Showing posts with label Back to Basics. Show all posts
Showing posts with label Back to Basics. Show all posts

Monday, July 22, 2013

Back to Basics: Playing Broadway cards

Cleaning out the posts I have in "Draft" form, I came across this post from July, 2011.  It applies to online poker, but you certainly can make the leap to live poker.  You need to translate the VPIP / PFR to live raising tendencies.

In continuing my series on Back to Basics, this latest installment deals with how to play broadway cards.  Broadway cards are generally defined as two cards that are Ten or better.  Examples are AT, KQ, QT, KJ, etc.  I consider this to be a follow-on to the section on Back to Basics: Suited connectors.

The more I play, the more I find that players (more live than online, but certainly both are guilty) have no understanding of broadway cards and how to play them.  Broadway cards are perhaps the most difficult to play, and the easiest to lose money with by virtue of the fact that if the board pairs your hand, your flopped top pair may or may not be the best hand.  Not only could your top pair hand be dominated by a better kicker, but a top pair hand is more difficult to fold than a suited connector hand.  In comparison, regular suited connectors, most of the time, are not going to flop top pair - and when you do, you know it is a very vulnerable top pair.  Regardless, people play all broadway cards, despite getting proper odds or understanding the reasons behind it.  In a nutshell, they think: "KT!  Two paint cards!  That's a good hand!  I can call this raise and be good on a King high flop or a Ten high flop," when the reality is that there are many hands that have KT crushed... namely AK, KQ, KJ, AT, AA, KK, etc., and proceed to stack off their top pair hand to any of the listed hands.

There is a defined pecking order of broadway hands, where clearly, some hands are better than others.  At the root is the idea of expected value (EV).  Fundamentally , The very best non-paired hand is AKs, AKo. AQs, AQo, AJs, are in the second tier, followed closely by AJo, ATs, KQs, KJs, etc.  I have given you a loose definition of the Hold'em Heat Map - a chart which you should study and be comfortable with.  There are many such examples of actions to take based on cards and position, available on the web; google "holdem starting hand chart groupings" and you'll get there.

The exact groupings of the starting hands are up to you; it defines you as a player, and delineates your VPIP / PFR.  If you are a loose PF player, your premium hands may include AK and AQ.  If you decide to be a tight PF player, you may only include AKs.  However, the lower you go down the starting hand chart, the higher the possibility that your starting hand may be dominated, as discussed in the prior paragraph.  AK clearly dominates all Ax hands - if an Ace hits the flop, unless your opponent has flopped two pairs, your AK is crushing all other Ace X holdings.  The same can be said for a King high flop holding AK.  You have what's known as TPTK, or top pair, top kicker, a very strong flop holding.

With the understanding of relative strength of 2 high cards, an interesting concept I want to introduce is the idea of raisable, limpable and callable hands.  I will likely write about position in a later post, but for now, believe that position is one of the most critical elements to poker.  Having the ability to act after your opponents gives you the power to see your opponent's actions prior to making a decision on your own.  In short, you have more information.  This principle applies for all streets of Texas Hold'em; the BTN is the strongest position at the table, in order on down to the SB being the weakest.  In order to call a raise from either of the blinds, or raise the bet based on your hand strength, you must have solid holdings.

Where am I going with this?  Well, it's interesting that, for example, while you may raise an unopened pot with QJ from the BTN or CO, you should likely fold QJ from the UTG position or MP1.  Taking this example a step further, a consideration in your mind should always be, "What happens if someone 3bets me (re-raises my original raise)?  Is my hand strong enough to either call a 3bet or 4bet?"  Moreover, a consideration should be, "What happens if someone raises my limped QJ?"  Although there is no clear answer, QJ in most cases cannot stand a 3bet...  particularly from a tight opponent, but others as well.  Assuming you call a 3bet, automatically, you're committing [what in most cases would be] about 10BBs, or 10% of your stack, PF with cards that may already be drawing very thin.  Referring back to prior paragraphs, you may already be in a 70/30 situation up against an AQ, AJ, AK type hand.  Needless to say, in a 3bet situation, you may be up against AA, KK, QQ, JJ as well...  all dominated situations, too.  Are you really looking to invest 10% of your stack on those kind of odds?  I don't mean to paint such a glum picture, so you certainly could be up against lower pocket pairs as well (depending on how loose of a 3better you have), where you have 50% equity.  Following the Back to Basics post on hand ranges and equity, if you called the 3bet, you're not giving yourself much of a chance; you're not going to hit your non-dominated card's 3-of-a-kind or a straight often enough to justify those poor odds AND PLUS, you'll need your opponent to stack off to you in those situations where you do hit the nuts like that - not always a likely scenario, in order to pay for all of the situations where you miss and have to fold your hand on the flop.

So why do I say that QJ is fold-able from UTG, yet raise-able from late position?  Control and position.  If you limp and/or raise QJ from an earlier position, there are many opponents who will likely have a hand ahead of you - who will be raising their hands or at least calling you.  What happens when you get that Q T high 2-tone flop you were looking for, cbet and are flatted by your opponent?  Does he have KQ, AQ?  Does he have a flush draw?  Does he have a straight draw?  You can't positively believe that you are good here a large portion of the time (I know you can never believe you are good without holding the actual nuts, i.e. a set, etc.).  What happens if he is on the flush draw holding AKs?  He's actually ahead of your equity without holding a made hand - he has the inside straight draw to a Jack (making your would-be hand much harder to get away from, holding top two pair), he holds 2 overcards to the board and any card of his suit...  3 + 9 + 6 = 18 outs or >50% equity.  By the turn and or river, he expects to have the best hand; should you keep betting and building a pot for him to take away from you?  You've potentially put yourself in a terrible situation by playing out of position with weak relative holdings.

Are you looking to throw money away or put yourself to tough decisions with every hand?  Just fold it and wait for a better opportunity with less players to raise / call... i.e. from the later positions.  As a fact, the later positions have as few as 2 or 3 players to react to your move.  From the BTN, all you need worry about is the SB and BB.  Chances are, with 2 players, you have the best hand here.  If so, you will likely win the blinds - a 1.5BB addition to your stack for very little risk.  Additionally, with future action, you will always act last and have the advantage of seeing what your opponents are doing / how they're betting.  More often than not, a loose player in the blinds will fold to a cbet (continuation bet) on a non- Ace high flop.

Therefore, for beginners, I suggest following an algorithm based on the one defined on wikipedia; Hold'em Heat Map, where the Mason and Malmuth hand grouping is:

Tier Hands
A AA, AKs, KK, QQ,
B AK, AQs, JJ, AJs, KQs, TT
C AQ, ATs, KJs, QJs, JTs, 99
D AJ, KQ, KTs, QTs, J9s, T9s, 98s, 88
E A9s...A2s, KJ, QJ, JT, Q9s, T8s, 97s, 87s, 77, 76s, 66
F AT, KT, QT, J8s, 86s, 75s, 65s, 55, 54s
G K9s...K2s, Q8s, J9, T9, T7s, 98, 64s, 53s, 44, 43s, 33, 22
H A9, K9, Q9, J8, J7s, T8, 96s, 87, 85s, 76, 74s, 65, 54, 42s, 32s
Hand grouping chart

Action Early Position
(UTG,UTG+1,SB,BB)
Middle Position
(UTG+2,MP1,MP2)
Late Position
(CO, BTN)
Raise A A, [40% of the time] B A, B, C, D +
all pocket pairs
Call 3Bet JJ, B JJ, B, 99,C TT, [60% of the time] B,
[20% of the time]D
4Bet / all-in [without JJ] A [without JJ] A A
Actions when facing limpers / folds to your action

Action vs. Early Open vs. Middle Open vs. Late Open
3Bet / Raise A A, sometimes TT A, TT
Call 22+ 22+,
[60% of the time] B
22+, B, C
Actions when facing a first time raised pot

As you become comfortable with this starting hand range and associated actions, you can deviate away from the initial algorithm, expanding one tier and shrinking another, or vice-versa.  For example, I tend to raise all pocket pairs from all positions, raise 25% of my suited connectors and limp (with others in the pot) or fold 75%.  I play 25% of AJo from EP, yet raise from MP+.  I raise a full range of hands from CO or BTN.  However, I caution you before you start messing with the algorithm: if you're a beginner and/or not profitable at poker, become the nit described above.  You may not optimize on all of your hands, but you should be profitable and will become more comfortable with starting hand strengths and positions.

I had put the above 2 charts detailing actions to hand groups awhile ago; I would like to include the notes that I had in there when I came up with the algorithms at the time:

"Obviously, depending on the table, you can adjust your ranges up or down (if a LAG has a VPIP +30 & PFR +20, then you can widen your RR / calling ranges.  However, this should provide you a good idea of what you should be playing / doing.  Additionally, it serves to say if you run into significant resistance (3 and 4 bets prior to your turn, you really need to narrow your ranges even further.
Finally, there is no leak if you simply fold a hand because you are unsure.  Certainly, there is the cost of lost opportunity, which does cost winnings.  However, you can't lose if you fold.  By sticking to the above charts, you should be able to handle at least 2 tables at once, and keep yourself from making difficult, marginal decisions.  In other words, you will usually have the best of it unless there is a slow played PP or set or something like that (less likely at our micro stakes).

Finally, you can semi-adjust your play to make certain assumptions about players when you see their VPIP over a longer hand history.  You can clearly see the top 20% of hands.  If you see a VPIP of around 20, you have a pretty good feel of what they're limping / raising with as well, based on the hand grouping chart.  If you see a VPIP of 30, you can surmise that they are adding in the AT / QT / KT / etc. type hands as well as Axs.  Upwards of 30 shows they are playing suited gappers (i.e. 97s, etc.), or even random suited / connectors (i.e. J3s / 87o / 86o).  Those VPIP >30 players are the ones you want to hammer on constantly when you're in position, in my opinion.  Punish them for limping when you have a hand.  Get them heads up and c-bet good flops which likely missed them.  Make them pay for their junky-pair-type hands that you have the best.  Put them to difficult decisions, constantly.  Keeping to this chart gives you a good feel for where you are, as you have no direct read on the opponents you face other than the information you have collected prior.  The idea is to laugh in your opponent's face and say 'my range is better than yours.' "




Tying it together (I have suited connectors and broadway):
Full Tilt Poker $0.25/$0.50 No Limit Hold'em - 9 players
The Official DeucesCracked.com Hand History Converter

BTN: $57.70
SB: $30.80
Hero (BB): $87.45
UTG: $71.40
UTG+1: $88.20
UTG+2: $94.00
MP1: $34.25
MP2: $110.80
CO: $42.75

Pre Flop: ($0.75) Hero is BB with Tc Qc
5 folds, CO raises to $1.50, 1 fold, SB calls $1.25, Hero calls $1
In a multi-way pot, I have both a suited one-gapper and 2 broadway cards, which may, in & of themselves, be able to stand on their own as a single top pair-type hand.  However, I treat this hand with as much power as a normal suited connector; I'm not going broke with a top pair hand.  I love seeing a multi-way pot with this hand.

Flop: ($4.50) 3c 6h 2c (3 players)
SB checks, Hero checks, CO bets $2, SB calls $2, Hero raises to $8, CO folds, SB folds
This flop is likely to have missed my opponents, yet I want to give the CO a chance to bluff at it.  My check / raise is a semi-bluff; I have 2 overcards (25% equity), but I also have a flush draw (32% equity) to go along with it.  I am fairly certain that no one else is on the flush draw, so I can feel safe that *AT WORST* I have 32% equity.  However, let's assume that I have a "dominated" Queen or "dominated" Ten - i.e. someone else has AQ, KQ or AT, KT, then I can safely give myself at least 3 outs to the best top pair, assuming no one else has an overpair (which I think my raise will establish very quickly.  So, I give myself another 3 outs to the 9 flush outs, a 44% equity hand at worst... plus the check / raise that I put in is a pretty strong move - increasing the likelihood that the hand won't even continue past the flop. 

Final Pot: $10.50
Hero wins $10.00
(Rake: $0.50)

This would probably be a bad call:

Full Tilt Poker $0.25/$0.50 No Limit Hold'em - 9 players
The Official DeucesCracked.com Hand History Converter

CO: $93.50
BTN: $75.30
SB: $18.25
BB: $79.05
UTG: $52.50
UTG+1: $144.90
UTG+2: $14.85 - 15 VPIP / 9 PFR
MP1: $18.75
Hero (MP2): $79.70

Pre Flop: ($0.75) Hero is MP2 with Kc Qc
2 folds, UTG+2 raises to $1.50, 6 folds
Note that I will not be calling anything against this player's open (without JJ+ in which case I'm 3-betting him).  There are no implied odds here to warrant a call... in most situations... EVER!  Note multiple things here:
  • He is a 15/9 which is a pretty tight range to open pots.
  • He is opening the pot from early position, which increases the likelihood that he has a legitimate hand.
  • We are playing for effective stack sizes of $15.
There are no implied odds here to warrant a call - in fact, this is considered a "reverse implied odds" situation.

Final Pot: $1.25
UTG+2 wins $1.25

Monday, August 9, 2010

Back to Basics: Thinking about your opponent's hand ranges

It's been awhile since I posted a "Back to Basics" segment, and was feeling motivated by Matt Tag's post on F*@! the math.  Therefore, I tried throwing this together.  I know this goes beyond a "basics" segment, but I was thinking about calculation of hand ranges anyway, so I wanted to get it out there.  Let me know what you think.

My chosen career, software engineering (systems engineering), was selected as a way to avoid using math directly in my head.  See, ironically, I'm maths challenged. Therefore, I try to avoid using math.  When I do, though, I am always looking for the "easy way out" - a shortcut or way to make the maths easier.

Figuring out equity, at any point, when faced with an all in situation, is somewhat easy, if you can do memorization and/or addition and multiplication.  We covered that in Back to Basics: Pot Odds, Hand Equity and Implied Odds, where you can count outs and multiply by either 2 or 4.  The more you do it, the quicker you'll become, as well.

However, figuring out your opponent's hand range is more difficult, because you have to deal with weightings and rough math; i.e. unless you know you're opponent's exact holdings, you cannot come to a precise number.  Let's go through the basics, first.  There are 6 hand combinations for any specific pocket pair (e.g. AA), 4 hand combinations of a specific suited combo (e.g. AKs), and 12 hand combinations of unsuited cards (e.g. AKo).  FYI: Surprisingly, it is statistically rarer to hold a specific suited combo (AKs) than it is to hold AA; you will hold AKs roughly 4/6 or 2/3 of the times than you will hold AA...  look it up in your HEM or PT3 databases (assuming you have enough of a sample size).

Okay.  We have covered hand combinations.  Let's talk about real-world examples:

Given that we now know there are as many combos of 2 pocket pairs as there are any combination of specific offsuit cards, AKo, for example, we can start to think about and assign ranges to our opponent.  We're in a PF situation, facing an all-in bet.  We hold QQ.  Regardless of how we arrived at the shove, let's assume that we know our opponent is capable of this play with precisely 4 hands: AKo, AKs, AA, and KK.  From the Back to Basics: Pot Odds, Hand Equity and Implied Odds post, we know that we have 20% PF equity vs. any overpairs to ours, but against 2 overcards, we have 50% equity PF.  So we assign a weight of 50% to the 16 combos of AK (4 for AKs + 12 for AKo) and 20% to the 12 combos of AA and KK: .5 * 16 + .2 * 12 = (.5 * 16 =)8 + (.2 *12=)~2.5 (figured out in my head by 2 * 12, move the decimal over one place) = 10.5.  Take that number divided by the total amount of combos (16 + 12 = 28)  is 10.5 / 28 = a little better than 35% equity in this hand (I took 10/30 = 33%, but the top number is bigger and the bottom number is smaller so I estimate around 35% equity) to make the call.  Therefore, we need a price better than 2:1 pot odds to make the call...  in other words, at best, we're splitting and at worst, we're dominated.  Given the range, this is an easy fold for most cases.

Let's move on to a post flop example:

Once again, we hold QQ and have seen a flop of 2 5 9 rainbow.  We're facing another all in situation and whether or not to call.  We hold a simple overpair and put our opponent on a fairly wide range of hands: 22-AA, AK, 87s.  I don't care what the PF action was, because I'm telling you what our opponent's range is precisely.  Do we really have to go through all the addition, multiplication and division to get to whether we're making a good call or not?  Well, let's think about it and do some shortcutting: 22, 55, 99, KK, AA have us dominated.  However, we're crushing 33, 44, 66, 77, 88, TT, JJ.  Therefore, we can roughly cancel out 5 pair combinations of domination / crushed because they are equal with equal weights (remember that all pocket pairs have the same number of combinations: 6 ), leaving us with 2 pair combos which we have crushed by an 84% margin.  This cancellation process gets us a lot further down the road, and more quickly.  What other hands are we dealing with here?  AKs, AKo, 87s.  There are 16 combos of AK @ 75% equity (remember that we have 75% equity on the flop vs. 2 overcards from the discussion on figuring out equities) and 4 combos of 87s at 68% equity (again, an open ended straight draw has roughly 32% equity).  The maths are as follows: 2 * 6 (the two remaining pair combos) *84% + 16 *75% (the AK combo) + 4 * 77% = [in my head] 12 * 80% + 16 divided in 4ths + 4* 75% = 9.5 + 12 + 3 = 20.5 out of 12 + 16 + 4 or 32.  Given the hand range we put him on, we are likely very far ahead of his range - roughly 66% equity to his 33%, thus any call will likely be profitable here.

What's that you say?  Your opponent isn't likely to be shoving 33, 44, 66 on this flop?  Or maybe he's likely to shove those types of hands on a bluff a certain percentage of the time?  Well, you can adjust your numbers and weights to play with the formula.  If you take out 33, 44, 66, the numerator increases and the denominator decreases, decreasing the likelihood that you are ahead.  Like I said, the world is not perfect; you will not be able to come up with an exact number that will tell you whether you're profitable or not if you make the play.  The idea is to come up with a rough notion of what to do.

You can certainly perform this type of evaluation in your head; the more you practice it, the better you will become.  There is a TON of further reading on the subject, if you care to get into the maths, as well as more detailed explanations.  I rather enjoyed Foucault's article on hand ranges, check it out if you're so inclined.  Finally, there is a tool out there available called PokerStove, which happens to be totally free.  You can compare equities on opponent's ranges vs. your holdings to figure out your equity in the hand.  It is a critical tool in your poker arsenal, if you're not already using it.

Remember: The overall goal of the exercise of putting your opponent on a range of hands is to determine that if you make this move in a vacuum 1 million times, will you be net profitable, net neutral or a net loser.  Take a few seconds, the next time you are facing an all in situation - or any action for that matter - and think about ranges and equities to the hand.  I am sure it will help you.

Comments welcome; please feel free to point out discrepancies.  I may not have explained the math perfectly - if you find problems, please let me know & I will correct them.  My goal at the end of the "Back to Basics" segment is to have a primer for which I can send friends and people I know  to better understand the game.

Monday, May 17, 2010

Back to Basics: Pot Odds, Hand Equity and Implied Odds

I'm starting to realize that some of my readers are quite new to poker... or perhaps don't have basics and fundamentals down pat.  In addition to my random strategy posts, I plan on starting a new segment call "Back to Basics."  To most readers, this will be elementary, but I feel it serves good purpose to hammer down fundamentals of pre- and post- flop play.  Perhaps I will learn a thing or two from the comments section, as well.  I can't promise anything, but I do plan on trying to post a new "Back to Basics" every Monday.


As a quick recap of prior posts, readers interested in this series would be best served by reading my thoughts on Poker Tracking / Datamining software, Bankroll Management, Rakeback Agreements, and Pre- / Post- Game Process Parts I, II, III & IV, to have a good footing on terms, assumptions and an understanding of my poker philosophy.  Also see prior "Back To Basics" back-posts.

Welcome back to the second segment of Back to Basics.  This entry will cover two fundamental poker formulas: pot odds and hand equity.  The two term, for the most part, go hand-in-hand, for the simple fact that a player can comprehend the formulas and instantly apply them to his or her own game.  It should be noted that a player not using these two ideas who begins to apply them to their game is a better player than before, but these ideas should not be used in a vacuum; i.e. as a good player, you need to consider your opponent's holdings vs. your own.

That said, let's get into the definition of both terms.

Pot Odds:
As defined by wikipedia (the internet gospel on *EVERYTHING* :-) ) it is "... the ratio of the current size of the pot to the cost of a contemplated call. In other words, if the pot contains $100, and a player must call $10 to stay in the hand, then the player has 100-to-10, or 10-to-1 (commonly expressed as 10:1), pot odds. Pot odds are often compared to the probability of winning a hand with a future card in order to estimate the call's expected value. Indeed, a common usage of the term is to say that one "has pot odds", meaning that the present pot odds, compared to one's estimated chance of winning, make it profitable to call."

Personally, I am terrible with ratios, so I like to convert these ratios to percentages, since I am a lot better equipped to handle one simple number... therefore I add the two numbers together and divide by the first (in my head, so I give a rough estimate of the number).  For the example above, to demonstrate my thought process, I add 10 + 1 (=11), take the 1 from the ration and divide it by the sum 11.  I know that 1 into 11 does not go evenly, but 1 into 10 does (=.1 or 10%), so I'm going to rough the number by saying it equals about 8-9%; slightly less than 1 into 10...  It's a simple shortcut, but I don't need to be exact since poker is not a game of exact numbers. (You're making educated guesses at your opponents cards anyway, right?)

What do pot odds tell us in layman's terms?  They tell us the price we're being offered to act upon (fold, call, raise).  I don't know about you, but I want a bargain when it comes to purchases; I don't want to overpay for things that I can get cheaper.  The same holds true with poker; if my opponent is offering me a bargain, I take it.  If not, I fold.

What?  I don't understand!  Who cares?  Allow me to illustrate the concept in terms of flipping a 2-sided coin: for every coin flip of heads you pay me $6 and for every flip tails, I pay you $4, you would be getting (in this case straight, not pot, because we're talking about coin flips, not cards) 4-to-10 on your bet, or 40%, on what we all know to be a 50/50 (50%) true odds bet.  I'm giving you an awful bet, and you should [rightfully] say "Go pound sand," or something less polite :-).  Perhaps in the short term, 1, 2, 5, even 25 flips, you may hit more heads than tails and actually make money.  In the long term, though, you know you're going to lose money - flip that coin every day for the rest of your life and you'll be a big loser.  However, if the situation is reversed, I'd become your best friend because I'd essentially be giving money away.

Implied Odds:
Again, courtesy of wikipedia (the internet gospel on *EVERYTHING* :-) ), implied odds "... are calculated the same way as pot odds, but take into consideration estimated future betting. Implied odds are calculated in situations where the player expects to fold in the following round if the draw is missed, thereby losing no additional bets, but expects to gain additional bets when the draw is made. Since the player expects to always gain additional bets in later rounds when the draw is made, and never lose any additional bets when the draw is missed, the extra bets that the player expects to gain, excluding his own, can fairly be added to the current size of the pot. This adjusted pot value is known as the implied pot.

Example (Texas Hold'em)
On the second to last betting round, Alice's hand is certainly behind and she faces a $1 call to win a $10 pot against a single opponent. There are four cards remaining in the deck that make her hand a certain winner. Her odds of drawing to one of those cards is 10.5:1 (8.7 percent). Since the pot lays 10:1, Alice will lose money by calling if there is no future betting. However, she expects her opponent to call her additional $1 bet which she will make when she makes her draw. She will fold when she misses her draw (and lose no additional bets). Her implied pot odds are 11:1 ($10 plus the expected $1 call, to her additional $1 bet). This call now has a positive expectation."

Simply put: What are the odds that I will get the rest of my opponents stack by making the play in question.  How does all of this tie into Hand Equity?

Hand Equity:
Every hand holds a particular value.  Each hand has a different value, or chance of winning vs. a different hand (or set of hands).  If everyone were dealt hands face up, you could compare two hands against one-another and draw certain mathematical facts.  It is from these hand values that you can conclude your percentage chances of wining a particular hand.  Just as in the coin flip example above, where you know if you flip a coin an infinite number of times, you will be exactly 50/50 on your heads and tails, if you were to deal a combination of cards against one another an infinite number of times, (although there are many more variables) the particular hand in question vs. the opposing hand is going to win a certain percentage of the time.

  • From a pre-flop perspective, there are hand rankings where the strongest hands have more equity vs. the weakest hands.  For example, AA, the strongest starting hand in Hold'em, has ~80% equity when seeing a flop heads-up vs. KK (the second strongest starting hand in poker), which is true for all pairs vs. lower pairs all the way down to 33 vs. 22.  On the same vein, any pair vs. any two overcards (e.g. 88 vs. KJ or 22 vs. AK is worth roughly 50% equity.  If you are interested in running a Monte Carlo simulation on hands vs. other hands, there is a GREAT free tool available, called PokerStove, which allows you to simply plug in 2 or more hands and compare them against each other.  Since there are 1326 possible starting hand combinations in Hold'em (just trust me, I'm not going to do the math), the pre-flop hand comparisons are fairly static in nature.  In other words, over time, you will be able to memorize the average strength of hands against other hands, which is why pre-flop hand selection is so critical to a winning player.  For more information on starting hand strength, see my post Odds Scenarios.  It may be a tremendous help the fledgling player.

    Realize as I'm sure you have by now, that any two cards can win a hand.  You can play 72o (which is the theoretically worst starting hand combination in hold'em) against AA and win at a clip of 12.5% of the time if both players see the hand through to the river. Will that win you money over the long term?  Perhaps, if your opponent is dumb not intelligent and you can get all of the money in the center when you're ahead (in the 12.5% of the time), and are able to fold the other 87.5%.  You have the implied odds to play just about any two cards against him, even though you are not getting appropriate pot odds.  However, the real world is not a vacuum, and not all players hold AA to your 72o, nor are they always willing to push all-in on your 72o against a board of 7-7-2 or A 3 4 5 x.  Therefore, your hand selection is important, because 72o, when played over the long run, is a money loser.

    Tying directly into pot odds, though, let's say UTG (who is an extremely tight player who would only raise holding AA) raises 3x BB on a 9-person table.  You sit in the big blind holding 72o, and watch as the entire 7 players preceding him call.  The pot would contain 9 (players) * 3x (big blinds) + 1 (for your big blind) 28 total big blinds.  You'd be getting 28 to 3 (by my math, roughly 9%) pot odds to make the call with literally ANY TWO CARDS; it'd be well worth it to you to make the call in that spot.
  • From a flop and beyond perspective, though, you can now calculate your direct equity from the hand you hold.  Since you can now complete a 5 card hand, you can compare your 5 card hand and, if you feel it is an underdog, calculate the odds of improving to the winning hand.

    At the heart of this process of odds calculation is your ability to count the number of cards which will improve your hands by the turn or river.  You need to be able to somewhat accurately put a hand to your opponent.  For example, if you are holding AK, and a flop of 5 7 T hits, you need an A or K on the turn or river to potentially improve your hand to the winner (assuming your opponent has a pair of Queens or lower.

    To continue with the example above, you can calculate your available out cards as the 3 remaining Aces in the deck (4 total, you hold 1, therefore 3, in theory remain), and 3 remaining Kings (same logic as counting Aces), which gives you a total of 6 out cards to improve your hand.  Keeping with imperfect math, we want to get a rough idea of the percentage of time our hand will improve to the winner.  We can do this by multiplying the number of outs we have for improvement by 2x the number of cards we expect to receive on future streets.  Given the above example, we are on the flop and expect 2 more cards (turn and river).  Therefore, we multiply our 6 out cards x 2 (the magic number) x 2 cards expected to receive to get our estimated chances on having a winning hand by the river.  The product of 6x2x2 = 24%.  P.S.  If you've ever watched the World Series of Poker, or any other poker series (High Stakes Poker, etc.), you'll see percentage odds on the side of your screen for each hand in play.  Armed with the rule of 2x and 4x, you too can quickly (and roughly figure out the equity percentages of each hand.

    Note: Pertaining to the example above, you need to be sure that your opponent did not flop a set (pocket pair + 3rd of the rank on the board for 3-of-a-kind), because even if you turn an Ace and river and Ace, you are holding 3-of-a-kind to his rivered [Tens, for example] full of Aces for the rivered boat.  Following, you are almost drawing dead on the flop to a set.  Just the same, you need to carefully put your opponent an appropriate hand; i.e. if he holds AT to the 5 7 T board, only a King will improve your hand because a turned or rivered Ace will give him 2 pair and you one; the rule of 2x 4x would give you 3 outs, or 3 x 2 x 2 = 12% to the winning hand in that case.

    One more example: a popular one; flush draws:
    Referring to the previous post Back to Basics post on suited connectors, let's create a scenario where I hold 9s8s and the flop comes As 2s Jd.  Assuming that my opponent does not have a higher flush draw, but holds a pair of Aces or Jacks, I can count my out cards as follows: 13 total spades (as with every - 2 on the board - 2 in my hand leaves me with 9 spades.  I expect 2 cards to come, yielding me a hand equity of 9 (outs) x 2 (turn card) x 2 (river card) = roughly 36% equity in the hand.

    Now, let's change the flop around a big and give ourselves a flop of: 6s 7s Ad... we have a flush draw, a straight draw, and a straight flush draw.  At this point, for all intents and purposes, we have a MONSTER hand which holds at least 50% equity against almost all hands.  How?  We need to take care in counting our outs, because we don't want to count cards twice, a common mistake, but here goes:  We know we have 9 outs for the spade draw, as in the above scenario.  However, we also have an additional 4 5's and 4 Tens, which will give us a straight.  Ooops!  Are there really 4 5's and 4 Ten's though?  We've double-counted our ranked cards because we've already counted the 5s and the Ts in our spade out cards as 2 of the available 9.  Therefore, there are really only 3 5's and 3 Tens which we can cleanly count, giving us 6 straight out cards.  9 flush + 6 straight out cards gives us 15 total out cards x 2 (turn card) x 2 (river card) = 60%(!?!?!?!?!) equity.  How is that possible?  I'm actually ahead without having a made hand... which emphasizes the power of a suited connector (yes, you are ahead of a 1 pair made hand such as Aces or pocket pairs).  If you put your opponent on a pair, it would not be incorrect to get all of the money in the middle given any pot odds.  Look at the same example and figure out your equity if you put your opponent on a set of 6's or two pair: Aces and 7's .  What about if your opponent has the AsKs (answers at the bottom)?
Tying it all together
If you haven't already jumped to the conclusion, let me sum it up for you.  A simple / quick estimate of whether you're getting an immediate bargain is comparing your hand equity to the pot odds offered.  Simply, if the pot odds are less than the hand equity, then it's an easy call (if you're facing a 20% pot bet but your hand equity is 32%).

If the pot odds are not as good as the hand equity, but you feel as though making your hand would get your opponent to stack off his remaining stack to you, then mix in the element of implied odds (such as the example of playing 72o vs. AA).  You usually want to have a good amount of your villain's stack remaining on the river in order to get proper implied odds.

* Given you hold 9s8s and the flop is 6s7sAd:
  • If your opponent holds 6 6, your equity is reduced by one out, the As, which would give him 6's full of Aces vs. your Flush; 14 (outs) * 2 (turn) * 2 (river) = 56%.  Your equity is also reduced by another TBD (to be determined) card on the turn, 13 (outs) * 2 (river) = 26% chance of improving from the turn to the river.
  • If your opponent holds A 7, your equity is reduced by one out, the As, which would again, give him Aces full of 7's vs. your Flush.  However, you do not lose an out card on the turn because the As is the only card that will make your hand while betting his.
  • If your opponent holds AsKs, then you are in a whole new ballgame; the only out cards you have are any 5 and any Ten, making you either a straight or a straight flush.  Therefore 4 5's + 4 Tens = 8 * 2 * 2 = 32%.

Monday, May 10, 2010

Back to Basics: Suited connectors

I'm starting to realize that some of my readers are quite new to poker... or perhaps don't have basics and fundamentals down pat.  In addition to my random strategy posts, I plan on starting a new segment call "Back to Basics."  To most readers, this will be elementary, but I feel it serves good purpose to hammer down fundamentals of pre- and post- flop play.  Perhaps I will learn a thing or two from the comments section, as well.  I can't promise anything, but I do plan on trying to post a new "Back to Basics" every Monday.

As a quick recap of prior posts, readers interested in this series would be best served by reading my thoughts on Poker Tracking / Datamining software, Bankroll Management, Rakeback Agreements, and Pre- / Post- Game Process Parts I, II, III & IV, to have a good footing on terms, assumptions and an understanding of my poker philosophy.

It is my feeling that the reason most losing players are net losers is because they have lost their hand before they've even seen the flop.  I'm not a coach (perhaps I will be in the future :-) ), but I have no doubt that a coach's "easiest" job is taking a losing player and turning him (or her) into a break-even [at minimum] player.  Therefore, the inaugural segment of "Back to Basics" today will focus on pre-flop hand selection (there are many places which talk about pre-flop hand selection; being the lazy blogger that I am, I looked in my bookmark list and could find one of note: Dee's Nutz "Every Decision Counts" entry), particularly focusing on how to play suited connectors.

I've seen far too many losers (henceforth referred to as "donkeys") play suited connectors, no matter the cost.  When facing a 3x raise from any and all positions, they look down and see 7 6 suited or 5 4 suited and think: "I got Ace crackers!  CALL!!!!"  While the donkey mindset is not necessarily always wrong, he is not generally getting the right odds to make that call nor does he understand the how's and why's of the play, thus a leak is sprung from his bankroll / stack.

First: Why do we play suited connectors, and why are they valuable?
  • Suited connectors are easier to fold.  A flop can come as good as 8 4 2 (with your suited connectors being 8 7) and you can fold them, depending on the action...  would you be so prone to do that, holding, say AA?  Depending on the action and your opponent, a flop such as described above could be a very scary flop for AA; over-called pocket pairs flopping sets, etc.  However, you can throw away a top pair, no kicker (TPNK) hand away without a second thought to significant action.
  • Suited connectors have many possibilities.  You can flop / draw to a non-nut flush.  You can flop / draw to a straight.  You can also flop / draw to a straight flush, where your un-made hand is actually equity-wise ahead of all pairs.  (We will get into equity and figuring out your hand equity in a later Back to Basics segment.)  They also hold the standard non-paired hand properties where you can flop 2 pair, or 3-of-a-kind.
  • The point is that with suited connectors (SCs), we have many different options  to potentially (and deceptively) hit the flop, while holding a hand that can be also easily folded.
Second: How much should we pay to play suited connectors?
  • The rule of thumb I generally use is that I am not going to pay more than 1/10 of effective stack sizes called the 5/10 rule (for a good explanation, click link), given the correct conditions (described below).  That is not to say that I am calling a raise of 10% stacks right off the bat; I am simply saying that given a multi-way pot... particularly if I *KNOW* my opponents hole cards (i.e. he holds AA, or KK to take an extreme example), I want to know that I can potentially get 10x my initial outlay for my risk of playing these speculative cards.  What I am touching on in the last sentence is the concept of implied odds, another topic I will also get into in later segments of Back to Basics.

It is my view (and many other "experts," not that I'm an expert by any means :-) ) that suited connectors play very nicely in multi-way pots.  What does that mean?  It means that I want to play my suited connectors if there is at least one caller in the pot already: there was a raise and a flat caller, or a limper and you opt to limp as well.  Why?  Assuming there is no squeeze (we're playing lower stakes poker here, so we're not really concerned about a squeeze play, another topic to be addressed in a later Back to Basics post), you are guaranteed at least 2 players in (addition to yourself) to see a flop.  That, my dear reader, is the definition of a multi-way pot.

Personally?  I'm sometimes limping suited connectors when facing a limped pot, sometimes raising suited connectors (usually from in-position), and sometimes folding suited connectors in the situations not favorably described above.  Why?  It adds deception to my game- my raises are not necessarily broadway (AK, KQ, etc.) cards nor pairs; my opponent must put me on a wide range of hands.  For the reasons described above, I'm usually over-calling suited connectors in conditions where I'm facing a raise with a flat caller, or with a smaller percentage of the time (opponent dependent), 3-betting the original raiser (and folding to a 4-bet).

A few quick hand examples of an appropriate overcall with suited connectors to leave you with:
BTW, as an aside, I was debating blocking out the results (because the results are not the point), but will show this hand in its entirety.

Full Tilt Poker $0.02/$0.05 No Limit Hold'em - 9 players
The Official DeucesCracked.com Hand History Converter

BB: $4.45
UTG: $4.15
UTG+1: $10.08
UTG+2: $5.00
MP1: $2.00
MP2: $3.17
CO: $4.94
Hero (BTN): $7.44
SB: $9.60

Pre Flop: ($0.07) Hero is BTN with 7s 8s
UTG calls $0.05, UTG+1 raises to $0.22, 1 fold, MP1 calls $0.22, 1 fold, CO calls $0.22, Hero calls $0.22, 2 folds, UTG calls $0.17
I get 1, 2 players calling before me and then UTG comes along for the ride - we see a flop 5-way!  AWESOME for 87s.

Look at my potential winnings (also known as implied odds); anywhere from $2.00 (MP1) who is *NOT* getting good odds to call with whatever hand he has, all the way to $7.44 (me, since UTG+1 has me covered), and some combination in between.

Flop: ($1.17) 8h 7c Qd (5 players)
UTG bets $0.05, UTG+1 raises to $0.90, MP1 folds, CO folds, Hero calls $0.90, UTG calls $0.85
GREAT GREAT FLOP!!!  I know exactly what UTG+1 has - an overpair or AQo... (crappy luck for me if UTG+1 has a set of Queens) based on his bet sizing / raise; I'm going to assume KK or AA though.  I have position and don't want to slow him down one bit.  I also want UTG coming along for a little extra juice.  Moreover, I'm going to be extra careful because the board pairing (non- 8 or 7) could spell disaster for my hand.

Turn: ($3.87) 3c (3 players)
UTG checks, UTG+1 bets $3.87, Hero raises to $6.32 all in, UTG folds, UTG+1 calls $2.45
The 3c is as safe of a card as I can get.  It is a non-paired turn, meaning that UTG+1 is drawing to 6 board pairing outs (3 Queens left, and 3 3's left) + 2 Kings / Aces (or 3 Aces + 2 Queens) or whatever he has.  I'm actually hoping he has KK or AA because he has 3 less outs cards that way.  I have an 80% edge here, whereas on the turn I maybe had 60-70% equity...  I have no qualms about getting it all in here because he's committed to the pot.

River: ($16.51) Jd (2 players - 1 is all in)

Final Pot: $16.51
UTG+1 shows Kh Kd (a pair of Kings)
Hero shows 7s 8s (two pair, Eights and Sevens)
Hero wins $15.41
(Rake: $1.10)

Another example:
Full Tilt Poker $0.25/$0.50 No Limit Hold'em - 9 players
The Official DeucesCracked.com Hand History Converter

CO: $33.55
Hero (BTN): $83.65
SB: $57.20
BB: $247.80
UTG: $55.70
UTG+1: $49.50
UTG+2: $34.60
MP1: $17.70
MP2: $123.80

Pre Flop: ($0.75) Hero is BTN with 7d 9d
1 fold, UTG+1 raises to $1.50, UTG+2 calls $1.50, MP1 calls $1.50, 1 fold, CO calls $1.50, Hero calls $1.50, 1 fold, BB calls $1

Flop: ($9.25) As 6s Kh (6 players)
BB checks, UTG+1 bets $5.50, UTG+2 folds, MP1 folds, CO folds, Hero folds, BB folds

Final Pot: $9.25
UTG+1 wins $8.80
(Rake: $0.45)

Here's an easy fold:
Full Tilt Poker $0.25/$0.50 No Limit Hold'em - 9 players
The Official DeucesCracked.com Hand History Converter

BTN: $22.00
SB: $35.45
BB: $60.20
UTG: $103.95
UTG+1: $43.75
UTG+2: $64.55
Hero (MP1): $82.15
MP2: $31.20
CO: $20.85

Pre Flop: ($0.75) Hero is MP1 with 6c 7c
8 folds
Terrible position, coupled with no limpers.

Final Pot: $0.50
BB wins $0.50

A limped pot where I flop very good:
Full Tilt Poker $0.25/$0.50 No Limit Hold'em - 9 players
The Official DeucesCracked.com Hand History Converter

BTN: $17.20
SB: $20.85
BB: $49.00
UTG: $31.20
UTG+1: $81.85
UTG+2: $19.50
MP1: $32.75
Hero (MP2): $116.55
CO: $53.45

Pre Flop: ($0.75) Hero is MP2 with Td 9d
1 fold, UTG+1 calls $0.50, 2 folds, Hero calls $0.50, 3 folds, BB checks

Flop: ($1.75) 8s Qd 6d (3 players)
BB checks, UTG+1 bets $0.50, Hero raises to $2.50, BB folds, UTG+1 folds
I flopped a diamond flush draw + double belly buster straight draw (Jack or 7).

Final Pot: $2.75
Hero wins $2.65
(Rake: $0.10)

Finally, I leave you with a terrible play by my opponent.  Can you spot the errors?
Full Tilt Poker $0.25/$0.50 No Limit Hold'em - 9 players
The Official DeucesCracked.com Hand History Converter

CO: $49.20
BTN: $26.50
Hero (SB): $106.55
BB: $30.25
UTG: $15.00 - He's an 18/7, BTW; this is not a play I expect from that type of player.
UTG+1: $77.95
UTG+2: $92.40
MP1: $20.30
MP2: $330.05

Pre Flop: ($0.75) Hero is SB with Th Ts
UTG raises to $1.75, 6 folds, Hero raises to $5.50, 1 fold, UTG calls $3.75
I like the raise here, but with $13.25 behind, but when you make the call of my 3-bet, you're essentially committed, no matter the flop.  Not to mention that you only have $15 total to win if you hit your flop perfectly.  This is a CLEAR violation of the 10x rule!

Flop: ($11.50) Js 7h 6c (2 players)
Hero bets $9.50, UTG calls $9.50 all in
You're calling a 3-bet pre-flop and a flop shove (what other move can I make here; $11.50 in the pot and my opponent has $9.50 behind.  It's either all or nothing at this point.

Turn: ($30.50) 4c (2 players - 1 is all in)

River: ($30.50) Kc (2 players - 1 is all in)

Final Pot: $30.50
Hero shows Th Ts (a pair of Tens)
UTG shows 8s 6s (a pair of Sixes) - This is a prime example of how NOT to play SCs!!!
Hero wins $29.00
(Rake: $1.50)

Good luck playing your suited connectors.  I hope these series of posts help you.

If you have a good Back to Basics topic that you would like covered, or would like to write a Back to Basics entry yourself, please leave a comment or send me an email (contact information on the right side of this blog).

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