Posts Tagged ‘game theory’

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...

OK, this has sparked a lot of interest among commenters, so I think I will offer a few of my own thoughts on the hand after all. In terms of what durrrr may have been thinking and why he was successful, I don’t have a lot to add to the very good analysis I already linked. Instead, I’ll focus on what I think Greenstein and Eastgate could have done differently.

(If you don’t know the details of the hand, Geoff recently shared a link to a YouTube clip: http://www.youtube.com/watch?v=3SKwhb_nJVQ)

I’ll start with Eastgate, because my advice for him is easiest: fold pre-flop. By my count, the pot is $16,200 when it gets to Eastgate, who must call $2100 more with his 42o in the Small Blind. The 8:1 pot odds are nice, but he will be very deep out of position against 6-7 good to world-class players with a hand that virtually never makes the nuts or anything close to it. Even suited, this should probably be a fold, since with so many in the pot he’s looking at reverse implied odds even when he makes a flush. Post-flop, his play is fine, and this is just a spot where he’s going to lose money against a very good player. Hence why he should not be playing 24o.  Read the complete post...

Full Tilt Poker, $5/$10 NL Hold’em Cash Game, 2 Players
LeggoPoker.com – Hand History Converter

Hero (SB): $2,434.50
BB: $3,954.50

Pre-Flop: T K dealt to Hero (SB)
Hero raises to $30, BB raises to $100, Hero raises to $255, BB calls $155

Flop: ($510) 3 A 2 (2 Players)
BB checks, Hero bets $199, BB calls $199

Turn: ($908) K (2 Players)
BB checks, Hero bets $480, BB folds

Results: $908 Pot ($0.50 Rake)
Hero mucked T K and WON $907.50 (+$453.50 NET)

If he called the turn, I was shoving the river. Position, deep stacks, and judiciously employed small bets are a lethal combination. It’s exceedingly difficult for him to show up with enough big hands to prevent me from exploiting him with river shoves.

If both players employ game theoretically optimal strategy, the advantage will obviously go to the player in position. His EV in the game will be a function of the pot size and the number of betting rounds, meaning that it behooves him to structure the betting so that there is roughly a pot-sized bet remaining on the river. He can then maximize his edge by making better decisions than his opponent about when he wants that last bet to go into the pot.  Read the complete post...

I like this line a lot in this spot, but not against the table fish:

Full Tilt No-Limit Hold’em, $20.00 BB (6 handed) – Full-Tilt Converter Tool from FlopTurnRiver.com

MP ($2000)
CO ($1850)
Button ($1329)
SB ($8366)
Hero (BB) ($2197)
UTG ($2274)

Preflop: Hero is BB with Q, K
3 folds, Button raises to $40, 1 fold, Hero raises to $144, Button calls $104

Flop: ($298) J, A, 3 (2 players)
Hero checks, Button checks

Turn: ($298) 2 (2 players)
Hero bets $203, Button calls $203

River: ($704) 7 (2 players)
Hero bets $550, Button calls $550

Total pot: $1804 | Rake: $3

Results:
Button had A, 10 (one pair, Aces).
Hero had Q, K (high card, Ace).
Outcome: Button won $1801

Most of the time that I check this flop after 3-betting pre-flop, I’m going to have something with some showdown value. And if I then bet hard at the turn and river, it will be because I was slowplaying a monster or at least pot controlling something pretty good like AK.

So, I like a similar line with a big draw, as compared to just betting the flop and then making a pot-committing turn bet. Maybe I’ll get to check-raise the flop if Villain throws out a feeler bet/bluff, or make a concealed flush (since he probably wouldn’t expect me to check a flush draw on the flop)- with all my outs, I certainly don’t mind seeing a free turn card.  Read the complete post...

My latest poker strategy article, Creative Bet Sizing, is now appearing in the December edition of 2+2 Internet Magazine. The article examines underbetting and overbetting as examples of how to add unconventional plays into your arsenal. Here’s an excerpt from the section on overbetting the pot:

Big bets are simply harder to play against than smaller bets. Any edge that you have over an opponent, whether it is position, better cards, or superior skill, is magnified by pot and bet size. This doesn’t mean that every bet you make should be all in. But if you believe that an opponent will make comparable mistakes whether you bet 70% of pot or 125% of pot, the latter option will be far more profitable.

A good rule of thumb about overbetting is that the larger your bet, the more likely it is to induce a raise-or-fold response from your opponent and the less likely it is to be simply called. How exactly you use that information will depend on factors like your hand, your opponent, and the size of the effective stacks.

Eugene asked a great question about my recent post, A Random Call, which reminded me that I’d meant to post this hand as well. It happened not long after I snapped off a 2x pot river bluff with top pair, weak kicker. This was against the same opponent but on a different table:

Full Tilt Poker, $10/$20 NL Hold’em Cash Game, 6 Players
LeggoPoker.com – Hand History Converter

Hero (CO): $4,732.50
BTN: $4,231
SB: $4,144.50
BB: $5,019.50
UTG: $2,000
MP: $7,734.50

Pre-Flop: 9 9 dealt to Hero (CO)
2 folds, Hero raises to $70, BTN raises to $240, 2 folds, Hero calls $170

Flop: ($510) 4 2 2 (2 Players)
Hero bets $222, BTN raises to $700, Hero raises to $1,178, BTN calls $478

Turn: ($2,866) 7 (2 Players)
Hero checks, BTN bets $2,813 and is All-In, Hero calls $2,813

River: ($8,492) 6 (2 Players – 1 is All-In)

Results: $8,492 Pot ($3 Rake)
Hero showed 9 9 (two pair, Nines and Twos) and LOST (-$4,231 NET)
BTN showed K K (two pair, Kings and Twos) and WON $8,489 (+$4,258 NET)  Read the complete post...