a WSOP bracelet (as quoted in Larry Phillips, The Tao of Poker, p. 214):

I just played 22 hours of Omaha high-low.... Of that 22, 17 hours were like watching paint dry, 3 hours were even duller, and about 2 hours was like bungee-jumping from a helicopter into a vat of flaming eels.

Search engine amusements (non-grumpy content)

I was just looking over a report of where my reader traffic is coming from. One of the sources is Google, when people do a search for "poker clothes." With those words in quotation marks, I come up 16th; without the quotation marks, it's 28th. What's funny, though, is that the post such surfers get directed to is one which may discourage the purchase they were probably thinking of making when they typed "poker clothes" into Google: http://pokergrump.blogspot.com/2006/11/ugly-poker-clothes.html

Going south (and not for the winter)

After hanging out in poker rooms for not too long, you learn that one of the rules is that you can't take chips off the table until you take them all off when you're getting ready to finish your session. For example, you can't buy in for $200, win a big $600 pot, and put that profit in your pocket, keeping just the original $200 on the table to play with.

From the point of view of the other players, after you've had a nice win they want to have a chance to win their money back. From the point of view of the casino, more chips in play means bigger pots, higher rakes, and more players eager to join a table where there's lots of money to be won.

Those new to live play, however, sometimes don't know this. It's not terribly common, but maybe once a month or so, on average, I see somebody taking chips off of the table. It's usually quickly clear that they have no idea that this is against the rules and considered unethical. For the most part, as soon as somebody explains to them the rule and its purpose, they comply (or occasionally decide to leave, if they have made a big score and want to lock it up).

But I can recall at least two instances in which people rebelled. At Binion's once, a guy had had an amazing run and had accumulated something like $1300 in chips, which is pretty rare in a $1-2 game. A couple hundred of them had been mine. I was disappointed when he got up to leave. But I was surprised when he came back maybe 15 minutes later and bought back into the game for only about $200.

Most casinos have a one-hour rule, meaning that if you're gone for an hour or more you can re-enter the game for whatever minimum/maximum buy-in everybody else does, but being gone for less than an hour means that you have to put back into play whatever amount you left with, if it's over the maximum. This is to prevent people from getting around the rule by leaving and immediately returning, which would effectively be no different from just pocketing chips right at the table.*

Binion's has enough tables and traffic that it's easy for somebody to leave and come back soon thereafter without anybody noticing anything unusual. But when this guy came back to the same table he had just left, we all certainly noticed. I quietly walked over to the supervisor and told him what had happened. He was absolutely perfect about it--I wish I could remember his name and give him credit. He didn't embarrass this player at the table, but just asked to speak to him in private.

Well, their "private" didn't last long, because the troublemaker quickly became very loud and agitated. He didn't deny having taken away a large amount in chips, nor that he had been gone just a short time. Rather, he insisted that the floor guy was just wrong, that there was no such rule. This is a syndrome I've seen many times, and it always perplexes me: players (particularly out-of-town visitors) telling the room supervisor what the general rules of poker are, or, even more mysteriously, as in this case, telling him what the house rules are. The guy insisted that the same thing had happened the night before, and the shift supervisor there said there was no problem with his actions. Both I and the supervisor talking to him were extremely dubious that such a conversation took place.

Anyway, this imbecile kept arguing the point for maybe ten minutes. It was just nutty. He had several easy remedies: Come back in with the same amount he took off the table (he said he couldn't, because he had given it to his girlfriend, and she went somewhere else with it); sit out for the remainder of the hour; or just walk across the street to the Golden Nugget and play there instead. He could even have spent the hour playing a limit game at Binion's, because if you switch to a different game or different limits, it's as if you're starting out fresh, and what you won previously does not have to be put into play. I never did figure out why this guy got so agitated over something for which there were so many easy solutions, or why he instead chose the harder--impossible, actually--route of trying to convince the floor person that Binion's had no such rule. Well, other than the fact that he was a complete psychopath. That would kind of explain it.

The other time was at the Hilton. A tourist tried to give his friend something like $150 in chips to place a sports bet for him. I caught the dealer's attention to point out quietly what was happening, and the dealer informed him that he couldn't do that. The player wasn't happy about it, but didn't make much of a fuss.

But then just a few minutes later, when I looked up after being involved in a hand, I noticed that the guy was gone, and there were a lot fewer chips at his seat. Obviously, he had surreptitiously taken them away. I pointed this out to the dealer, and when the guy came back the floor person confronted him. He couldn't pretend not to have known the rule, since everybody had heard the dealer explain it to him. The guy admitted it, but still protested that he thought there shouldn't be such a rule. He finally agreed to put all the rest of what he had on him into play by buying more chips, but it was only about $50. (This appeared to be sincere--he emptied his wallet and pockets, and it didn't at all look to me like he had prepared to put on such a performance. He pretty clearly thought nobody would notice what he had done.) The rest of the money was now tied up in his sports bet, and he couldn't exactly get it back. The floor person accepted this, after explaining the situation to the table and asking if anybody objected. The dude was a really bad player, so we were happy to have him come back for whatever he had, even if it wasn't as much as he had disappeared with.

I've heard the term "squirrelling" applied to players who slip high-denomination chips off the table in knowing violation of the rule. (It's hard to do that with a large volume of low-denomination chips.) I had never heard the phrase "going south," for the same conduct, until the first time I watched Season 1 of GSN's "High Stakes Poker" (the re-viewing of which today triggered this post).

In one of the episodes, Freddy Deeb left the table to go smoke a cigarette. As he left, he hiked up his pants. Johnny Chan saw something that he thought was Freddy slipping chips into his pocket. On the tape it's pretty clear that he's just tugging on his pants, though he hand is right near the pocket. The producers later verified through their ongoing chip counts that no money had been removed, but the players didn't know that at the time. When Deeb returned, it caused five minutes of heated argument.

The strange thing about how the incident ended is that the floor guy they hired for the show (Bob Thompson) never resolved the question of whether Deeb had, in fact, removed chips from the table. Maybe he just thought (correctly) that it was extremely unlikely that Deeb would do such a thing, so the accusation didn't deserve actual investigation. (It does seem highly improbable. Even without cameras rolling and producers monitoring every pot to track who has how many chips all the time for the broadcast, Deeb is supremely confident in his ability to keep winning; he's not afraid of losing his profit, and if, for whatever reason, he felt like locking up a win, he would just quit the game.) If I had been in charge of settling the matter, I would have asked the table, "Does anybody claim to have actually seen Mr. Deeb remove chips when he left?" If the answer was no, then I would say, "All right, then, no more talk about it. It's done." If somebody claimed to have seen something, then it could be investigated.

Incidentally, this was another thing wrong with the poker in the awful movie "Lucky You" that I now realize I forgot to include in my previous list of criticisms (see http://pokergrump.blogspot.com/2007/08/why-do-poker-movies-have-to-be-so-awful.html). On their first date, the two main characters go to Binion's poker room. She stakes him, because he's broke and she just got her first paycheck in Vegas. (Today's helpful hint: Borrowing money to play poker may not be the best idea for a first date.) He scores a pretty good win, with her watching all goo-goo-eyed at his prowess. Then she has to leave to go to work, but he's going to keep playing. He picks up a couple of stacks of chips, representing her share of the profit, and hands them to her. The writer of the script did at least have the decency to insert a line of Eric Bana's character asking the other players if anybody minds, and nobody does. That's where it became unbelievable. In the real world, somebody absolutely would protest the removal of that much of his stack from the table.

I used to be so paranoid about not violating this rule that if I received in a pot some sort of unusual, commemorative chip mixed in among the regular ones, and I wanted to add it to my collection of special-issue chips, I would ask the table if anybody objected to my keeping it as a souvenir. After doing this a few times and getting only "what kind of a dork are you?" looks, I realized that nobody is quite that obsessive about the rule. Since nobody would or could possibly object to, say, giving a cocktail waitress a $5 chip as a tip, it's a bit crazy to think that anybody would care about removing the same amount of money as a souvenir.

That said, after I had come to realize that I really didn't need to seek the other players' approval to stash away one chip, I got "caught" (I put that word in scare quotes, because I wasn't trying to hide anything about it) by a dealer at Caesars Palace. He assumed I didn't know the general rule. I told him I did, but I didn't think anybody would mind one commemorative chip. He agreed that it's unlikely anybody would care, but in the future I should ask anyway. I didn't argue the point, but I think his is a minority view. I have since then politely ignored his advice and have continued to give myself permission to put the occasional souvenir chip in my pocket without asking anybody, and without feeling guilty about it. If anybody has even noticed, they haven't said anything about it.

Some poker rooms will also allow a player to use chips from the table to buy into a tournament that's going to be starting soon. This isn't unreasonable or unfair to the other players, since the person in question is presumably going to be taking all of his chips away pretty soon to play in the tournament.

But in general, if you have some reason to want to remove, say, more than 5% of what's in front of you, you should definitely ask the dealer if it's OK. He or she can then tell you the rule, or poll the other players, or have the floor person make a decision. If you're told you can't do it, for heaven's sake don't be a dickwad about it. Find some other above-board (i.e., not squirrelling) way to accomplish whatever it is you need to do, or just end your poker session right then. There's always another game going on somewhere else, or at the same place later, that you can get into.

And above all, don't argue about it. You will lose the argument, sour everybody that's exposed to your stupid ranting, and just end up looking like a jerk in the process.


*I wish that casinos would push the time limit up to, say, three hours. There is at least one regular at the Hilton who routinely locks away any decent-sized win by leaving and watching sports for one hour, then coming back and starting out afresh. It's seriously annoying--and unfair--to the other players. Three hours would be enough that much of the table composition would have changed, and it wouldn't feel as if somebody is just skirting the usual convention. The casino I used to play at most in Wisconsin had a three-hour rule, and I was suprised, when I moved here, to learn that most places have only a one-hour rule.

Blogger championship

Finished in 800th place out of 1337 in the PokerStars blogger freeroll. Hmmm. Maybe not my most impressive performance ever. But I did outlast Wil Wheaton!