The results are in

Four months ago I told you that I was among the choices available for a reader survey by Ante Up magazine. I subsequently forgot all about it.

Yesterday afternoon I was at Caesars Palace waiting for a seat be available and started flipping through the October issue. When what to my wondering eyes should appear...


 

So there you have it.

You can vote for me

Ante Up magazine has an online reader survey. One of the questions asks, "What is the best poker blog?" The options are Shane Schleger (Shaniac), Hard Boiled Poker, Full Contact Poker, Phil Galfond, and Poker Grump.

You can go here to start the survey. There are small prizes to be awarded to survey participants. The caveat is that you have to give them your email address in order to answer the questions, and I have no idea how much they'll pester you thereafter with annoying emails. Furthermore, there's nothing in it for me even if I should happen to get the most votes. All of which means that this is of virtually no importance to me, and you shouldn't feel any sense of duty or obligation to participate. Furthermore, if you do decide to participate, honesty requires me to point out that there's a strong argument to be made that Shamus deserves your vote more than I do.

But it's there if you feel like it. Do as seems best to you.

Ante Up magazine cover

I have now seen the April issue of Ante Up magazine, and it included a brief note from the publishers about the anomaly on the March issue cover, which I mentioned here:

On a quick side note, we'd like to thank the pranksters at Beau Rivage for putting two 9s in front of John Dolan in the Million Dollar Heater victory pose we ran on our March cover.

We were seeking a quick way to find out how many people actually look at our cover, and judging by our full inboxes and bloated voicemail from readers wondering how Mr. Dolan won an event with two of the same card, we happily have our answer.

Anomalies

Two odd poker-related visuals have caught my eye this week.

First, I got an email from Bovada (formerly Bodog), saying how much they've missed me since I haven't played there in a few months. It includes a nice tournament ticket, which I will definitely use, so I kept this in my email in-box to remind myself to check the schedule for when I can use the ticket. But the longer it sat there, the more I thought something didn't look right. I finally looked closely and realized the problem:

It's the geography. Paris is indeed just across the street from the Bellagio, but that establishes that we're looking south on Las Vegas Boulevard from Flamingo Road. But then we see Caesars Palace further south, and facing us. This is wrong, because CP would be behind us, and facing east, the same orientation as Bellagio.

Then there's this weird cover photo from the March issue of Ante up magazine. Pay particular attention to the cards:

This is what has become pretty much the industry standard tournament winner's photo, with all the chips, the winner's trophy, and the hole cards the winner had on the last hand. (The only thing missing is the traditional cash.)

But did he really win the final hand of the tournament holding a nine of spades and ANOTHER NINE OF SPADES? Let's all say it together: "Fouled deck. Take your bets back."

Weirdness abounds.

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.

Kandu Challenge

I was just reading the newest Ante Up magazine, and found a brief article by attorney Marc Dunbar. (Available online here, page 62.) He is discussing recent legal cases in which courts had to determine whether poker is predominantly a game of skill or of chance. He thinks the courts are getting it wrong by usually ruling it a game of chance.

His discussion mentions a case I had not heard of, so I looked it up. It's Three Kings Holdings v. Six, from the Kansas Court of Appeals, June 10, 2011, available here. I found a couple of references on poker-related sites about the trial court decision in 2009 (e.g., PokerPages story here), but not a word anywhere in the poker media about the recent appellate decision. I don't think I had ever heard of either the game or its legal history before tonight.

Kandu Challenge is Texas Hold'em with one significant twist: After the cards are shuffled, but before any are dealt, the deck is spread out in front of the players face up for three to five seconds, allowing players a chance to memorize the order of as many cards as they can. The dealer then gathers the cards without disturbing their order, cuts the deck, and shows the card at which the deck was cut. In theory, if you had been able to memorize the entire order, you would now know exactly which cards would be dealt to every player, as well as what would be coming on the flop, turn, and river. Wouldn't that be nice?!

The game was offered at some sort of card room in Wichita, but within a few months was shut down by the state attorney general as a violation of state gambling statutes. The game's owners sued, arguing that skill dominated over chance in determining the outcome. They lost and filed an appeal.

The appellate court basically rehearses the trial court's decision and endorses it at every crucial step. Most interestingly, this included a lengthy discussion of whether the skill/luck determination should be made based on a single hand or based on some undefined longer period of time. This is a question that other courts have touched on briefly but without much rigorous analysis.

It's true that the "spread the deck" twist adds a feature not found in regular poker, and it might arguably increase the skill factor, because quick memorization of many cards would clearly grant a significant edge. But the courts didn't put much stock in this, based on witnesses saying that they could usually only memorize four or five cards in the allotted time, and they had not found that doing so had helped them win.

The courts, then, analyzed the case just as they would for Texas Hold'em--which is why the discussion of whether the legal determination on the skill/luck question should be made on a single hand versus some "long run" (a session of a few hours or more) is potentially important to other courts that will face the same question in the future.

Their decision is, I think, hard to argue with. The rules allow a player to play just one hand and then leave, even if few people actually do so. A winner is unambiguously determined at the conclusion of every hand, but there is no unambiguous way to determine a "winner" if you extend the period of consideration arbitrarily. Most importantly, if the analysis isn't done on the basis of a single hand, then there is no other logical unit to apply.

Once the courts had almost entirely discounted the ability to memorize the order of the deck--Kandu Challenge's only unique feature--and had decided that the skill/luck determination had to be made, for legal purposes, on the basis of a single hand, well, the outcome was in the cards, so to speak. I don't think anybody can seriously debate the proposition that what cards one is dealt and what cards come on the board are more determinative of the outcome of a typical hand of poker than the relative degree of two players' skill. If Joe Tourist and I play two hands, one where I beat his straight with my flush and one in which those hands are reversed, my greater skill might cause me to win more than he does with the flush, and lose less than he does with the straight. But no amount of skill can make a straight beat a flush.

I summarized and posted pointers to the other recent state appellate court cases a few weeks ago here. You can now add the Kansas decision to the growing list of cases in which courts view the skill versus luck question entirely differently than we as poker players are inclined to do. At least in this case the courts made explicit the basis for their rulings, and the underlying logic, rather than just waving off the overwhelming expert testimony that poker is, in fact, a game of skill.

Daily tournaments

I frequently hear tourists at poker tables asking dealers and locals where to find tournaments at a certain time of day, or of a certain length, or in a specified buy-in range. There is, of course, the comprehensive database maintained at AllVegasPoker.com, here. But it's a daunting list--bewildering for having so many options from which to choose.

Yesterday I picked up the September issue of Ante Up magazine, and found that Michael Hamai's column points to some specific suggestions based on buy-in and game type, which I think will be helpful in narrowing down the long list of possibilities for out-of-town visitors. You can read it online, though it's a little awkward, requiring either Flash or a PDF download. See here, page 32.

P-p-p-poker face, p-p-poker face (mum mum mum mah)

I was reading the current issue of Ante Up magazine, and came across an interesting column by psychologist Stephen Bloomfield. He discusses the results of a study that I had not heard about elsewhere. It's available online here (in fact, it seems to have been published only online, not in a traditional peer-reviewed scientific journal).

Here's the formal citation: Schlicht EJ, Shimojo S, Camerer CF, Battaglia P, Nakayama K (2010) Human Wagering Behavior Depends on Opponents' Faces. PLoS ONE 5(7): e11663. doi:10.1371/journal.pone.0011663

The gist of it is this: They took a bunch of volunteers and made them play lots of simplified Texas Hold'em hands against an imaginary opponent. The subjects' only decision in each case was to call a raise to 5000 chips, or fold and lose the 100-chip blind they had posted. The only information they had available on which to make the decision each time was (1) their own hole cards, and (2) an image of the face of the opponent.

There were actually 100 different artificial opponents, i.e., 100 different synthetic faces, each of which could be presented in a neutral variant, a trustworthy variant (relaxed, smiling, friendly), or an untrustworthy variant (scowling, hostile). The central research question was whether the subjects would tend to alter their betting patterns based on which type of face they were looking at, when their hole cards were held at a constant absolute value.

The answer: Yes. But only in one direction. The trustworthy facial variant triggered more folds than the neutral one, but the untrustworthy facial variant did not cause more calls than the neutral one. Most of the shift in betting patterns occurred, as might be expected, where there was not much difference in expected value between calling and folding. In other words, a trustworthy face tended to tip the decision toward a fold only where it was already a close, difficult choice to make.

The increased influence of trustworthiness on reaction time (Figure 3B) and correct decisions (Figure 4B) around the optimal decision boundary suggests that people are using face information most for medium-value hands. This could be explained by optimal data fusion [33]–[35], which states that the more uncertainty people have about the value of their hand, the more they should weigh face information when making a betting decision. Since participants in our experiment were novices (12 of 14 play less than 10 hours/year), they may have a more reliable estimate of high-value hands since those tend to be more salient/memorable (e.g., face cards, aces, pairs, etc.) than medium- and low-value hands. Indeed, participants in our study took significantly longer to react to hands in the optimal fold region (Figure 3B), and also made significantly more mistakes for medium- and low-value hands (Figure 4B), supporting this notion.

It is also interesting that all of the changes in wagering decisions were observed against trustworthy opponents, while untrustworthy opponents did not yield any significant results. This asymmetry is even more fascinating given that people's perception of trustworthiness is more sensitive to changes between untrustworthy and neutral faces, than between neutral and trustworthy faces [27]. One possible explanation stems from the assumption that people use a random opponent decision criterion in this task, unless there is information that an opponent is betting with non-random hands. In this respect, neutral and untrustworthy faces are functionally the same: neutral faces do not provide information about an opponent's style, while untrustworthy faces may suggest that opponents are betting with poor hands. However, if participants are already assuming opponents bet randomly, they cannot decrease their criterion any further. In agreement with this proposal, Figure 5B shows that the inflection point for the neutral (Green) and untrustworthy (Red) curves is very close to the optimal decision boundary for a random opponent. However, trustworthy faces may provide information that the opponent has a high-value hand, leading to the observed shift towards more conservative wagering behavior.

(Incidentally, I think the fact that these subjects were not proficient players puts significant limits on the generalizability of the results. Even if they hadn't specified this, you could infer it. Inexperienced players tend to want to play every hand; they're reluctant to throw anything away, which explains the increased reaction time and increased frequency of mistakes with poor starting hands. What an expert would muck instantly (bluffing not being an option), the amateurs tend to want to play. Given that the researchers set the opponent's raise size at a rather ridiculous 50 big blinds, good players would immediately start with the assumption that their best strategy will be to reject all but the strongest starting hands.)

The authors' bottom-line conclusion:

Interestingly, contrary to the popular belief that the optimal poker face is neutral in appearance, the face that invokes the most betting mistakes by our subjects is has attributes that are correlated with trustworthiness. This suggests that poker players who bluff frequently may actually benefit from appearing trustworthy, since the natural tendency seems to be inferring that a trustworthy-looking player bluffs less.

I suppose there's some truth to that, but it seems to give opponents little or no credit for being able to learn. (There was no opportunity to learn and therefore adjust strategy in this study, because each trial involved a different opponent.) Frequent bluffers get sniffed out even by inexperienced opponents. After some period of time of frequent raising, everybody is going to be thinking, "He can't have a real hand every time." No facial expression is going to change that reaction. At best it might delay it a bit. And what about the player who isn't bluffing, who wants to induce calls from weak hands held by weak opponents? The information from this piece of research doesn't seem to offer any assistance there. I suppose you could try adopting the trustworthy face when you're bluffing and not when you want a call, but again, any opponent with two neurons connected inside his skull will figure out that obvious ruse before too long.

Still, I found it interesting that there is at least a modicum of empirical evidence to support Mike Caro's frequently repeated maxim that being friendly and open, chatty, relaxed, fun-loving will win you extra calls compared to the guy making the same bets with the same hands, but who is silent, scary-looking, deadly serious, intimidating, or insulting. Caro's reasoning has to do not so much with the issue of trustworthiness, but just the fact that recreational players don't mind losing money to people they like and who they know will not criticize or embarrass them for making a bad call, so they're more willing to make what they know is a likely futile or "keeping you honest" or mere curiosity call.