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.

Basics of HORSE poker

HORSE itself isn't so much a game as a rotating selection of games. Play rotates periodically between five different poker variants, all played with fixed limit betting. The games can rotate every hand, every orbit around the poker table, or after a prescribed period of time. The small bet and big bet limits are often listed with the game at a cardroom. HORSE $3/$6, for example, indicates the small bet is $3 and the big bet is $6. This number doesn't vary from game to game, though the rules regarding betting rounds can vary from game to game.

HORSE consists of the following five games:

H: Texas Hold'Em

The most popular game in poker today. Texas Hold'Em is played with each player receiving two cards face down before an opening betting round at the small-bet limit. Once betting completes, the dealer burns (discards) a card and lays down three community cards, known as the flop, followed by another round of betting.

Following this round, the bet limit increases to the big bet size, and a 4th community card is dealt, known as the turn. A betting round proceeds as before, before a 5th and final community card, known as the river, is dealt, and one final betting round takes place before players turn over their cards, and the best five card poker hand receives the pot.

O: Omaha Hi/Lo (Eight or better)

Gameplay in Omaha Hi/Lo (also known as Omaha 8) proceeds just like Hold'Em except for two major differences:

1. Players receive four cards instead of two. Whereas with Hold'Em, players can use one, both or none of their cards to make a hand... in Omaha, you MUST use two of your four cards, and you MUST use three of the community cards. No exceptions. For example, if the board has a 7, 8, 9 and 10... in Omaha you do not have a straight if you have a Jack... but you do if you have a 7 and a Jack, or a Jack and a Queen. And if the board has a 7 and 8, you do NOT have a straight if you hold a 9, 10 and Jack.

You can only use two of your own cards to make your hand. Not three, Not one. Only two.

2. Hi/Lo games split the pot in half. Half the pot contests for the best high poker hand as always. However, the other half contests for the Low: five unpaired cards that are all 8 or lower (Ace counts as 1). The best five card low possible is 5,4,3,2,Ace. The worst possible is 8,7,6,5,4.
It is possible for no low hand to be possible, if the board does not have at least 3 unpaired cards 8 or lower. In this case, the high hand wins the entire pot.

R: Razz

Razz is like Seven Card Stud, except that you're trying to make the best low hand possible: five unpaired cards whose high card is the lowest. Straights and flushes don't count against you, but pairs do. 5,4,3,2,Ace is the best low. Unlike the low rules in Omaha and Stud Hi/Lo, you do not need all your cards to be 8 or lower. Jack-9-6-4-3, for example, can win a Razz pot (it's not common, though: a typical winning low's high card is usually 8 or lower).

Lows are measured by the highest card in the lowest five card hand possible. Forexample, if you have Ace,2,3,4,9... you are beaten by 8,7,6,5,4 because the 8-high is lower than you 9-high.

S: Seven Card Stud

Each player in 7 Card Stud receives two cards face down and a 3rd card face up before betting begins at the small limit (this round is referred to as 3rd street, the number referencing the number of cards everyone has). The conclusion of that round brings a 4th card and another round of betting after that. If a pair is on the board after 4th Street, players may bet at the big limit if they wish.

However, after this round all betting is at the big limit, and a 5th card is dealt before another betting round. Play continues until the 7th and final card is dealt face down, and when the final round of betting is completed, players turn their cards over and the best five card hand wins.

E: Seven Card Stud Hi/Lo (Eight or Better)

Play in 7 Card Stud Hi/Lo proceeds exactly like regular 7 Card Stud except, as with Omaha Hi/Lo, the pot is split, and the best low-hand with all cards eight or lower wins half the pot. As with Omaha, if there is no low hand, the high hand takes the entire pot.


HORSE is a very involved game, and it takes some degree of competence in all five games listed. Your best bet, unless you wish to play for fun, just to sample the different games, is to practice and get better at each game individually before you attempt to play HORSE competitively. Each game in itself is very complex and winning strategies at each take considerable time and practice to develop.

This can be a challenge if you don't play poker online, as games like Razz, Stud and Stud Hi/Lo at affordable stakes can be difficult to find even if several cardrooms exist in your area. A good idea is to download online poker software and practice for free at freerolls and the play money tables... or to play at home with friends.

As a result, if your local cardroom does spread HORSE at low stakes, it may be worth your while just to bite the bullet and play. Be observant, play carefully, and try to learn all you can about every game spread when you play.

Best of luck.

A digression: No Limit Hold'Em tournament research

We'll return to our 3/6 Limit Hold'Em research shortly, but first I wanted to touch on some of my ongoing No Limit Hold'Em tournament simulation research, conducted for the most part of Donohoe Digital Software's DDPoker simulator, which allows me to customize tournament formats.

For a while, I lost my sense of how to play fast no limit hold'em tournaments. Arnold Snyder's suggested strategy in Poker Tournament Formula has its flaws, especially once everyone gets short stacked, though that was the approach I cut my teeth using. Later, I replaced Snyder's short stack strategy with the one used in Kill Phil, where you are prepared to shove with a fairly wide range that gets wider as you get shorter or as you gain position.

A while back in my tournament trials, I stumbled into an approach that worked very, very well in my simulations and routinely got me deep into tournaments that by all other definitions should be far too fast to play profitably. I posted a bunch of first places because I would either tear through with a big stack or gain such a commanding chip lead at the final table that 1st place was academic.

The preflop strategies I utilized would vary, but one consistent approach came when my stack was above average but around 20 big blinds or less, which is generally considered the high end of short stacked. Once I reach this short stacked point, I would open all playable hands with a minraise. At this point, a minraise was such a large part of any player's stack that playing back at it took as strong a hand as calling a standard raise earlier in the tournament did.

If I'm going to play against a raiser in front at all, I either want to reraise or fold, or get the other guy all-in when he's short. I want to establish that pots played with me will be expensive. I tend to reraise a preflop raiser no matter what when I have a strong hand that I feel would play well heads-up against a preflop raising range. The typical goal is to get a pot heads up on the flop (though obviously when you have AA or KK, you reraise for value, and when you 3bet a lot, you get more value from your reraises since they're not taken as seriously). Once heads-up on the flop, I will have position on my villain. If the villain checks to me, I can fire out a large bet or take a free card, depending on the opponent and flop scenario. If he bets, I can go away if the bet is too large for comfort or I don't have enough of the flop to continue.

Others behind me can call a preflop reraise at their own peril, and in the few cases when they do, great. If someone or the original raiser re-reraises, I can get out of the way unless I have a top hand or a ton of chips relative to the bet. If we see a 3+ way flop, sometimes I hit the flop hard and stand to win a very large pot, and can bail in the instances when I don't and another player bets out.

Again, once the blinds get up there and the average stack has ~20 big blinds, I switch to a minraise mode, which puts any short stack in peril if they play. I open with this raise with strong hands out of position and with lesser but playable hands in position. I avoid playing pots raised in front of me unless the raiser is loose or I have a strong hand, in which case I will reraise, and if the raiser is short enough I will reraise him all in. I make it clear I am either prepared to play for all my chips or prepared to make you play for all your chips.

I have finally devised a simple preflop strategy that I can use out of position in any position regardless of stack size. In position when 1st in, I will raise a LOT, and put the onus on opponents behind me to call or reraise to continue playing. Even when not 1st in, if there's a couple of limpers I may make a huge raise on the button, knowing I will have position when called. If folded to when in the small blind, I will use my read to decide how often to raise the big blind. Often I will just call and look to see a cheap flop heads up out of position. If the blinds are high, I will raise the big blind more often, and again put the onus on that big blind to pay to play.

For hand selection, I use proportion. At a 10 handed table, I open raise with the top 10% hands. If you're at a 10 handed table, raise 1/10th of your hands and get the blinds uncontested as a result, you break even. Obviously, you will raise more often in position and should get ahead of the game, but such a selection can help you stay above water when you're struggling to find spots to raise and take pots. This is easy to remember and makes little difference when used in middle position or early position.

I rated all 169 possible hands by their win% against popular raising hands that many players are willing to get all-in with preflop, such as pocket pairs 7 and higher, Ace-King, Ace-Queen, Ace-Jack and King-Queen. I sorted these hands by win% and selected from the top of the list down in PokerStove until it told me I had the proper percentage of hands. The resulting 10% looks a bit odd in selection and omits some hands you would expect to see, but the key is to have maximum equity against the sort of hands people will call a raise with.

The top 10%: AA-99, AK-AJ, A10s, A5s-A3s, KQ, KJs, K10s, QJs, Q10s, J10s

If the table is 9 handed, again we go proportional, using the top 1/9th of available hands, 11.1% total: AA-99, AK-AJ, A10s, A5s-A3s, KQ, KJs, K10s, QJ, Q10s, J10s

A tournament table often drops to 8 handed, and SPO typically plays 8 handed and below. 1/8 equals 12.5%: AA-99, AK-AJ, Axs, KQ, KJs, K10s, QJ, Q10s, J10s

7 handed (14.3%): AA-55, AK-AJ, Axs, KQ, KJs, K10s, QJ, Q10s, J10s

6 handed (16.7%): AA-33, AK-A10, Axs, KQ, KJs, K10s, QJ, Q10s, Q9s, J10s

You will almost always see 4-5 handed play at a final table where blinds are fairly high. At this point, play should be more straightforward and not require hand charts: Any seat not in the blinds is in position and you can raise most, if not all of the time and expect not to get called by strong hands. And if you do have a good hand, any two broadway, a decent pocket pair... you're ready to get it in against any short stacked player that raises you. You show more caution against other big stacks unless they're playing very aggressively, in which case you show them no respect when you have the goods, especially when in position.

If players are calling your raises a lot, you can use the following strategies to determine when to raise, which will lead to you folding hands in raising positions, which can allow you to regain table respect:

5 handed (20.0%): All pairs, AK-A10, Axs, KQ-KJ, K10s, QJ-Q10, Q9s, Q8s, Q6s, J10s-J9s, 10-9s

4 handed (25.0%): All pairs, AK-A10, Axs, A5, QJ-Q10, Q9s-Q3s, J10, J9s-J8s, KQ-KJ, K10s, K6s, 10-9s, 10-8s, 76s, 65s, 54s

3 handed (33.3%): All pairs, AK-A10, A5-A2, Axs, KQ-K10, K9s-K3s, QJ-Q10, Qxs, J10, J9s-J7s, J5s, 10-9s, 10-8s, 10-7s, 98s, 87s, 76s, 75s, 65s, 64s, 54s

Typically, fast tournaments will conclude once 4-6 handed due to the high blinds. Players will ask to make a deal, and given the crapshootish nature of the tourney at this point, it's typically best to take the split of the remaining prize pool and call it a day. This typically happens when the average stack has 5-10 big blinds or less. But sometimes everyone involved will still have enough chips to play, and it's a sound idea to have some sense of how to play these shorthanded high-blind situations.

Once heads up, the blinds should be fairly high, enough for minraises to hold significant value to both players, so continue minraising preflop. How you play will depend on your opponent's style, though if you're on the short end and he's raising a lot himself preflop, you're looking to get your money in with any decent hand, any Ace, most Kings, Queens with kickers 7 and higher, Jacks-7 and up, 10s-7 and up, though tend to only include the lower range when they're suited or your opponent's rising more frequently. Generally, see a lot of flops with decent holdings or in position, and look for a spot to get your money in, typically with at least 2nd pair or better, or a strong draw to better, on the flop.

On the other side, with a big stack, tend to punish your shorter stacked opponent with preflop raises. Bet a lot of flops and show him he will usually need to pay to continue. This will also tend to make a thinking opponent wary when you do check a flop here and there, as many will think you're slowplaying a monster if you usually bet out.

Another benefit of betting most flops is that, when you do catch a good hand, like top pair or better, or a strong draw to a straight or better, your opponent, knowing you bet a lot of flops, will tend to call you more often and thus pay off your strong hands more often. This is also key to getting him all in when you've got him beat. You want him to get all his chips in with a weak pair or Ace-high when you've got him crushed with top pair or better.

Kill Everyone tends to suggest that you put a short stack all in preflop when his M is 8 or lower. But this makes it too easy for your opponent to catch up, since he can fold all but his best holdings, and typically double through when he does call, which only makes the task of finishing 1st that much harder for us. Just play him straight and aggressive.

Given this approach, it's possible to consistently win at faster tournaments that are widely considered to be a crapshoot by even experts at their style of play. You just need to shorten the raises to meet the scope of play, while remaining aggressive and getting even more aggressive in position as the field thins.