So, you’ve played a lot of poker, know your starting hands, know how to read a flop, and know how to read your villains, but you want to kick your game up even higher. How do you do it? If you listen to what Tony Guerrera has to say, you learn the tools to deeply analyze your game. Killer Poker by the Numbers provides those tools. If you are diligent, you will learn how to calculate probability, construct hand analysis charts, learn a compact notation for hand distributions, and you’ll spend a lot of time poker stoving. The heart of the book is Guerrera’s “Hand Distribution Model,” (HDM) which he describes as a more generalized case of Harrington’s “Structured Hand Analysis” from the Harrington On Hold’em series. This book is aimed at the most serious students of the game, and recreational players will likely find their eyes glazing over. However, there’s a bonus for the recreational player too, which I’ll describe below.
To ease the reader in and provide motivation for the tough sledding ahead, the book starts with a very common poker conundrum: you raise with AK before the flop, it totally misses you, action gets checked around, and you make a continuation bet. How profitable is that play? We all have hunches, but Guerrera demonstrates the mathematics, concluding that a 2/3 pot bet is profitable against one or two opponents but not profitable against a higher number. Already, in the first few pages, I really felt like I was being handed the keys to the deeper poker kingdom, and Guerrera was demonstrating all his calculations, laying out his assumptions, assigning them probabilities, and empowering the reader to go through precisely the same steps, not simply take it on faith. Very exciting stuff!
After giving us a taste from a very commonly felt dilemma, he goes on to describe the tools on the belt that will take us through the rest of the book: modified poker charts (courtesy of Mike Caro) and interval notation (to compactly describe a set or sets of poker hands) are the tools to organize information. The tools to do the work are basic elements of probability theory: permutations, combinations, and complements. Don’t be frightened, though, because with a little grit, a pencil, and a pad of paper, you can learn to effectively wield these techniques.
With these weapons, you’re then ready for the real engine of the book (in my view) – the Hand Distribution Model (HDM). Using Guerrera’s elegant notational system, you can compactly put your villain on any possible distribution of hands to then use for analytical purposes. As a little taste, suppose you suspect your villain plays any pocket pair. In HDM, this looks like [AA,22]. If he plays any pocket pair and all aces down to ace-ten, then it’s [AA,22]||[AK,AT]. The notation is very elegant. But why is it important? Well, just from looking at that set, you can rapidly determine (once Guerrera has shown you how), that your villain plays 142 our of a possible 1326 starting hands. Thus, you can expect him to be in about 11% of pots before the flop. Also, if an ace hits the flop, you can expect him to have improved 70 of his 142 starting hands. If he comes betting out on the flop, there’s about a 50% chance that you’re up against a pair of aces with a decent kicker, and about 5% of the time you’re up against a set of aces.
As Guerrera points out, your distribution of hands may be incorrect for a certain opponent, but by thinking about a range of starting requirements, you avoid the trap of putting your opponent on simply *one* starting hand, which is a lazy and perilous approach to post-flop play. Also, if you find your villain actually in about 15% of preflop pots, then you probably need to widen your hand distribution. Thus, thinking carefully about the probabilities improves your reads! Poker psychology meets poker mathematics, a very satisfying outcome to toughing out Guerrera’s examples and word problems.
Guerrera then devotes several chapters to exploring common cases pre and post flop and what probability has to say about rational lines of play. An entire chapter is devoted to the play of pocket pairs and the next to drawing hands. These are broken down into the possibilites and probabilities once the flop hits, and the implications for play. What are the odds of hitting your set? What about improving to a full house or quads if your villain hits a straight or a flush? The drawing hands chapter explores common conundrums, starting with a great explanation of why “Any Two Cards” poker will probably lead to ruin over the long haul. Basically, your odds of flopping that weird two-pair or that miracle boat are so low that you can’t get sufficient pot odds or implied odds to justify even filling up the small blind under most circumstances. Plus, for every ten orbits where you fold the small blind, you’ve saved yourself five big bets, and a bet saved is just as spendable as a bet won.
The final two content chapters are devoted to the special cases of short-handed play, which Guerrera himself specializes in (online multi-tabling), and tournaments, where probabilities now must take into account the possibility of being micro-stacked, having a low stack-to-blind ratio, and being frozen out. The essence of tournament play which makes it fundamentally different from cash play is the pre-flop all-in race. This move is seldom justified in cash (with notable exceptions like AA heads-up), but it is frequently required in a tourney. Guerrera lays out the probabilities of surviving a race for various combinations of hole cards. Once again, he shows you how to calculate these things for yourself.
At the start of the review, I promised that the book contained material for recreational players. Indeed it does. Guerrera has wisely factored in the probability that a majority of the book’s purchasers simply won’t pull out pad and pencil. So, he has included fully explained answers to all his problems. More crucially, all his key probabilities are summarized into highly digestible tables at the ends of major sections and chapters. If you haven’t the inclination or desire to learn probability theory, even committing some key figures from the tables will put you in good stead.
Overall, this is a terrific book. Yes, it is technical, but it makes that claim right up front, so there’s no bait and switch going on here. Guerrera’s prose style can tend toward the dry side, but compared to wading through David Sklansky’s writing [http://www.pokerbookreport.com/davidsklansky.htm], Guerrera is a prose stylist of the highest caliber. Furthermore, the material just is dry and technical, but it can punt your game up into the stratosphere if you diligently engage with it. So kids, dig out those scientific calculators, brew a big mug of coffee, and get your hands on “Killer Poker by the Numbers.” Actually, don’t do that. Don’t do that, and please come sit at my ring game.