Weighing The Odds in Hold'Em Poker by King Yao. A review.

Day trader turned card shark King Yao's Weighing The Odds in Hold'Em is a personal tour de force on Limit Hold'Em that is heavy on numbers and explanation, though much of the advice is open ended.

Weighing the Odds is an odds and stats book, more than a how-to book on playing effective limit hold'em.  It assumes a rudimentary knowledge of the game at least, and is aimed either at novice players looking to form a winning style, or for experienced players looking to build a stronger foundation to their game.

Yao's initial chapters on reading opponents and bluffing show this book's strategies may not work as well in looser low-limit games, where players are oblivious to other players' strategic moves (like bluffs), and many more players will call to see the flop and later streets with poorer draws or made hands regardless of who is betting and when.

Yao later admits his strategic advice works best at a table with two good players, three 'decent' players and three bad players, which is a tougher game than the typical low limit hold'em game at a cardroom.  The relatively high rake at the lower limits would ensure no one in Yao's ideal game was a winner in the long run.  Yao's strategy is certainly best suited for middle and higher limits, where players are generally smarter and the rake has far less impact.  It can also work in online games, as online poker sites take a lower percentage of rake and players in relatively low levels play with greater skill.

That said, Yao's book features lengthy discussion on counting outs and brings two valuable concepts to the table.

1) The DIPO Method: Yao's acronym stands for, "Do I have Pot Odds?"  Yao composes a simple method for determining whether a call is correct when drawing to a particular number of outs.  Using a "Good Number" and a "Bad Number," a player that knows his/her number of outs can more quickly determine whether a call on a particular street is correct.

2) A detailed starting hand selection.  About halfway through the book, Yao presents a table about five pages long with detailed instructions on playable starting hands in each position.

For every position (early, middle, late) Yao provides instructions for each hand (or a group) on how to play the hand whe 1st in, against limpers, against a raise, and against a raise with callers.  He follows this with an explanation on how to play the blinds, common mistakes to avoid in each position, and what you should try to do when you play each particular group of hands.

You will not find a more complete starting hand guide to Limit Hold'Em out there, not even in Small Stakes Hold'Em.


True to the title, Weighing The Odds centers around the mathematically correct plays to make, the plays that will net the most expected value.  The book is math intensive and fairly dense to read through, like a Two Plus Two book, but with less theory and more statistical math.

A beginner may want to seek out simpler materials before moving up to this book, but anyone looking to improve their game, move up to more advanced games, and make more statistically correct plays will gain from reading this text.

Full Tilt Tournament Strategy Guide, a review

Full Tilt Poker's Tournament Strategy Guide reeks of a gimmicked attempt by the popular online poker site to capitalize on the poker book boom.  But Michael Craig's compilation of poker essays from the site's top pros carries a lot of useful, in some cases groundbreaking material.  Albeit, some of the material also leaves a lot to be desired, remaining too general in scope and adding little more than general ideas and basic tips.

Full Tilt founder Chris Ferguson writes several of the books chapters, and while he throws out a variety of useful ideas, figuring out how to situationally apply his advice is left entirely up to the reader.

In fact, this is a universal theme of the book, just like many other poker books.  A lot of principles and ideas are not too fleshed out, and calling the book a Strategy Guide may be abit misleading, as few of the chapters do much to guide the reader.  It's a lot like telling a lost tourist, "Well, you'll want to follow the signs, and pay attention to landmarks."

As the chapters were written by different perspectives, many of the chapters disagree with material and ideas in previous chapters, and some are written better than others.

• Howard Lederer's chapter on leverage brings forth a neat concept but Lederer never elaborates on concrete principle application of the subject.
• Gavin Smith's ideas on big stack play are so basic that they should be common sense.
• Mike Matusow has a couple of neat ideas in his Omaha Hi-Lo chapter, but the chapter has little more use than a random magazine article.
• Richard Brodie's ideas on sit & go play are covered in far greater depth by other materials (like Colin Moshman's Sit N' Go Strategy).
• The gimmicky textual conversation on Razz between Huck Seed and Ted Forrest doesn't give the reader much of use.
• And Ted Forrest doesn't seem sure himself of what exactly he's discussing in his chapter "(Don't) Pay Like Ted Forrest."

But as weak as some chapters, some of the material has very strong, concrete strategic advice.

Andy Bloch strikes the motherload in his chapter "Play Before The Flop," which goes into great detail on hand selection in No Limit Hold'Em tournaments.  Bloch provides multiple charts that focus on win percentages against particular ranges of hands, plus a chart that provides a framework for the reader to create his own selection of starting hands.  Bloch does provide a sample chart of starting hands, but it's almost an afterthought once he provides the methodology for the reader to create their own.  This chapter alone might be worth the purchase of the book for an aspiring No Limit Hold'Em tournament player, even granted the filler that precedes it.

Other chapters prove useful as well.

• Chris Ferguson puts better work into his No Limit Hold'Em chapter "Play After The Flop" as his examples infer more concrete ideas the reader can cross-apply.
• Phil Gordon's chapter on "Short Stack Play" has some useful, unique ideas.
• Howard Lederer provides great detail on situational strategy in his Limit Hold'Em chapter, though he provides a tight, limited hand selection chart without Bloch's advice on how the reader may frame his own.
• Keith Sexton gives useful, applicable advice on Stud Hi-Lo.

The Full Tilt Tournament Strategy Guide has some useful concepts, but you have to sift through a lot of jumbled, sometimes hollow material to get to the good stuff.  Certain sections may hold enough value to warrant the purchase themselves, but purchasing this book is akin to purchasing an album with a few good songs surrounded by filler tracks.  If the songs are that good, the album's worth getting, but you may pass if you're in it for the collective product.

Bloch's chapter is groundbreaking, and experienced players looking for random ideas to cross-apply to their tournament game may find the book worth their while.  However, if you're looking to play tournament Stud, Omaha, or H.O.R.S.E., you may still be better served learning the hard way: through trial and error at minimal expense.

The cost of this book may not significantly improve your overall game, as once you've read it... true to the context of the book, you're still completely on your own.

EV comparison of hands in early position: Limping vs raising

The following hands were tested over 100,000 trials each from 2nd position at a 9 handed $3/$6 table under two conditions. In the first scenario, every hand listed was limped in. In the second scenario, every hand was raised. The simulator entered every pot that wasn't raised in front by the under the gun player, except in cases of big hands like AA-QQ, sometimes JJ, and AK. However, in the limped trials, no more than one small bet was placed in the pot unless the pot was raised, in which case the simulator reraised.

I notated the net expected value (EV) per hand and winning percentage of each hand over 100,000 hands.

Net Value in dollars for given starting hands
(Pairs and Ace-Broadway suited)

Hand	Limp EV	Limp Win%	Raised EV	Raised Win%
AA	12.63	67.9	12.98	74.4
KK	8.63	56.6	8.90	63.1
QQ	5.57	50.3	5.94	57.2
JJ	3.23	44.6	3.83	52.0
TT	2.05	39.7	2.63	47.5
99	0.88	34.5	1.57	31.5
88	0.40	29.5	0.48	35.8
77	0.05	26.9	-0.05	24.1
AKs	2.70	46.0	4.23	54.3
AQs	1.55	39.6	2.18	49.7
AJs	1.28	34.6	1.34	45.3
A10s	1.12	30.3	1.15	39.6

Net Value in dollars for given starting hands
(Offsuit and Marginal Hands)

Hand	Limp EV	Limp Win%	Raised EV	Raised Win%
AKo	1.13	42.9	1.94	51.2
AQo	0.20	34.6	1.94	47.2
AJo	-0.19	31.5	0.23	40.8
KQs	0.78	36.1	0.80	42.1
KJs	1.13	27.3	0.62	34.7
K10s	0.68	25.7	0.18	30.2
KQo	-0.36	29.5	0.52	30.3
QJs	0.72	28.3	0.28	33.7
Q10s	0.24	24.5	-0.04	29.4
J10s	0.23	26.2	-0.23	28.6
A9s	0.35	29.3	0.30	36.4
A8s	0.08	28.7	-0.10	35.0

Though it's considered common knowledge, the above data confirms that raising before the flop raises the EV and the chances of winning for nearly all of these hands, let alone the top hands, with few exceptions.

Some of these hands maximize their EV when limped instead of raised, though in some marginal cases (like 77 and A8s), the maximum EV is so small that you can argue the hand's not worth playing at all.

The gray area between greater EV when raised and greater EV when limped fell around the AJs/A10s area. With pairs, the shift only occured with 7's, which are a marginal play in any case: any pairs 8 and above are maximized when raised. King high suited hands, save for KQs, showed a greater profit when limped. K9s, not listed above, showed a very marginal EV of 0.05 when limped, and showed a greater loss when raised. The Queen high and Jack high suited hands listed all showed greater EV when limped.

The obvious risk with raising the strongest hands while limping the marginal hands is that, to astute opponents, you may telegraph the strength of your hand when you limp in from early position. For the most part, your opposition in 3/6 limit won't be nearly attentive enough to notice, assuming you limp more hands in middle and late position. If anything, a high enough frequency of raises run a greater risk of tilting the table. Once a player starts raising too often at a low limit table, frequently the other players cease having fun, they tighten up, and will join in the raising act, replacing the profitable loose-passive environment with a tighter, more aggressive game, which vastly reduces profitability at a low limit game where the rake and drop alone leaves you with very little margin for error.

The good news in early position is that few of your hands are playable. Assuming we eliminate the marginal A8s and 77, you will only see a playable hand in early position 9.2% of the time according to PokerStove, and if we base our decision to raise on the highest EV possible per the above chart, we will only raise 7.4% of the time, only one in 13.5 early position hands. If we devised a separate strategy for under the gun, as we'll explore soon, the starting requirements would tighten slightly, meaning even fewer instances of playable hands. In a 4 hour session (roughly 120 hands) or even an 8 hour playing session (240 hands), even if your opponents take notice of your raises, it's highly unlikely you will make enough raises from early position to drive the table nuts and screw the game up.

In fact, once we explore strategies in later positions, we'll find that opportunities to play are so infrequent that we shouldn't get in the way of our opponents very often, which, ultimately, is what we want. We want our weaker opponents pushing most of the action. This way, they're more likely to have fun and remain motivated to keep their money on the table, if not buy-in once they bust and add even more money to the table.