Posts Tagged ‘game theory’

The Wired blog yesterday reported on a recent experiment in which robots “learned” deception autonomously, without specific instructions from their programmers:

I’ve had some deep runs lately in the Saturday $300 6-max, so I was looking forward to this event. Unfortunately, it didn’t really go my way. I lost a big pot (though not my stack) with AJ vs. AQ on a AJ7Q9 board in a 3-bet pot. My bust-out hand requires a little explaining. The guy who open limps had been doing that a fair bit, I think he was playing like 32/15. I’d just shoved over his limp the hand before.

The guy who shoves had been pretty shove-happy in general. I think he’d even open shoved like 30-some BB’s once. I recognized his name, so I don’t think he was a maniac, just a tourney donk who understood unexploitable shoving and was more comfortable playing that way.

Full Tilt No-Limit Hold’em Tournament, 100/200 Blinds (6 handed) – Full-Tilt Converter Tool from FlopTurnRiver.com

Button (t3372)
Hero (SB) (t4393)
BB (t13870)
UTG (t10287)
MP (t11968)
CO (t11704)

Hero’s M: 14.64

Preflop: Hero is SB with K, Q
2 folds, CO calls t200, Button bets t3372 (All-In), Hero raises to t4393 (All-In), 1 fold, CO calls t4193

Flop: (t12358) 5, Q, A (3 players, 2 all-in)

Turn: (t12358) 2 (3 players, 2 all-in)

River: (t12358) 8 (3 players, 2 all-in)

Total pot: t12358  Read the complete post...

Verlyn Klinkenborg, who regularly contributes interesting and well-written little essays  to the New York Times Op-Ed page, writes today about four-way stops and what a surprisingly successful tidbit of human cooperation they are:

What a four-way stop expresses is the equality of the drivers who meet there. It doesn’t matter what you drive. For it to work, no deference is required, no self-denial. Precedence is all that matters, like a water right in Wyoming. Except that at a four-way stop on the streets of Rancho Cucamonga everyone gets to take a turn being first.

The underlying theme here is nothing less than the importance of  rational games playing to a functioning society. As poker players, we tend to focus on game theory’s competitive applications in zero-sum situations, but game theory is equally as applicable to cooperative interactions that realize non-zero-sum benefits. (For more on this subject, see my review of Robert Wright’s Nonzero.)

In fact, I just record a video for Poker Savvy Plus yesterday in which I used traffic lights as an example of a Nash Equilibrium. The really remarkable thing about the four-way stop is that it is largely self-governing, as opposed to the traffic light, where drivers obey orders from (literally) on high. Yes, there are rules for how to behave at a four-way stop, but their application in a particular situation are almost always left to the individual judgment of the drivers. There is no flashing light or other signal to tell you when it is your turn and when you must defer.  Read the complete post...

The player that I ended up sucking out on yesterday was the reason I was sitting in this 40/80 game. I didn’t recognize his name, so I sat in and started playing a bit. It quickly became apparent that he was one of the most loose and aggressive players I’d ever played with. My HUD showed him running at something like 45/32/9, which was telling even over a small sample size. I had never seen him fold to a continuation bet, either.

Not that he was terrible. He actually seemed to play reasonably well post-flop, but against good players, I just don’t think it’s going to be possible to show a profit playing 45% of your hands at a 5-handed table. Still, figuring out how to adapt to such aggression was tricky. Here’s a hand I’m still not sure about:

Full Tilt No-Limit Hold’em, $80.00 BB (5 handed) – Full-Tilt Converter Tool from FlopTurnRiver.com

Button ($12588)
SB ($16658)
BB ($16438)
UTG ($24125)
Hero (MP) ($10647)

Preflop: Hero is MP with 9, A
1 fold, Hero bets $240, Button calls $240, 2 folds

Flop: ($600) J, 2, 3 (2 players)
Hero bets $444, Button calls $444

Turn: ($1488) K (2 players)
Hero checks, Button bets $1200, Hero calls $1200

River: ($3888) K (2 players)
Hero checks, Button bets $2800, Hero calls $2800  Read the complete post...

My tournaments results have been pretty good the last few months, culminating most recently in two PCA seats and a win in the FTP $300 Saturday 6-Max. I attribute this improvement to a disciplined effort to avoid bringing the aggressive play needed to win in high-stakes cash games over to a tournament setting where my opponents are far more passive and far less tricky.

Last night, in the $300 rebuy FTOPS event, I was rolling along nicely and then fell off the wagon:

Full Tilt No-Limit Hold’em Tournament, 170/340 Blinds 25 Ante (6 handed) – Full-Tilt Converter Tool from FlopTurnRiver.com

BB (t13511)
UTG (t19356)
MP (t20140)
CO (t18855)
Button (t12236)
Hero (SB) (t19919)
Hero’s M: 30.18

Preflop: Hero is SB with 8, K
4 folds, Hero bets t1020, BB calls t680

Flop: (t2190) 9, 2, 7 (2 players)
Hero bets t1333, BB raises to t3125, Hero raises to t18874 (All-In), BB calls t9341 (All-In)

Turn: (t27122) 2 (2 players, 2 all-in)

River: (t27122) A (2 players, 2 all-in)

Total pot: t27122

Results:
Hero had 8, K (one pair, twos).
BB had A, 9 (two pair, Aces and nines).
Outcome: BB won t27122  Read the complete post...

Robert Wright’s Nonzero is not a poker book. I picked it up because it claimed to apply game theory to human evolution, both biological and cultural, and to offer a sweeping and prophetic account of humanity’s history and future. Yes, that’s a pretty ambitious goal, and the author acknowledges as much. Wright does indeed provide a fascinating, fast-paced survey of the history of human civilization that, despite occupying only one-third of a not particularly long book, rarely feels rushed. His predictions for the future are spotty, which can be forgiven, but he could at least provide more guidance about what the world’s leaders ought to do to continue to pursue mutually advantageous relationships. As nothing more than an educated layperson, I found Nonzero to be a quite compelling introduction to the continuing evolution of human civilization, with at least a glimpse into what the future might hold as well.

I also found most of the content to be not nearly as controversial as the author seemed to expect it would be. This, I think, is due to the fact that I was not previously familiar with the academic literature that Wright engages. The central thesis of Nonzero is that, at both the cellular level and the cultural level, the possiblity of realizing nonzerosum gains rewards cooperation and complexity and punishes those who go it alone. Though I found it unremarkable to suggest that life on earth is evolving towards ever-greater complexity and that this evolution is not solely motivated by changes in the external environment, Wright exerts a good deal of effort refuting some prominent academics who argue otherwise. In his defense, he does provide a very accessible introduction to these long-standing debates.  Read the complete post...

Small Stakes No-Limit Hold ‘em
by Ed Miller, Sunny Mehta, and Matt Flynn

Professional No Limit Hold ‘Em, Volume 1 (PNLHE) is one of my all-time favorite poker books and the one that I recommend to anyone looking to get started to the game. I eagerly awaited the publication of Volume 2, which was rumored to deal with short-handed games and more advanced concepts, and mourned its loss when its authors parted ways with Two Plus Two Publishing.

Ed Miller, Sunny Mehta, and Matt Flynn ultimately self-published the book now known as Small Stakes No-Limit Hold ‘Em (SSNL), and it’s even better than I’d hoped.

Read the full review including my “Two-Minute Recommendation” in the Book Reviews Section of the site.

Read the full review

Even though I’m too sloppy/lazy/uneducated to work out the details of complicated problems, I’m quite interested in the mathematics of poker. I feel like I do have a broad grasp of the game theory that underlies many situations and can use that to aid in my decision-making. Recently, I’ve been curious about how to quantify exactly the value of seemingly abstract concepts like position and implied odds. I think I may have come upon a sketch of how to work some of it out, though I doubt I’ll ever follow up on it.

We start with the “exploitability”, the idea that there is something about how you play that an opponent could potentially take advantage of. Conversely, “unexploitable” means that there is nothing an opponent could do to take advantage of how you play. Importantly, unexploitably is not always the most profitable way to play. Often, you will do something exploitable in order to exploit something exploitable an opponent is doing.

Suppose that you hold AQ in the big blind in a $1/$2 NLHE game. The action folds to the SB, who open shoves for $20. If you know that this opponent will only shove JJ+ and AK, you can fold your AQ. Though itself exploitable, this fold exploits your opponent’s excessively tight shoving range.  Read the complete post...