Staying uncommitted

It feels good to be playing my "A" game.

My results have been OK but not great as donkeys get it in bad and suckout repeatedly. What's gratifying is that I haven't been making many major mistakes for my stack when drawing slim. I know this probably means I'm getting bluffed sometimes, but I've also caught my fair share of big bluffs.

One of the reasons I haven't been going broke as much with overpairs or top pair is the guideline in "Professional No-Limit Hold 'em" that you're close to being committed after putting in more than 1/3 of your stack. By paying attention to how much I've invested and how much my remaining stack is, I've been able to slow down before the pot gets too large to resist. It has given me more confidence 4-betting when I feel I can take down a 9BB to 16BB pot preflop without feeling bad when I have to fold after getting 5-bet or called. And sometimes, I'll flop a decent draw and go with it in these large pots.

This train of thought got me thinking about adjustments in aggressive games. If most pots are being 3-bet preflop, how can you see a flop with drawing hands when you don't have implied odds? For example, if I raise from the cutoff with 76s and get 3-bet from the button, I can't really profitably call very often with 100BB or smaller stacks. I could 4-bet as a semibluff at times, but folding is usually the best choice.

Some would argue for limping or minraising more often in these kinds of games, and there's probably some merit to that, but it's not my style at all. If I'm going to open a pot, I'm coming in for a 3X+ raise.

Your options are limited when 3-bet out of position. I'm going to raise or fold almost every time unless I want to mix it up by smooth calling with AA-JJ.

In position, I'll be more likely to see a flop or reraise. But the reason for seeing a flop isn't necessarily to flop huge. In addition to draws and some pair hands, I also have to bluff a bit against highly aggressive opponents. This kind of situation comes up after raising something like 76s or Q9s from the button.

It isn't always comfortable to play medium-sized pots with these weakish hands, but there's not a good way around it except to try to outplay your opponents postflop. I wonder how often folding preflop may be the better play, even in position.

Low pockets folo

A few days ago, I wrote, "Calling 3-bets preflop with low pocket pairs is not profitable if you have to count on hitting a set to win the pot."

While making my point, I intentionally neglected the times when it is profitable to call reraises with low pocket pairs.

My favorite situation occurs when I'm against a very tight raiser from the blinds. I'm talking about players who almost never raise, and when they do from a bad position, it means AA or KK. Calling a reraise against these guys is a no-brainer because their hand range is so narrow, increasing your implied odds. If you hit, you'll stack them. If not, you can fold.

A similar circumstance occurs when you're against a huge calling station. Some of these players will pay off so liberally that you do have odds to flat call and set mine.

Another good time to call a 3-bet with a low pocket pair is when you think you can bluff postflop. In addition to the chance of hitting a set, you also have another way of winning a medium-sized pot with a bet or a raise. It's almost like a combo draw because you have some fold equity postflop, an idea a couple of commenters pointed out.

I'll never try bluffing with a low pocket pair against a calling station, but it works well on a variety of mildly coordinated flops against fit-or-fold type opponents. In general, it doesn't perform as well on completely uncoordinated or high-card flops.

One thing not to do with these low pocket pairs is 4-bet or push with them. It's almost always a disaster unless your opponent folds immediately.

I don't think this is right

Perhaps I'm misunderstanding Bob Ciaffone, but his "open-book test" in this month's issue of Card Player Magazine seems wrong to me:

Let's look at a similar type of situation in no-limit hold'em. Here is an open-book test: The pot is $100 and both you and your opponent have $400 left. You have top pair and your opponent is drawing. He acts first and bets the pot ($100); what strategy should you adopt if each of you can at this point now see each other's holecards? The proper answer is found by counting the outs. If the made hand will be better than a 2-to-1 favorite with two cards to come, you can lock up the pot by moving in on the flop, as the money odds offered to the draw when a pot-size bet is made are exactly that amount. However, if the made hand is less than a 2-to-1 favorite, the better play is to see what comes on the turn. If the draw hits, you fold. If the draw misses, you move in. This is a good illustration of the scenario that the draw wants to avoid.

OK. Let's assume the drawing hand is a flush draw, which is a good example hand because it gives that player close to a one-third chance of winning the pot with two cards to come.

In that situation, the player with top pair can expect to win the $900 pot about two-thirds of the time if he pushes in on the flop and the drawing hand calls, giving the top pair player an expected value of $300.

But if the player with top pair waits until the turn, his expected value is only $180 because he'll lose the current $300 pot 20 percent of the time when the flush card hits and win the $300 pot 80 percent of the time.

He's giving up a lot of value!

It's entirely possible that I'm thinking about this problem incorrectly, and please let me know if that's the case. But it seems to me that Ciaffone believes that just because the flush draw has to call given the pot odds, the top pair hand should give the drawing hand a free card.

That just isn't right because the top pair hand will still win most of the time, and the pot will be larger.

---

Don't forget the Ultimate Blogger Cash Game coming up Wednesday during the Mookie. Please let Fuel or me know if you plan to play.

Expanding games

Wow, the 3/6 and 2/4 NL games on Full Tilt have been incredibly loose over the last few weeks.

I can't explain it. Maybe it's the holiday season, the cold weather keeping people inside or the ease of making deposits. Whatever the reason, I'm not complaining. I've said this many times before: anyone who tells you the online games are filled with rocks is wrong or lying.

Now is the time to play and make the most of this opportunity. I know the games won't be this good forever.

On a separate topic, I'm impressed with a CardRunners video by CTS that I watched last night. In the vid, he plays three guys in heads-up 5/10 NL games and just demolishes them for 3.5 buy-ins over 225 hands. Sure, he runs pretty good. But he also makes ballsy plays based on reads and experience that are almost always correct.

I like the math he uses to find that a bluff he makes with an open-ended straight draw into a large pot needs to only be successful 17 percent of the time to show a profit:



What really stood out to me was his commentary on the importance of learning to play heads-up. It reminded me a lot of when I heard similar suggestions years ago about switching from full ring to shorthanded games. I struggled with 6-max games for a long time, but now they're my most consistent moneymakers.

The skills acquired from playing shorthanded directly result in higher profits, better hourly winrates and practice playing in tough situations.

I've had mixed results in heads-up cash games and backed off them entirely since I lost several buy-ins last month. I now realize I was playing too tightly preflop and I failed to properly identify and respond to my opponents weaknesses. Most actions can be countered by varying your play appropriately. I need to improve HU to bring my game to where it needs to be.

Specifically, I want to learn more about narrowing my opponents' hand ranges, correctly playing middling hands that gain value in HU situations and effectively increasing my bluffing frequency. I'm excited about the challenge.

HOTD-Outs 'n' rags

This hand of the day played out well.

http://www.pokerhand.org/?1625641

FullTiltPoker $3/$6 - 4 handed
Dealt to smizmiatch [6c 5d]
CO folds
smizmiatch raises to $21 from Button
SB folds
Villain calls $15 from BB <-- He's very loose from the blinds.
*** FLOP *** [4c 2d 8d] <-- I flop great with a double belly buster
Villain bets $25
smizmiatch calls $25 <-- I call rather than raise because my hand is well-disguised and I figure my opponent caught a piece of the flop
*** TURN *** [4c 2d 8d] [6s]
Villain bets $60 <-- I don't know what to put him on. Some kind of draw? Some weird BB two pair hand? Why would he bet it out on two streets?
smizmiatch raises to $180 <-- I'm going to try to put an end to this right now with about 5 trillion outs
Villain raises to $300 <-- Wtf is up with the minraise?
smizmiatch has requested TIME

Here is where I go into the tank. I think about going all in, but the villain has shown nothing but strength. I'd hate to call drawing dead to a 7. But really, I think I'm up against some random two pair at this point, in which case I also don't want to go all in.

If I'm not going to push, I guess I have to do the math. I fumbled around on my keyboard for a second before finding the Windows calculator.

My pot odds were better than I thought they'd be at 21 percent (120/575)! With as many as 13 outs, I'm calling here for sure.


Click for enlarged view

smizmiatch calls $120
*** RIVER *** [4c 2d 8d 6s] [8h] <-- Actually, a great card because it would counterfeit a hand like 64 or 55. But my read is fuzzy.
Villain bets $256, and is all in <-- Is he doing this just because I took so much time on the turn?
smizmiatch has requested TIME
smizmiatch calls $254, and is all in <-- The pot is offering 3:1 odds. I think I'm good more than a quarter of the time. For some reason, my spider sense is telling me he doesn't have an 8.
Uncalled bet of $2 returned to Villain
*** SHOW DOWN ***
Villain shows [7h 3h] a pair of Eights <-- Missed his gutshot draw
smizmiatch shows [6c 5d] two pair, Eights and Sixes
smizmiatch wins the pot ($1,201) with two pair, Eights and Sixes <-- El doble!
Villain is sitting out

I don't know how to feel about this hand. I sensed weakness somewhere, but my read was wrong.

It must have been the minraise on the turn that seemed weak, even though it was meant to look strong.

Housekeeping

I found Kick Ass Poker Blog's breakdown of the UIGEA regulations to be informative.

Check it out here (don't let the multipart format scare you):

Inside the UIGEA Regulations, Part I: Introduction and Background
Part 2: Implementation
Part 3: Deputizing the Banks
Part 4: Comments and Timing

So what we have here is a law that doesn't specifically mention poker, explicitly permits paper checks to be used, relies on banks for enforcement and is still many months away from going into effect, more than a year after it was originally passed as part of a port security bill. Great.

---

I realized the other day that I've been overestimating the probability that two unpaired cards will flop a pair. I think the math should look like this: 1 - (44/50 * 43/49 * 42/48) = 32.4 percent.

Or it's easier just to look it up on the Internet at a site like Planet Stacked that has all kinds of odds listed.

---

Lee Jones says he'll bet $10,000 with Daniel Negreanu that you shouldn't be able to show one card to an opponent when two people are in a tournament hand heads up.

But he doesn't explain his reasoning. I don't get it. Why shouldn't you be allowed to show a card? Someone fill me in please.

Coinflips

I love coinflips.

In a cash game, I'll take them any chance I can get, especially if I'm the one able to put the pressure on.

Only good things can happen when you put your chips in with a 50 percent shot at winning the hand. Your opponent could fold, giving you the existing pot. At worst, your opponent calls, which isn't the end of the world because of pot odds.

When there's decent money in the pot already and you have an even chance at winning, you want to fight for that money. Sometimes, even when slightly behind, the money in the pot is enough to make a big bet worthwhile.

Hands with a pair and a flush draw are the classic example. These hands have about 14 outs and they're not dominated by much except for sets and higher flush draws. Even then, there's a significant chance of sucking out.

There's also some utility preflop in betting big with AK because it's a coinflip at worst against anything except AA or KK. Even if QQ or JJ makes a read and calls your preflop all-in, you're in fine shape to win the pot half the time. I'm not advocating pushing all-in with AK frequently, but there's some value in making a move when you think you can pick up a growing pot preflop.

Just don't do it when your opponents have you dominated!

I hear people all the time say they'd rather "wait for a better spot" than get it all-in on a coinflip. While this may be correct at times in tournaments, it's rarely right in cash games.

While you're waiting for a better spot, your aggressive opponents are picking up lots of small and medium-sized pots uncontested.

---

Here's a hand of the day:

In a full ring 5/10 NL game, everyone is playing normally except for one maniac. He general strategy is to raise and then push all-in against anyone's reraise. His stats are about 45/38/5.

At first, everyone respects his all-in raises, but it doesn't take long for people to figure out that he has hands worth less than trash.

That became abundantly clear when he raised from middle position to $40, and I re-raised to $120 from the button with AA. He pushed all-in, and I had an easy call to make. He flipped over T5s and somehow didn't suck out, giving me a $2,084 pot.

After that hand, everyone at the table wanted a piece of this guy's money before it ran out.

A few hands later, an early position player limps, and I make it $45 to go with KQs from MP. The cutoff player calls the $45, and then the maniac on the button goes all in for nearly $700. It folds around to me.

What should I do with KQs? It's behind any Ace and dominated by AK or AQ.

But I figure I'm ahead of this crazy guy's incredibly wide range. I'm a tiny bit worried about the player behind me, but I only had one move. I raised all-in to isolate the maniac and try to bust him with what I figure to be a decent enough hand. I don't think I had ever raised all-in preflop with KQs, but the time was right against this guy.

As I hoped, the cutoff player folds. What does the maniac turn up?

Jh. 5c. Just as I suspected.

Flop comes 26J. Turn is a J, and I had doubled the maniac up.

But that's OK. I still netted about a $500 profit because of the AA hand, and I got it in with KQ against J5, which I'll take any day of the week.

My only regret is that I couldn't get the rest of the maniac's money. He busted out soon afterward with his AK vs. QQ.

I won a tourney!

I took down the monthly WPBT event today. It was a pretty solid field. I only really got lucky on the last hand, when I hit a set of Queens on the flop against AA. The rest of the tourney I just tried to play my game and take all the chips I could. I guess tourneys don't have to always be donkfests.

I enjoyed playing with Mattazuma, Schaubs, stevenwe, Patchmaster, StatikKling, Kameelah, bdidde and columbo. (Screenshot linked from Mattazuma's site -- please let me know if you that's uncool.)

---

I got an interesting comment from Ryan to a post I wrote about Casino Arizona recently:

I need help. I play daily at Casino AZ. I recently left medical school and a 100K per year job so i could move out west to be with my sick father. I am readig/studying/playing poker non stop when i am not with my mom and dad so that i can spend more time with them later as opposed to the rigid schedule of a 9 to 5 job( or Dr.) I'm doing well... but could be doing alot better. I havent been able to find any postings or books on the particularly unique type of poker they play there. 5/150 is a semi spread limit/no limit game. I have a good undertstanding of it but i would really like some help/tips from all of you pros on how I could improve my game at this level. I could go to vagas and play true no limit but that would defeat the fact that i need to be close to my family right now in this very tuff time. I work hard and dont quit, and really feel poker is my calling. SO any tips would be greatly apprecated. Thanks for you help in advance.

The Casino Arizona 5/150 games come in two varieties -- one with a $350 buy-in and another with a $1,000 buy-in. The $350 buy-in game has 3/5 blinds and a $150 maximum per betting
action. The $1,000 buy-in game has 5/10 blinds and the same betting maximum.

The cap doesn't isn't very relevant in the $350 buy-in game because one max bet and another max raise will get players essentially all in unless they've built up a deep stack. I didn't play the $1,000 buy-in game while I was there, but I imagine the cap plays a bigger role, making me think the game would need to be played with more of a pot limit-type strategy. That means players will more often have pot odds to call with their draws and there will be more suckouts. But the cap also minimizes losses when those suckouts occur, so it goes both ways.

The real difficulty in trying to play this game full time will be making significant money off of it. Yes, it plays loose, on par with almost every live game I've ever sat in. That's a good thing, and I believe these games are beatable.

But the problem is the slow rate of play, the rake and the jackpot drop. I'm not sure what the rake is (probably 10 percent of the pot with a $5 max per hand -- please correct me in comments if I'm wrong). The $1 jackpot drop is taken out of the blinds, so even if everyone folds around and the blinds chop, they still lose $1 from a pot that no one even played. That's pretty ridiculous.

So if you anticipate playing 30 hands an hour and winning three of them, you'll probably pay somewhere between $12 and $18 an hour in rake and jackpot drop. If you're beating the $350 buy-in game for 10 bets an hour, that's up to $18 taken out of your $50 winrate, which is significant. The rake wouldn't appear to be as damaging in the $1,000 buy-in game if you're a solid winning player -- $18 or so out of a $100/hour rate. Even these figures are optimistic however; I'm not sure how feasible a 10 bet per hour winrate is. Five bets per hour may be more realistic, which means the rake's cut of your winnings would be much more damaging to your profitability.

Ed Miller wrote about this topic in a recent post.

My primary advice would be to supplement live poker with online poker. Live poker is a tough grind, and you can play so many more hands online, thus improving your hourly earnings. I wouldn't want to try to make a living at live tables at the stakes Casino Arizona spreads.

I'm sure Ryan would appreciate any other advice commenters could contribute.

---

Here's a fun hand I (mis)played at 2/4 today where I won a nice 400-bet pot with a mere pair of 5s. I put my opponent on an overpair, so I gave myself up to 18 outs -- nine for the flush, two for trips, three for two pair and three for the gutshot.

The problem is that I miscalculated the pot odds. The pot was $604, and I had to call $480 on the turn, which means that even 18 outs weren't enough. I should have folded, given my read.

Fortunately, I'm a lucksack. My flush outs were no good, but my little pair of 5s held up!

*** HOLE CARDS ***
Dealt to smizmiatch [4c 5c]
3 folds
smizmiatch raises to $14 from the button
1 fold
JustCuts raises to $46 from the big blind
smizmiatch calls $32
*** FLOP *** [6c 9c 2d]
JustCuts bets $65
smizmiatch calls $65
*** TURN *** [6c 9c 2d] [5s]
JustCuts checks
smizmiatch bets $190
JustCuts raises to $743, and is all in
smizmiatch has 15 seconds left to act
smizmiatch has requested TIME
smizmiatch calls $480.90, and is all in
JustCuts shows [Ac Kc]
smizmiatch shows [4c 5c]
Uncalled bet of $72.10 returned to JustCuts
*** RIVER *** [6c 9c 2d 5s] [Td]
JustCuts shows Ace King high
smizmiatch shows a pair of Fives
smizmiatch wins the pot ($1,562.80) with a pair of Fives

One more time

I was really bored and couldn't sleep on the flight back from Phoenix to Honolulu, so I ended up doing some lengthy poker math.

Here's what I wanted to find out: When you hold QQ in the big blind against a late position raiser and a small blind re-raiser in a 5/10 shorthanded game, is it better to call or push?

I addressed the first part of this question in a few previous posts, where I estimated the EV of calling with QQ and pushing any flop without an Ace or King. The number I came up with was $180.12, which is a high estimate because it doesn't consider the ~7:1 chance of my opponent flopping a set. But I think it's safe to say that making this play is well in positive figures.

So on the plane, I figured the EV of pushing with QQ in that same situation. The results were much worse: -$40.90.

Pushing with QQ preflop against two raisers is a donkey move. Call and push any undercard flop in this specific situation.

---

The Math:

(Chance that both LP and SB will fold * winnings) + (Chance that LP will fold and SB will call with QQ * winnings) + (Chance that LP will fold and SB will call and be ahead * losses) + (Chance of LP or SB calling when ahead but QQ sucking out * winnings) + (Chance of both LP and SB calling when ahead but QQ sucking out * winnings) + (Chance of both LP and SB calling when ahead and QQ losing * losses) + (Chance that SB will fold and LP will call when behind * winnings) + (Chance that SB will fold and LP will call with QQ * equity * winnings) + (Chance that SB will fold and LP will call when ahead * equity * losses) =

(.75 * $145) + (.016 * $17) + (.16175 * -$1,000) + (.03325 * $1,035) + (.0075 * .15 * $2,000) + (.0075 * .85 * -$1,000) + (.0315 * .15 * $1,110) + (.0315 * .04 * $55) + (.0315 * -$1,000 * .81) =

-$40.90

Overpairs on monochrome boards

Here's the problem: You have AA or KK and raise in late position. The big blind calls. The flop comes down single suited, like 3c 6c 8c, and you have the Kc for the second nut flush draw. You bet, and the blind check-raises you all in. What's your move?

OK, maybe this is obvious. You need to fold because you're a dog in most situations, even though it's tempting to call with a big overpair and a redraw.

Against a flopped flush, you're essentially dominated because your redraw to the higher flush has only 7 outs. Against a strong draw, like the nut flush draw or a combo straight and flush draw, the KK is still way behind your opponent's range.

PokerStove:

equity  win  tie        pots won  pots tied
Hand 0:  37.624%   37.62%  00.00%  7822   0.00   { KcKh }
Hand 1:  62.376%   62.38%  00.00%  12968  0.00
{88, 66, 33, QcJc, QcTc, JcTc, Tc9c, 9c7c, 7c4c, 5c4c, AcKd,
AcKh, AcKs, AcQd, AcQh, AcQs}

Even if you had a suited AA instead of KK, your odds only improve to about 40-60. So I think a fold is still appropriate in that situation against your opponent's range.

A few hands later, I played a similar hand the same way.

I raised a few limpers with AA from the button and got called by the big blind and an UTG limper. As in the last hand, I bet the monochrome flop, and the UTG player went all in.

Again, I was behind my opponent's range, which is much tighter this time after he limps UTG.

equity win tie pots won pots tied
Hand 0: 39.766% 39.07% 00.69% 6189 110.00 { AdAs }
Hand 1: 60.234% 59.54% 00.69% 9431 110.00
{ 99, 8c8d, 8d8h, 8d8s, 77-66, KdQd, KdJd, QdJd, JdTd }

For what it's worth, I called with both of these hands even though I should have folded. I won the KK hand and lost the AA hand.

What can I say? I'm still fishy at times, but at least I'm learning something. And hey, I had outs!

http://twodimes.net/h/?z=2831839
pokenum  -h jc tc  - kc kh  -- 8c 3c 6c
Holdem Hi: 990 enumerated boards containing 8c 6c 3c
cards  win   %win  lose  %lose  tie  %tie     EV
Jc Tc  677  68.38   313  31.62    0  0.00  0.684
Kc Kh  313  31.62   677  68.38    0  0.00  0.316

http://twodimes.net/h/?z=2831923
pokenum  -h ad as  - 8d 8s  -- 9d 6d 7d
Holdem Hi: 990 enumerated boards containing 9d 7d 6d
cards  win   %win  lose  %lose  tie  %tie     EV
As Ad  647  65.35   331  33.43   12  1.21  0.660
8s 8d  331  33.43   647  65.35   12  1.21  0.340

Monster Draws

The sting of tax day still hurts. I hate losing bankroll because it sets back future earning potential and makes my goals for the year harder to reach. I've always wanted to get my bankroll up to $100,000, but it looks like it'll take few more months to get there. I guess that's the cost of doing business. Bleh.

---

I'm a big fan of pushing my big draws on the flop, especially when I flop a pair and a flush draw. With 9 outs for the flush and as many as 5 for two pair, I often tell myself that I have close to 50 percent equity to hit one of my draws on either the turn or the river. And even if I'm slightly below 50 percent, I figure that fold equity can make up the deficit.

But a recent post from MiamiDon got me thinking about the times when it may be foolish to push draws that look good at the time but may not stand up against strong hand ranges. In his post, MiamiDon flops top pair Aces with the nut flush draw, but he's still worried about the pot growing too large on the flop.

In the end, he calls the flop, makes the nuts on the turn and busts his opponent, who held a set of 5s. A third player in the hand folded the turn. Presto not so gold.

I ran the numbers, and I was a little surprised to find that the so-called monster draw was in bad shape against other strong holdings:

http://twodimes.net/h/?z=2584057

pokenum  -h ad 3d  - 5c 5s  -- ah 8d 5d
Holdem Hi: 990 enumerated boards containing 8d 5d Ah
cards  win   %win  lose  %lose  tie  %tie     EV
Ad 3d  304  30.71   686  69.29    0  0.00  0.307
5s 5c  686  69.29   304  30.71    0  0.00  0.693

http://twodimes.net/h/?z=2584069

pokenum  -h ad 3d  - 5c 5s  - as kd  -- ah 8d 5d
Holdem Hi: 903 enumerated boards containing 8d 5d Ah
cards  win   %win  lose  %lose  tie  %tie     EV
Ad 3d  256  28.35   641  70.99    6  0.66  0.287
5s 5c  635  70.32   268  29.68    0  0.00  0.703
As Kd    6   0.66   891  98.67    6  0.66  0.010

http://twodimes.net/h/?z=2584071

pokenum  -h ad 3d  - 5c 5s  - 6d 7d  -- ah 8d 5d
Holdem Hi: 903 enumerated boards containing 8d 5d Ah
cards  win   %win  lose  %lose  tie  %tie     EV
Ad 3d  161  17.83   742  82.17    0  0.00  0.178
5s 5c  506  56.04   397  43.96    0  0.00  0.560
7d 6d  236  26.14   667  73.86    0  0.00  0.261

The lesson here is that jamming on the flop with a big draw isn't a good idea when you smell genuine strength in a multiway pot. While folding on such a great flop would be very weak, that doesn't mean you always need to go crazy.

Poker Odds

There are many sites that provide information about poker odds, but none provides a comprehensive single source for basic odds knowledge in Texas Hold 'Em. So here is an attempt at compiling a reference list for what I feel are the most essential probabilities. I recommend memorizing all of these because knowing them off the top of your head gives you an edge in any game.


Pot Odds

Calculating pot odds is a necessary step in determining whether you are justified in playing a hand that may be an underdog at the moment but stands a chance of improving to the best hand. Pot odds are defined as "the ratio of the current size of the pot to the bet that you must call." Put simply, you want the probability of making your hand to be higher than the percentage of money you must invest in the pot.

The best way to quickly compute pot odds is to memorize outs expressed as a ratio. I'm constantly surprised at the number of players who refuse to remember this set of numbers that can be worth so much money at the tables.

Outs | Break-Even Pot Odds with one card to come
1 | 45:1
2 | 22:1
3 | 14.3:1
4 | 10.5:1
5 | 8.2:1
6 | 6.7:1
7 | 5.6:1
8 | 4.75:1
9 | 4.1:1

Another common way to estimate your probability of making a hand is by what Phil Gordon calls "The Rule of Four" and "The Rule of Two."

I have found a quick and easy way of figuring out how often I will draw to a winning hand after the flop.
First I count my "outs," or the cards that will give me a winning hand. For example, let's say I have Tc 9d and I put my opponent on A-K ... The flop comes Ac Td 7s. My opponent is in front, of course, having flopped a pair of aces, but there are five cards -- the two remaining tens and the three nines -- that will put me in front. In other words, I have five outs.
I can calculate the approximate odds of catching one of my cards on the turn or the river by multiplying the number of outs I have by four. In this case:
5 X 4 = 20 %
According to this "Rule of Four," I have about a 20 % chance of catching a winning card on the turn or the river. The actual odds turn out to be 21.2 %, a tiny difference that is irrelevant for most purposes.
With only the river card to come, the "Rule of Four" becomes the "Rule of Two." (Meaning you multiply your outs by two instead of four)

Preflop Odds

Higher pair vs. lower pair: 4.5:1
Pair vs. two higher cards: 55 percent to 45 percent
Pair vs. two lower cards: 5:1
Pair vs. a higher and lower card: 5:2, or about 70 percent to 30 percent
Domination (AK vs. AQ): 5:2, or about 70 percent to 30 percent
Two higher cards vs. two lower cards (AQ vs. 86): 5:3, or about 60 percent to 40 percent
One higher card vs. one lower card (A5 vs. KT): About 55 percent to 45 percent

Odds of being dealt a specific hand

AA: 220:1, or 0.45 percent
Any pair: 16:1, or 5.88 percent
AK suited or offsuit: 82:1, or 1.2 percent
Suited connectors: 46.4:1, or 2.11 percent


Odds of flopping ...

A set from a pocket pair: 7.5:1, or about 12 percent
A flush draw with two suited cards: 8.1:1, or 11 percent
A pair from any two non-paired cards: 2.1:1, or about 33 percent
Two pair from any two non-paired cards, using both of your hole cards: 49:1, or 2 percent

Sources:
"Phil Gordon's Little Green Book," by Phil Gordon
"Harrington on Hold 'em: Expert Strategy for No-Limit Tournaments, Volume 1: Strategic Play," by Dan Harrington
"Small Stakes Hold 'em: WinningBig with Expert Play," by Ed Miller, David Sklansky and Mason Malmuth
Bodog poker, as published by FilmZone.com
Mike Caro University
Two Dimes