PokerNews article #106

A new study of the psychology of Rock Paper Scissors can teach you something about poker, too.

http://www.pokernews.com/strategy/make-your-poker-game-less-exploitable-rock-paper-scissors-24419.htm

Roshambo-playing robot

Way cool. See here: http://goo.gl/2Qcu3

Hat tip: Pokerati.

Heading back to Vegas in the morning.

Trivial pursuits

I've mentioned a few times here that in recent weeks I've been participating semi-regularly in a weekly team pub trivia contest run by Vegas Pub Quiz. The team, "Quiz On Quiz Off," is a loose and ever-changing group anchored by Katie Baxter and Bob Lauria. The team has been privileged to have as guest players such luminaries as Shamus, Julius Goat, and Matt Matros.

There was a series of ten weekly contests constituting league play, and our team came in first from those playing at McFadden's. Saturday night was the season finals, gathering together the top finishing teams from all of the pubs in which VPQ runs the contests--16 teams in all.

Unfortunately, we were seriously handicapped by the fact that Katie recently decided to move back to the Washington, D.C., area. If there was one team member who most reliably was alone in knowing some obscure bit of information, it was her. But it was a freeroll, so we gathered at Quinn's Irish Pub at Green Valley Ranch, and did what we could.

We aced the first round, 100%, but then stumbled badly on the next two rounds. Things were so tight that it seemed impossible for us to have any room in which to make a comeback. After the completion of the first five (I think) rounds, when they announced standings, I counted eight teams listed ahead of us, and two more tied with us. Only the top three won the cash prizes. It was looking grim.

But then we pulled off a stunning rally in the final round, where questions are harder and point values are doubled. On no less than five questions, none of us knew the answer, but we put together weird combinations of uncertain fragments of wispy memory, reasoning, and good guesswork--and nailed every one of them. These included such oddities as the kind of bird the character "Flit" was in the Disney Pocahontas movie, the popular store chain known for having a "You break it, you bought it" policy, a rock band named by combining parts of two of its members' names, and the number of freedoms FDR listed in a speech.

Amazingly, we did so well in that last round that when they announced the final standings, we had advanced into a three-way tie for second! First prize was $500, second was $250, third $150. Fourth place team would receive nice commemorative keychains. (Insert "loser" tuba sound from "The Price is Right" here.)

The tiebreaker question: How many bottles of wine does the average American buy per year? We guessed 9. They gave the answer as 15. (Poking around the web now, I think the real answer is probably closer to 13, but whatever.) Apparently one team nailed it and was awarded second prize. Our team and one other were left to fight for the min-cash.

Strangely, and without forewarning, they announced that this would be settled by Rock, Paper, Scissors, rather than by another trivia question. Which seems to me kind of like resolving a tied tennis match by playing a hand of gin rummy, but they didn't ask my opinion.

Stalwart team member Chris Minton was forcibly pushed volunteered to go up on stage. Just before he went, I had one bit of advice for him.

I pause in the story here to tell you that I am by no means a Roshambo expert. I do know enough, however, to understand that it is, or at least can be, far from just a quasi-random means of settling disputes, which is the only way most people know of it. I first became aware that there were serious students and players of the game maybe six or seven years ago when people like Annie Duke, Phil Gordon, and Rafe Furst put together Roshambo contests for charity in conjunction with the World Series of Poker. (Why did they stop that? It was fun to watch!) After hearing about those hijinks, I followed a few web links, and discovered that there is a whole subculture of people who take the game very, very seriously.

My most eye-opening moment came when I read Furst's chapter on Roshambo in The Full Tilt Poker Strategy Guide. Perhaps your first reaction, like mine, was, "Why is there a chapter on rock, paper, scissors in a poker book?" Well, Furst explains some of the basics of the leveling and mind games that go into serious Roshambo, and shows how the same principles are relevant to poker.

People may try to be random in their selection between rock, paper, and scissors for any particular throw, but, in fact, we humans are terrible randomizers. Most people end up with fairly easily observed patterns. The experienced and attentive player can predict what his opponent will do (and sometimes even influence what he will do) with sufficient accuracy that a rookie has nearly no chance to beat a good player over a string of, say, 100 throws. People are predictable enough that a computer can beat most players over the Internet, even though it can't observe tells telegraphing what the opponent is going to throw, the way expert live players can often do. (I wrote about failing to beat the computer here. You can see all of my posts that discuss Roshambo here.)

So, as I said, I'm not an expert, but I've read enough from the those who are to have picked up a few basic pointers. Among them is what I think must be the single most easily exploited fact when facing an unknown opponent who one presumes is not a serious student of the game. It was that bit of well-documented observation that I whispered to Chris just before he left to do battle for our team:

"If they send a male, go paper. Most men will throw rock the first time." *

He looked surprised, but accepting.

Chris and the other guy get up in front of the crowd. The announcer counts down the fist pumps with them: "One, two, three, SHOOT!"

Other guy: Rock.

Chris: Paper.

And just like that, team Quiz On Quiz Off slides into the min-cash and chops $150 among our five team members.

After all of the strange things we had to know or guess at in order to win the league from McFadden's and then squeak into a tie for second place, it was that one bit of knowledge about game theory that ended up the difference between getting cold, hard cash and getting keychains--a fact that I knew only because of having read about Roshambo due to its interesting psychological parallels with poker.

I have to admit, I still can't stop grinning when I think about how it ended. Sure, first or second prize would have been nicer, but it was pretty sweet to snatch third place from the jaws of defeat, not by virtue of us knowing an extra piece of trivia knowledge, but by virtue of being better game players.

They'll still be running the weekly trivia contests at McFadden's and elsewhere, but I'm no longer going to make it a priority, as I had been doing recently. The prizes are reasonably generous, but they are all in bar tabs. Since my standard is to get one $3 lemonade to sip while we play, there's really not much incentive to spend a couple of hours a week at it. It's been fun, but I think I've had enough for now. I might revisit when friends are in town (I have reason to believe that Cardgrrl would crush the competition, which would be fun to watch) or some such other special occasion, but not every week. I'd rather spend the time making money at poker.

Or rock, paper, scissors.

* Of course, this doesn't apply to people who are aware of it (which, fortunately, is a slim minority of the populace). In fact, Furst's chapter describes some of the Jedi mind tricks he plays on opponents. For example:

My power move against new opponents is to say, "I'm going to throw rock," and nothing else. I am doing this to induce in you a belief that I'm not going to throw rock, at which point I will throw rock. Or if I think you are the type to believe that I will do as I say, then I'll do so with the intention of throwing scissors (or paper, depending on whether I think you will be aggressive or not).

Bonus footage: Lisa and Bart Simpson play Roshambo:

Play roshambo against a computer

This is more interesting than it has any right to be. Try the "veteran" version. It's positively creepy to feel the computer analyzing your moves and guessing what you'll do next--especially since it's so good at it. Out of 100 trials, I won 25, tied 41, and lost 34. It seemed not to matter whether I tried to be random, or tried to deduce what the computer would be expecting and then counter it. Either way, I lost more than I won.

For the second round of 100, I decided to enlist a little computer help of my own. I used Excel to generate a random number 1, 2, or 3, and entered my choice accordingly. That allowed me to improve to 37 wins, 32 ties, and 31 losses. Ya gotta fight fire with fire.

Thinking too high

This post from Shamus today details Darvin Moon's recollection of the big hand in which he knocked Billy Kopp out of the World Series of Poker main event, just before getting to the final table. Shamus also points to this interview with Kopp, in which he lays out his thinking as the hand was progressing. I haven't been paying much attention the November Nine, so I had not been aware of either of these sources.

The contrast is stunning. Kopp is thinking, oh, about 17 levels ahead of Moon. Moon isn't even correctly aware of what the cards on the board are, let alone getting inside Kopp's head. He's playing somewhere between that infamous Level Zero and Level 1.

This reminds me of several things, all of which are basically making the same point. First is a little tidbit I read just today in Jeff Hwang's column in Card Player magazine (November 4 issue, vol. 22, #22):

In poker, we might assume that our opponent took a certain action for a
reason, when the reality may be that he has absolutely no idea what he is doing.

For example, your opponent--a tourist who has never played poker
before--bets $600 into a $1,000 pot on the river. You wonder what he has. You
wonder what he thinks you have. You wonder what he thinks you think he thinks
you have...and so on. And you try to analyze his bet amount.

For all of the multiple levels of thinking you've done, it's possible that
his bet size and action is completely random. Maybe the minute timer on his
watch read "00," and maybe a girl walked into the room who looked like a "6," so
he simply put the "6" and "00" together and decided to bet $600!

Next is this from Bryan Devonshire, which I posted as a "Poker Gem" last year:

I always laugh when people fail to realize when players are not paying
attention and try to put moves on them, because some people wouldn't notice if
an African elephant walked across the table, much less what your bluff bet was
supposed to be representing.

Then there was this from Dave Irish:

You can't play level 3 poker against people who don't understand Level
1.

And finally, there is a great chapter by Rafe Furst in the Full Tilt Poker Strategy Guide, in which he cogently discusses what can be learned about poker from roshambo (rock, paper, scissors). The basic idea is summarized nicely in this exchange between Furst and Michael Craig, the book's editor (p. 414):

FURST: Against expert roshambo players, you have to go many levels deep in your
thinking.
CRAIG: How many levels do you usually have to go to win?
FURST: The amount never varies: one level deeper than your opponent.

The point is, of course, that going one level too deep is just as disastrous as going one level too shallow, and that is true no matter what your opponent's depth of thinking might be.

Billy Kopp probably knew that before this year's World Series of Poker. If not, he learned the lesson in the most expensive way possible. Either way, my guess is that he will never, ever forget it.

Strong means weak, right?

I was just reading through the archives of a poker blog I've newly discovered, one that I'm liking a lot so far, and about which I'll tell you more later. For now, though, it's enough that a story there reminded me of an embarrassing, but, in retrospect, valuable lesson that I learned in one of my first attempts at playing poker in a casino.

I was living in Minnesota. About 90 minutes away in western Wisconsin was an Indian casino that held a weekly no-limit hold'em tournament for, I think, $50. I went to it pretty regularly. It had largely the same people playing every week, capped at about 70. (Small poker room.) I had read one or two poker books and watched the WPT regularly. Felt like I knew what I was doing (though I now realize that I had absolutely no clue--poker is like that, making you feel like you've got it pretty well figured out at every stage of your development).

I don't remember any details of the hand in question, except that there was a woman who was exhibiting all of the classic "tells" of weakness, in that she was acting strong. She was fast and emphatic and forceful about all of her movements, leaning forward, looking smugly right at me, etc. I had some mediocre crap, but she so perfectly fit the profile I had read and heard about--that acting strong means the player is bluffing--that I just knew I could call her down and win. I wasn't born yesterday! You can't fool me that easily, lady--I've read books, y'know!

Except that, oops, there's something that wasn't mentioned in those books and in Mike Sexton's commentaries (or at least I didn't remember it): Sure, the Hollywooding types who fit that "strong means weak" profile are pretty low on the ladder of skill and experience, else they would know how ineffective a ruse it is. But once in a while you run into somebody who is even lower on the ladder than that, and doesn't even have the good sense to try to disguise his or her weakness with signs of strength, and vice-versa.

These people are not being tricky. They are being transparent.

The woman in question in this hand was one of them. After I had called off nearly all of my chips to her, she turned over the flopped nuts and doubled up. I distinctly remember getting strange looks from several other players, which, if translated into words, would have said, roughly, "You moron--couldn't you tell she had the goods from how she looked?"

I had out-thought the situation. I was not exactly a deep thinker about poker back then, but I was thinking one level above where my opponent was, which is just as fatal an error as thinking one level below where one's opponent is. It's like when playing Roshambo. You have to know whether your opponent is (1) somebody who will always throw Rock the first time, (2) somebody who knows you think he will throw Rock the first time and will therefore go Scissors to catch your Paper, or (3) some other meta-level beyond that. Thinking one level too deep there is as deadly as thinking one level too shallow.

Several weeks after my embarrassing discovery, I was starting to become friendly with a local semi-pro who played at that casino a lot. I told her my story. She laughed, and agreed that that player was perhaps the most transparent regular the place had, but that there was no way to know that other than to watch her, then see her cards, and make the connection.

Of course, you have to discover that sort of thing by experience.

Fortunately, I'm now at least a little bit better at sensing the distinction between strong-means-strong transparency and strong-means-weak Hollywooding. But it was disconcerting and embarrassing to discover that I couldn't just interpret a given type of action in one way all the time. Dang--this game may be harder than I thought!

Just when I had come to expect that everything about poker was an attempt to deceive me, I found out that that's not quite so.

A poker player tries a different game, and wins (non-grumpy content)

I hadn't done anything with my UltimateBet account in a long time, so decided to see what was happening there. Sometime earlier this year, as it turns out, they added Roshambo (Rock Paper Scissors) to the games you can play. I had to try it out.

I went for the $0.50/match table (match is best of 3 throws). I knew that I would outthink myself and second-guess, third-guess, and fourth-guess myself into utter insanity if I actually tried to analyze what an opponent would throw and then take counter-measures. So instead I opened Excel, did a one-cell spreadsheet of =RANDBETWEEN(1,3), then hit F9 before every throw. This would generate a randomly selected integer between 1 and 3, and I would go with that, no matter what I thought my opponent would do. (After I got tired of switching back and forth between applications, I had Excel print out a list of 1000 of these random digits. It's easier to just run my finger down the page, but the effect is the same.)

24 hours later, I've done surprisingly well. I've made $11 in maybe 3 hours of playing online. Not exactly a huge rate of return, but it's the win rate that has me intrigued more than the dollar income. I've taken on 9 opponents and defeated 8 of them, all in sets of at least 3 matches, to a max of 19 matches.

Unless this is just the good side of variance, I don't get it. Using a truly random strategy, I shouldn't be able to win or lose. In fact, in the long run, I should lose exactly $0.02/match, which is the UB rake on the game. I'm obviously not outplaying my opponents in any meaningful sense, since I'm not even trying to strategize. But it seems to me that it shouldn't matter how "well" or "badly" opponents play, either--they could go for "rock" every single damn time and be able to tie me over the long haul. And, of course, they could have been using the same random strategy, for all I know (although I was quite sure I could pick up patterns against some of them).

What's more is that I'm confident I could have done better by occasionally departing from my random-number list, because there were times when I felt extremely confident what an opponent was about to do, and I was nearly always right in those spots. There was some definite bleed-over from poker habits involved here, because I could figure out what my opponent must be thinking that I was doing, based on what would appear to him/her to be a pattern I was engaged in.

So am I right that this initial success is just an unusually lucky run, or am I missing something? That is, is there some way that an opponent can systematically make his outcome against a random strategy worse than average? If so, I don't see how, but it's not something I've thought about in enough depth to have clear thoughts on yet.

The only things I've read about Roshambo strategy are Rafe Furst's chapter in the Full Tilt Poker Strategy Guide, but that's just about getting inside an opponent's head, which I haven't even been trying very hard to do. I also found a couple of pretty superficial online strategy guides, but haven't looked around enough to see if there are in-depth discussions, though I assume there must be.

For now, I'm pleased to be winning, even if it's only small amounts, and even if it is just dumb luck, because it's fun and a nice diversion from poker.


Addendum, November 11, 2007

Immediately after writing the above, the pendulum of statistical variance turned against me. Since then, I have engaged in 23 contests, ranging from 1 to 31 matches (each match being best of 3 throws), winning 5, tieing 5, and losing 13. Ignoring contests/sessions against particular opponents, and lumping together all of the results since my last post, there were 137 matches, including 62 wins and 75 losses. This is easily within the expected range given by the binomial distribution; a handy online calculator for such things (http://faculty.vassar.edu/lowry/binomialX.html) tells me that a coin flipped 137 times will have an outcome at least this skewed from an exactly even split about 31% of the time. That would have to be at around 5% or less to make me think that there was something other than pure chance operating.

The experiment has sufficiently convinced me of what I suspected before: that playing a random strategy basically yields random results. My initial success was a statistical blip, which has been reversed with the subsequent games. What's more, I've concluded that playing a random strategy is pretty boring, and playing with a non-random strategy is probably only a little less so. I may revisit the game from time to time for a bit of diversion, but I feel like I've pretty much exhausted my interest in it for the foreseeable future.