KKing David

Ruminations on poker

Archive for the month “October, 2017”

David and Goliath

“The excessive use of force creates legitimacy problems, and force without legitimacy leads to defiance, not submission.”

This quote comes from Malcolm Gladwell’s wonderful book, David and Goliath, which I just finished re-reading.  I posted it on Facebook; one of my friends commented “poker betting philosophy.”

Upon reading the quote again, yes, it definitely applies to poker.

The Facebook post was a follow-on to an earlier post of another quote from David and Goliath:  “When people in authority want the rest of us to behave, it matters – first and foremost – how they behave.”

Reading this “principle of legitimacy” on a fall Sunday afternoon brought to mind the ongoing civil disobedience of NFL players kneeling during the national anthem as a symbolic protest against racial injustice perpetrated by some law enforcement organizations.  It’s broader now, but that’s how it started.  POTUS and some team owners have attempted to force these football players to behave (i.e., stand during the anthem), even while their own behavior fails to create the necessary legitimacy.  Consequently (and predictably if you follow Gladwell’s reasoning), the number of NFL players protesting has increased.

Gladwell raises this concept in chapters about the decades-long conflict between Protestants and Catholics in Northern Ireland, law enforcement strategies in the Brownsville neighborhood of Brooklyn, pockets of French resistance to the Nazis during WWII, and the U.S. civil rights movement.

To be clear, poker is by far the least of our worries when considering the relationship between force and legitimacy.

In 1969, two RAND Corporation economists wrote a report on dealing with insurgencies.  It was based on a fundamental, yet fatally flawed assumption, “that the population, as individuals or group, behaves ‘rationally,’ that it calculates costs and benefits to the extent that they can be related to different courses of action, and makes choices accordingly… Consequently, influencing popular behavior requires neither sympathy nor mysticism, but rather a better understanding of what costs and benefits the individual or group is concerned with, and how they are calculated.”

Sure, just treat disobedient Irish Catholics, Brownsville hoodlums, French villagers, civil rights activists and pro football players like a math problem.  Make the cost of their insurgent behavior greater than the benefits, via use of excessive force, and they will stop.  Doesn’t everybody pencil out a few economic cost-benefit equations before starting a riot?

Uh… no.

There is a lot to learn here.

Back to poker.  Next time you are bluffing, ask yourself if you have established the legitimacy that leads to submission rather than defiance.  If your bluffs aren’t working, it might be more than just a math problem.

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Online Analysis, Part 1 – pre-flop 3-bets

I play a fair amount of online poker on the Ignition platform, almost entirely cash games.  So far this year I’ve been a winner, but not at a rate I’m particularly proud of.  Unless I compare it to last year when I won just a very tiny bit, or the year before which was worse.

One of the benefits of Ignition’s poker site is that after a few days have passed, the hand history details show all of the hole cards for all of the other players.  We can study hands that did not go to showdown and see exactly what each player was doing.  I can only see histories of the hands I played and on this site all players are anonymous – no avatars, no screen names, no other identifiers.  Still, this hole card visibility can be used to build a profile of the “typical” player (absent any specific observations) and to spot leaks in my own game (of which there are plenty).

So I’ve embarked on a study project, not using Poker Tracker or similar software for meta-data analysis, but scrolling through hand-by-hand, picking out hands with certain attributes or very large pots, and entering some of the data into a spreadsheet for further review when the sample size is larger.

It’s tedious, laborious work.  There are additional insights to be gained from the meta-data and maybe I’ll go there eventually.  For now, this is good enough.

At the top of my list of situations to analyze is pre-flop 3-bets.  When one player raises, then another re-raises (this is the 3rd bet, after the posting of the big blind and the initial raise), can we rely on any general conclusions about the strength of the re-raiser’s hand?  Do those ranges change – wider or narrower – as we move up or down in stakes?

The sample is still very small, but so far 3-bets have included:

AA – 11x     KK – 7x     QQ – 3x

88 – 1x      AK – 6x     AQ – 1x

AJ – 3x      Other/junk – 5x

I’ve seen some hands as strong as AK or QQ/JJ calling instead of 3-betting.  And the 3-bets made from the blinds after a cutoff or button opening raise, that look like a blind-steal vs. re-steal situations, are still dominated by the strongest hands.  The basic range here is QQ+/AK, which accounts for 27 instances of 3-bets in this sample (73%), with only 10 instances of a 3-bet outside of that range (27%).

Tentative conclusion:  respect the 3-bets.  It’s OK to call the smaller sized 3-bets with low-to-medium pocket pairs when the math is right for set-mining (especially in position).  Otherwise, as Idina Menzel sang in the movie Frozen, “Let It Go!”

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I can even fold hands as strong as JJ or QQ to the larger sized 3-bets, without bothering to set-mine.  Does this seem too nitty?  Let’s look at the math.  Using Poker Cruncher, I’ll set Player 1’s (my) hand as QQ, and give Player 2 (villain) a strong range of which 72% is QQ+/AK, to approximate the sample above.  Against this range, it’s a coin flip.  That’s gambling, and I have better things to do, unless I have a very player-specific read to go on.

        

 

Change my hand to JJ vs. a similar range that is 72% QQ+/AK, and my equity drops below 41%.  That’s worse than gambling at a casino, and I have much better things to do.

As the opening raiser from the cutoff or button against 3-bet by the small or big blind, I can let these go as well.  My initial investment will be small, and the data so far doesn’t suggest a high enough frequency of re-steal attempts to warrant fighting back.

It would be a mistake, however, to assume live players’ 3-bet follow the same pattern of distribution as online players.  This might be the case… or not.  Gathering enough data on live players would be vastly more difficult, as most of these hands don’t go to showdown nor get voluntarily shown on hands that end prior to a showdown.

In later posts, we’ll look at the ranges of hands involved in other common situations…

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Thanks for all the Respect

NOTE:  This entry was originally posted on a different site on September 7, 2016 and has been slightly edited prior to re-posting here.

“Thanks for all the respect!”

That was me being sarcastic, at a cash game after raising to 7 big blinds and getting four callers.  It was getting late, and I had told our host about eight minutes earlier that I’d be leaving in 10 minutes.  We were playing 6-handed, as one of our original eight players left early, and another left after going bust, driving to the nearest ATM for more cash, and busting again.

Nobody raised in front of me, and with Ad Kd in the small blind, I’m going to make it expensive for anyone who wants to see this flop.  I’ve been pretty quiet most of the night, but still nearly doubled my starting stack of 100 BBs thanks to one big hand where my KK doubled up through QQ.  It might look like I’m protecting my chips and running out the clock… until I raised to 7 BBs.

I wanted to thin the field, and going to the flop 5-handed from the worst possible position at the table is sub-optimal.  (First-world problems, I know that, but I digress…)

Flashback:  Early last year I was playing a cash game at the Aria.  It seemed like I had folded every hand for at least an hour.  Then I look down at TT and put out a nice raise.  Five other players call, like they are clueless that the nittiest player in all of Las Vegas has just raised.  TT is a fine starting hand, but with this many callers many more things can go wrong than right.  In my best, driest, most sarcastic voice, I commented “thanks for all the respect.”

Anyway, the flop was T42 rainbow, giving me top set.  Lack of respect instantly converts to generosity.  I’m feeling true love for each and every villain.  Everybody checks and a J on the turn improves another player’s AJ hand. There is a bet, call, raise, call, re-raise and shove.  Three of us are all-in, with my set of tens holding up over a set of fours (he thought he was trapping me!) and pair of jacks / ace kicker.  It was one of those wonderful moments when you can hear heavenly choir.

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And memorable for the phantasmagoric emotional shift from finally seeing a decent hand, to the sarcasm, to hating five callers to loving a monster flop to raking in all those chips.

[FLASHBACK ENDS]

Lightning strikes again.  The dealer turns over T32, all diamonds.  I have flopped the nut flush, the pot is already a decent size, and there are four other players.  Hopefully, somebody else also connected with this flop.

I make a smallish opening bet, about 1/3 of the pot.  The next three players fold, but the button (for purposes of this blog entry, I’ll refer to him as “Jason”) calls.  Jason is a pretty tight player who doesn’t make many crazy moves, but he can get stubborn at times when he just doesn’t believe the aggressor has it.  There is no reason for him to believe that I flopped a flush after my pre-flop raise.  The turn is Kh, I bet and he calls again.  The river is 5c.  Perfect… no more diamonds, no pair on the board, absolute nuts for me.  Jason hasn’t made any aggressive actions during this hand, so I don’t think an all-in bet will get called.  I bet a again, but still less than 1/2 of the pot.

Jason starts counting out chips as if he is going to raise.  Or perhaps just seeing how much he would have left over if he called my bet and lost.  Or perhaps just fiddling to kill time and see if I give off any tells.  “I’m all-in!” he announces, and slides his entire stack towards the center.  I feel ever-so-very-very-teeny-tiny-slightly bad for him.

I call and quickly turn over my cards.  He turns over Qd 8d, for a weaker flopped flush.  Poor guy, he was drawing dead on the flop and had no idea, although he handles this cooler very graciously.

[SCROLL UP AND LISTEN TO HEAVENLY MUSIC AGAIN]

Although it feels a bit like a hit-and-run, I had already told our host that I was leaving in 10 minutes, and now it is 14 minutes later.  Cash me out please…

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Variance is a Bitch

In poker, variance is a bitch.

But she’s our bitch, so try not to be mad at her.

In a cash game yesterday, I find myself in a 3-way all-in pot after the turn card.  There was $390 in the pot after the flop betting and the turn card gave me a flush draw along with an open-ended straight draw.  The action checked around to me and I shoved my last $260, hoping everyone would fold and knowing I had a lot of backup outs.  One player called with two pair, another re-shoved with the bottom end of a straight and the first player called again.  From a strictly EV (expected value) standpoint, this was a profitable play with two callers, as my final bet was 22.2% of the total pot and I have 27.4% equity in the hand.  From a math standpoint, my EV is $321 (final pot size of $1,160 x 27.4%).  The river misses, and my actual result is zero.

Later in the same game, another all-in ensues, this time heads up on the flop.  The pot is around $1,100 again and this time I’m ahead with top two pair, and the villain big combo draw.  He hits one of them right away on the turn and wins the pot.  This time my EV is $684 (final pot size of $1,100 x 62.2%).  My actual result, again, is zero.

On these two hands combined, my EV was just over $1,000.  Instead, nyet!  I buy-in again, and before too long my pocket aces are cracked by a set of sevens (by the same guy who flopped a set of eights v. my pocket jacks much earlier).  Time to go home.

Such is the nature of variance.  The actual result is always an all-or-nothing proposition.  The expected result is the average that should occur if the same scenario were to be replayed a million times.  Being a favorite doesn’t guarantee being a winner.

Over the long haul, if you are on the right side of the 60/40’s and 70/30’s more often than not, variance will be your friend, despite tormenting you often along the way.

In the short run, this was simply a day of being on the wrong side once (insofar as very large pots is concerned) and being on the right side once, but missing both sides.  Yes, the coin toss can come up heads twice in a row even though I always guess tails.

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MGM Hates Poker Players – This is How We Know

NOTE:  This entry was originally posted on a different site on March 13, 2017 and has been slightly edited prior to re-posting here.

I hate being a hater, but MGM National Harbor’s poker comps system hates me back.

Last week I played poker nearly every day at this new poker room.  Overall, it is excellent – spacious, comfortable, lots of action, competent staff and worthy of an overall highly favorable review.  I’ll definitely go there again.

At a comp rate of $2/hour, I earned some decent meal money.  Every so often, I get hungry.  When I get hungry, I want to eat.  The casino has an excellent variety of food options, all at resort prices.  To offset MGM’s resort prices, I want to use the comp dollars as much as possible.

Seems simple, right?

If you order food at the table, to eat while still playing poker, it goes like this… Realizing you are hungry, you ask a server for a food menu.  The server explains that there are separate food servers, and the beverage servers do not handle food.  Look for a server with a purple shirt and black vest.  Not seeing any, you ask the dealer if they can help locate a server.  No problem says the dealer, and he pressed a button on his control panel beneath the letter F (representing a special 4-letter “F-word,” of course I’m talking about Food) and a light goes on.  That should do it.  About 20 or 30 minutes later, a food server appears, looking sharp in a purple shirt and black vest.  The food menu is limited to a few options from each of the places in a food court, which includes a seafood vendor, fried chicken and donuts vendor, pizza, mexican, sushi, deli, Asian, ice cream shop, and Shake Shack.  Except not the Shake Shack or the ice cream shop.  And not everything at the other places, just 3 or 4 options from each.

I decide to go with the spring rolls from the Asian place.  I give the food server my mLife card (MGM’s customer rewards program is called mLife) and show my ID, and all is good.  40 minutes later, the server returns and asks me if I ordered spring rolls.  “Why yes I most certainly did, and I’m really looking forward to them.”  “Sorry, they’re out of them.  Would you like to see the menu again?”  Hungry turns into Hangry.  I go for the chicken tenders. Another 40 minutes later it is now nearly 2 full hours after the first hunger pains, my chicken tenders and fries arrive and I don’t really care how they taste.  My comps paid for it, and the server returns my mLife card.

For dining at the table, start the process at least an hour before you will be hungry.

But maybe you don’t want to eat at the table.  Maybe you want something that isn’t on the limited table service menu, or want to dine at one of the fancier restaurants and not the food court or you really like the Shake Shack.

In that case, you have to go to the poker check-in desk and ask the staff to transfer a portion of your comps balance, which is tracked on your mLife card, to a different category or bin or account which is also tracked on the same mLife card, in order to be able to use it at the food court or any of the fancy restaurants.  With a line of people growing behind you, the conversation goes like this:

Poker staff:  Where you are going to eat?

Me:  I’m not sure… I’m going to walk down to the food court and see what looks good.

Poker staff:  OK, that’s called The District.  I can do that, as long as you aren’t going to the Shake Shack.  If you plan to eat at the Shake Shack, I have to do it one way, because Shake Shack isn’t owned by the casino.  For the rest of The District, I have to do it another way.

Me:  Are you shitting me?

Poker staff:  No.  That’s really how we have to do it.

Me:  Out of curiosity, what if I wanted to eat at one of the fancy restaurants, like Jose Andres’ place?

Poker staff:  Then I have to specify which restaurant, just let me know and I can handle it.

Me:  I hear the Shake Shack is really good, but I haven’t been there yet and haven’t even looked at their menu.  I guess I’ll pass on that for today and eat somewhere else in the food court.

Poker staff:  How many dollars do you want transferred?

Me:  I don’t know… I’m still not sure what I’m going to get.  Does it matter?  If you transfer extra, the unused balance will be available to use later, right?

Poker staff:  Wrong.  Let’s say I transfer $20.  This is only good for one transaction.  If you only use $15, the $5 unused portion of your comps is forfeited.

Me:  Are you shitting me?

Poker staff:  No.  If you know what you are going to get and how much it will cost, you can transfer the exact amount.  Or you can guess and probably want to guess on the low side so you don’t forfeit any of your comps.

Me:  [glance over my shoulder, line is getting longer]  Uh… I guess transfer ten bucks and I’ll figure it out.  The food court is a couple hundred yards away, and I don’t want to walk down there just to plan my meal so I can walk back over here and wait in line to do this again so I can walk back over there to eat.

Poker staff:  You got it, my man.  Give me just a few seconds.  [He swipes my mLife card through a card reader, enters about the same number of keystrokes as a rental car clerk setting up a new reservation, then swipes my mLife card through a different card reader, a few more keystrokes, a fake smile and off I go.]

It’s clear that the poker room management didn’t design this system themselves.  I feel sorry for them.  Not every customer is as delightful to deal with as me.  The line moves slowly, including mostly players who just want to sign up to get on a waiting list.

The next day, while walking to a restroom, I pass by a glass door with a sign that says Casino Host & Credit.  On the way back, I decide to go inside and see if that would be the proper place to provide a little customer feedback.  There is a management looking guy standing by the door, wearing a suit and MGM nametag.  He looks very official.  For purposes of this blog entry, I’ll refer to him as “Vlad.”

I ask Vlad if the casino is interested in hearing feedback from customers about their experience there.  Yes, he says.  I ask where I should go to provide some, and Vlad says “you can talk to me.”  We are not inside the office, but outside the office near slot machines and other gaming.  With head-thumping music blaring.  Vlad does not invite me into a quieter place to talk.

Trying to explain that I feel sorry for the poker room staff who have to deal with this cumbersome system and resulting hangry customers, and that we’re all frustrated by the lack of integration of the poker comps system with the rest of the casino, I lay out my case.  I probably look highly agitated.  Partly because there is a very high base noise level and I practically have to shout just to be heard.  Partly because I am highly agitated.

When I reach a pause, Vlad responds.  First he explains that he has no involvement in running the poker room.  He knows their comp system is separate, but doesn’t know how it works, the rate at which comps are earned or any other details whatsoever.  But it’s that way because the poker room isn’t profitable and doesn’t make any money for the casino.  Then he explains that if it were up to him – and Vlad wants me to know that he’s worked in the casino industry in Atlantic City for over 25 years – there would be no poker room at all.  In Vlad’s opinion, poker is a waste of valuable casino space that could make a lot of money if it was used differently.

Translation:  Dear customer, if it was up to me, you would not be our customer!  So it is OK with me that the part of our business that you patronize is systematically pissing you off.

We actually chat for about 20 more minutes.  Vlad isn’t unpleasant; he just knows where he stands and isn’t shy about it.

My points goes like this:

  • If it was up to Vlad, there would be no poker room, right?  [Vlad:  right.]
  • But there is a poker room, so that means somebody other than you decided there should be one, right?  [Vlad:  right.]
  • And that makes the poker players in that poker room a subset of all of the customers of this glorious MGM National Harbor Resort & Casino, right?  [Vlad:  right.]
  • The poker room provides comp credits to its players, right?  Whatever the formula is, it is a non-zero amount.  [Vlad:  right.]
  • So if you are going to have a poker room and give the players comp dollars, why – when spending $1.2 billion dollars to build this place – would you design a comps system that systematically frustrates the poker room staff as it also systematically pisses off that subset of your customers?  [Vlad:  uh…]

Vlad gives me a long explanation of comps, how some comp dollars are automatically generated as a by-product of each game based on the amount of time and stakes played, and other comps are awarded at management discretion so he can give some extra meal money to some poor schmuck who loses his entire wad really fast.  All of which applies only to the non-poker parts of the casino.

As for the poker room, Vlad maintains that he doesn’t have anything to do with it, doesn’t know how it operates, but a different system is justified based on the bad economics of poker rooms for casinos.

The same approach to using poker room comps is used at all MGM properties.  At the Aria or Bellagio, however, you have to go to a different desk and not the player check-in desk, and get a paper voucher for the amount of comp dollars you want to use (or lose).  And poker comps earned at one MGM property can only be used at that property – you cannot use Aria poker comps to buy food at Bellagio or MGM Grand and vice versa.  It is equally maddening for the players, although not quite as bad as forcing the check-in desk to handle the comps too.

Given MGM’s otherwise strong commitment to poker, with large and active poker rooms in many of their properties (Bellagio and Aria are among the top poker rooms in Las Vegas; MGM National Harbor is now one of the largest poker rooms on the east coast), it is beyond my comprehension that they don’t integrate the poker comps with the rest of the gaming areas.  Maryland Live! does.  Caesar’s/Harrah’s/Horseshoe does.  Other casinos do.

Reader comments welcome below…

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Facing a Shove on the River With Just One Pair

NOTE:  This entry was originally posted on a different site on January 3, 2017 and has been slightly edited prior to re-posting here.

My previous blog entry explored turning a missed draw into a bluff, after my opponent checked on both the turn and the river, soliciting your comments on the villain’s range.

Last night another, bigger decision presented itself via an interesting puzzle. Let’s unpack the puzzle pieces, assemble them, and see if we can find the missing pieces…

This was at a private, house game (no limit hold’em) with blinds of $1/2. I’ve been having a rough night so far. Shortly after joining the table, I lost my entire stack when I turned a full house, only to lose to a larger full house on the river. I had TT, and the board ran out Qs Qh 6h – Th – Kh. Everybody checked on the flop, then my gin card arrived on the turn, also completing any flush draws. Unfortunately, the other player had KQ and got there on the river. Ouch!

I bought another $300 in chips, and continued trending down. Less than a full orbit prior to the Big Decision, I caught my first big break of the night, with AA > KK on a pre-flop all-in with the same player who had cracked my full house. She had frittered away most of the stack from that hand and had slightly less than $150 remaining, which I was glad to take.

Now I have about $395 in front of me, and look down at King-Queen offsuit. There is one limper in front of me and I raise to $12. Four players call, and I quickly decide not to make a continuation bet unless I connect with the flop.  Let’s protect these newly begotten chips.

Flop ($62): Kd 4d 3c

This is a very good flop for me.  Not huge, but my top pair / 2nd kicker should be the best hand, and I can get value from flush draws, straight draws and kings with weaker kickers.  Giving four other players a free card or ceding the betting initiative would be a mistake.  It is checked to me and I bet $35. While not much more than one-half pot, this shouldn’t look like a run-of-the-mill continuation bet with air as there are four other live players.

The player to my immediate left calls, and everyone else folds. For purposes of this blog, I’ll call him “Matt.” While I’m a long-time regular here, Matt is a newbie.  Solving the puzzle is going to require us to know as much as possible about Matt.  What do we know so far?

Matt is a young white guy, looks about 25 (but might be closer to 30). He has straggly hair that nearly reaches his shoulders, a beard, and has been wearing headphones. Before this cash game started, we both played in a small-stakes tournament here, and learned that he is a roving contractor, currently in the area working on the installation of Google fiber.  He’s polite and pleasant when he does engage in any conversation, which isn’t very much.

Matt looks and plays like a stereotypical loose-aggressive (“LAG”) poker player. Early in the tournament, he built up a formidable stack, showing AA, a nut flush, flopping a set of QQQs, etc. I made a mental note then not to confuse his LAGGY appearance and playing style with the fact that he kept showing down big hands. A bit later, he lost a large chunk of his chips in a 3-way all-in where he had AK.

I had joined the cash game about an hour or so after it started. The only open seat was on Matt’s immediate right. At the time, he had over $550 in front of him (the max buy-in is $300), and I anticipated the difficulty of playing with a deep-stacked LAG on my left.  Oy!  He can make my session miserable.

Sure enough, that’s what happened. Prior to my full house under full house debacle, Matt picked off my river bluff, after I had floated on the flop with a gutshot straight draw (that missed), then he checked behind on the turn, indicating weakness.  He has been raising and 3-betting frequently, including an OOP 3-bet as weak as A6o and several other hands that indicated a wide raising range, especially in position. He straddled regularly on the button (always for more than the minimum), demonstrated positional awareness, and attacked limpers often. His play definitely matches his stereotype as a LAG.

And he’s been hit by the deck!  Matt built up his stack to approximately $1,100, with multiple full houses, flushes, flopped sets, and bluff-catcher calls.  Other players commented on how hot he is running, although with his headphones on we don’t know if he heard any of these remarks.

Prior to this hand, however, he has started bleeding away much of his winnings. Some of his lighter, bluff-catching calls have been wrong, and he’s been caught bluffing / bullying several times, including several river bluffs. He also lost a large pot with flush < full house.  He still had nearly $650 at the beginning of this hand.

Back to the hand. After he called my flop bet, Matt and I are heads up, and he has position on me. The pot is getting bloated, with $132 in it.

Turn ($132): 4h. Now the board is Kd 4d 3c – 4h.

Thinking I very likely have the best hand, I bet $65.  I can still get value from flush or straight draws and perhaps a few other holdings.  Matt calls again.

What do you think Matt has here? A diamond flush draw is possible. A straight draw with 65 is possible. At the intersection is a combo draw with 6d 5d, although I think such an aggressive player would raise with that on the flop to apply maximum pressure with so many outs as a back-up. He could have a King and we are in a kicker battle. He could have a four and just made trips, or pocket 33s and flopped another set. But I think he probably would have raised on the flop with pocket 33s to protect against flush draws, as none of the other three players had folded yet when he called my flop bet. I also think he probably would raise now on this turn with any 4x (like A4s), to get value from any AA/AK/KQ or draw that I might have. Even as loose as he is, I don’t think he calls $12 pre-flop with A4o or K4.

River ($262): Th.  Now the board is Kd 4d 3c – 4h – Th

This should be a good card for me, as it misses all potential draws. The only hands that it helps are KT and TT.  I don’t think he has TT – his 3-betting range pre-flop is wide enough to include TT (but not necessarily 100% of the time), and even if he flatted with TT and called again on the flop, he probably would surrender on the turn.

If he has a missed draw, I’m not going to get any more value. In fact, the only hand that can reasonably pay me off on another bet is KJ.  So I target that and bet $85, which is a little less than one-third of the pot and might get a crying call from KJ.

With little hesitation, Matt announces “I’m all in!” and slides his remaining chips out.  The rhythm and tone with which he does this seems very strong.  This is hard to describe, but he seemed calm and confident.  The dealer moves my $85 and a matching portion of his stack to the pot, and there is nearly $450 more on top of that.  I have just under $200 remaining so I’ll have to do any math based on my stack, not his.

I have a collection of short essays on poker strategy from the late Bill “Ain’t No Limit” Hubbard, who was a highly regarded professional poker coach for many years specializing in live cash games. Over the holidays, I’ve been reviewing some of these essays and several concepts now come into play.

In his foundational essay, Bill says to practice SBRTA when faced with a big decision. Stop. Breathe. Relax. Think. Act.  I’m having a little trouble breathing at the moment, considering I’m on my second buy-in of the night and it would really hurt to be down 300 BBs.  How in the **** am I supposed to relax when the realization of what might be happening here almost made me shit my pants?  [Inhaling very slowly…]

In another essay, Bill drives home the strategy of playing small hands for small pots, medium-strength hands for medium-sized pots and big hands for big pots.  My hand is a medium-strength hand.  I have two pair, one of which is the pair of 44’s on the board. So my hand is really akin to top pair with 2nd best kicker (“TP2K”). By the river, this is definitely NOT a big hand, but often good enough to win. Bill says: “One of the most notorious leaks among live poker players is that they break the basic rule of playing a medium pot only with a medium sized hand. I think this is due to most players feeling that they must protect their medium strength hand and thus raise to protect the hand plus find out information.”  Was I doing that here? I thought I was betting for value, to get called by worse hands and draws (which some might call “protecting” against draws), but not really for information.

In other essays, Bill describes the central question for successful no limit Texas hold’em players: “What is the villain’s range and what will he do with this range?” Or “what does he have and how will he play it?” I’ll come back to this later.

In another essay, entitled “The Fold Button,” Bill notes that the most common mistake among live players is that they call when they should fold. Making big, successful hero calls is exciting, but far out-weighed by calling mistakes. Sometimes, we know we are beat, but call nevertheless to get to what he refers to as the “funeral for the hand,” a form of certainty and closure.  Calling forces the other player to show their cards, so now we know and can have closure (i.e., the funeral), albeit at a very high price.   This is closely related to the medium-strength hand –> medium-sized pot rule.  Before calling a large river bet, Bill advises us to ask: Is the villain capable of bluffing (in Matt’s case, yes)? Have we actually seen him bluff (yes)? Should the villain expect us to call this size bet? This is harder to answer. After bringing in my $85 and his raise (i.e., up to my stack size), there is approximately $630 in the pot and it will cost my last ~$200 to call. I’m getting 3.15-to-1 odds.  With those odds, if he is bluffing more than 24% of the time, calling is correct in a strictly mathematical sense.  If you feel compelled to call, what percentage of the time is it due to real factors you have considered vs. the overwhelming desire to call and simply see what the villain is betting with (this is really tough, so let’s consider the real factors)?

In another essay, Bill describes the principle of Occam’s Razor. Named after William of Ockham, a 14th Century British mathematician and logician, this principle states that among competing hypotheses, the one with the fewest assumptions should be selected. More simply, “If it walks like a duck, quacks like a duck and looks like a duck, then it is most likely a duck!” When we combine this with the medium hand / medium pot rule, Matt’s all-in bet fundamentally says “I like my hand more than you like yours.” Occam’s Razor instructs us that Matt has a hand worthy of playing for an $800+ pot, and I’m toast.

But still, I’m not convinced. Nor am I unconvinced.

First of all, what am I beating? In reality, the ONLY thing I am beating here is a bluff. There is no possible hand that he can be raising all-in for value here, where he is hoping I will call, thinking he has me beat, but he’s actually behind.  To do so would violate the medium hand –> medium pot rule even worse than I did.

There is a finite range of hands that beat mine, so we can explore each of them to figure out if Matt has it.  This is a reverse-engineering approach to Bill Hubbard’s central question of what does he have and how does he play it?  I went through this earlier in my turn betting analysis, but it bears repeating now.

  • Could he have Pocket AAs or KKs…?  Nope! He would have re-raised pre-flop.  Since he didn’t, I can eliminate AA and KK from his range.
  • AK… nope!  Again, Matt would have re-raised pre-flop. I’ve seen him 3-bet much lighter than that and use his position to put me in difficult spots pre-flop with hands weaker than AK.  Besides, if he had AK and planned to raise, he wouldn’t wait until the river.
  • KT… maybe, but I don’t think so. He might call me pre-flop with this, especially if suited (which would leave only 2 combos), but I don’t think he would shove all of his chips in on this river.  The way I’ve played this hand, betting every street, he has to consider AA as part of my range.  With the pair of 44s on the board, it would be a mistake for him to raise instead of just calling again.  But this combo worries me more than the others.
  • TT… nope!  As noted earlier, I think he 3-bets pre-flop with this hand at least some of the time, and also think he releases this by the turn when I show continued strength. My betting looks a lot like I have AA or AK here, especially when I C-bet into four opponents on the flop.
  • 4x… nope!  He might call $12 pre-flop with A4s or 54s, and call the flop C-bet too. But if that were the case, he would raise on the turn after improving to trips, to get value from flush draws, as well as the fact that I might have trouble letting go of AA or AK against a raise as it would look somewhat bluffy based on the board pairing and his image (if he has that level of self-awareness). I don’t think he calls $12 pre-flop with K4, although K4s is a very slight possibility. That would have flopped two pair, which I think he would raise on the flop, again to get value from flush draws.
  • 33… nope!  Again, I think he raises on the flop for the reasons mentioned. Keep in mind there were five players in this hand, it checked to me on the flop and I bet $35. He is on my immediate left, so three other players were still live when he called my C-bet.  He shouldn’t just call there with a flopped bottom set.  If he did and then improved to a full house on the turn, just calling my turn bet and waiting for the river to shove – perhaps hoping to see another diamond in case I’m the one chasing a flush – makes perfect sense. I don’t think he has 33, but this also worries me a little bit.

So here we are.  Out of six groups of hands that beat me, four are a definite “nope” and the other two (KT and 33) are probably “nope” too.  For better or worse, my analytical thinking concludes that with every possible hand that beats me, Matt would have done something different with that hand somewhere along the way. All that remains are bluffs, contradicted by Occam’s Razor and the medium-hand –> medium-pot rule that is screaming inside my head that I’m about to make a big calling mistake.  Matt’s all-in bet looks like a duck, which rhymes with ‘I’m about to get fucked!’

What would you do?  Taking a deep breath, I finally called and Matt tabled Kh 6h.  My hand was good!  He may have thought he was ahead with top pair and a weak kicker on the flop, but by the river realized he need to turn it into a bluff to take this pot.

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Should I Turn This Into a Bluff?

NOTE:  This entry was originally posted on a different site on December 30, 2016 and has been slightly edited prior to re-posting here.

A couple nights ago I was playing at a private house game, when this hand came up.

In a middle position, I get Td 9d, nice-looking suited connectors.  A player in front of me had straddled for double the big blind.  I call, hoping to see a relatively cheap flop.

There is one other caller, plus the Big Blind calls, and the straddler checks.  So far, so good.

The flop is 8d 7h 5d.  I have the top of an open-ended straight draw, a flush draw, and two over cards.  While the absolute strength of my hand at this point is only Ten-high, it has huge drawing power.  Even against a hand like 9-6, which would have flopped the nuts, I would have 52% equity in the pot.  That’s right, a favorite against the nuts.

On the other hand, against Ad 7d, which would give someone a nut flush draw and middle pair, my equity drops to 35%.  Still respectable…  Against Ad 6d, adding a straight draw to the NFD, my equity drops even further to 27.5%, primarily because a non-diamond 9 no longer improves my hand to a winner.  Against 88 flopping top set, my equity is 40%.

Although it is possible that one of my opponents has a hand as strong as 96, Ad7d, Ad6d, or 88, these are very specific combinations.  My equity against these hands, blended in with my equity against all of the worse options I might be facing, makes this a spot where I’m perfectly happy to get it all in right now.  At this game, the house allows the players to “run it” twice or three times by mutual agreement, which would be likely given my knowledge of the other players.  With that backup plan, I can apply maximum pressure.

The checks to the straddler.  For purposes of this blog I’ll call him “John.”  John is generally a somewhat loose, passive player.  For example, when this game started there were only four players.  John bought in for only 50 big blinds, then immediately posted a straddle on the button.  This effectively reduces his stack to 25x the straddle.  It’s like he has heard that straddling on the button is good, but doesn’t really understand why nor understand the value of having a larger stack-to-pot (“SPR”) ratio.  He rarely raises when straddling and no one else raises.  On another hand with still only four players, he called a pre-flop raise with QQ but did not re-raise.

Back to our hand.  With 8 or 9 big blinds in the pot, John bets 7 BBs.  He typically doesn’t lead out like this with a drawing hand, so most of his range is going to be one pair.  I decide to attack, and raise to 25 BBs.  That should get his attention.  At the start of this hand, I had about 125 BBs in my stack.  John appears to have about the same.

The next player folds, then the big blind ponders for a moment and looks very much like he wants to raise.  For purposes of this blog, I’ll call him “Rick.”  Instead of raising, Rick calls.  Rick is a much more aggressive player than John; in fact his bluffing frequency is higher than anyone else at the table.  He also respects my game (I’m classically TAG) and knows I’ll continue aggression when I have a strong hand, so his call here looks super strong to me.

Back to our hand again.  Rick’s call both surprises and scares me.  Did he flop a straight and now he wants to see if he can keep John in the hand by just calling?  Does he have a higher flush draw, counterfeiting many of my outs?  Is he setting a trap for me to walk right into?  When a player as aggressive as Rick check-calls a post-flop raise, knowing the original better (i.e., John) has the option of re-raising, this suggests that he likes his hand.  A lot.

John folds.  Now Rick and I are heads up.

The turn is Kh, putting 2 hearts on the board.  Having missed all of my outs, my equity is essentially cut in half.  Rick checks.

The pot is bloated now, with about 66 BBs, and I have ten-high.  If I want to try to get him to fold a somewhat strong hand, like 2-pair, it’s going to take quite a large bet and leave me pot-committed if he check-raises all-in.  I’m less enthusiastic now, with only one card to come.  As a general rule, it is usually a good idea to check back in position when you don’t have a clear plan for handling a check-raise.  I don’t like bet-folding here, nor do I like bet-calling.  He’s offered me a free card, so I decide to take it and check.

The river card is 3c, missing all of my outs again.  I still have just ten-high.

Rick checks again.  His faces looks slightly pained, like perhaps he has a bigger flush draw than mine and missed.  Or… he’s giving off a reverse tell – which I consider him capable of doing – having read my turn check as indicative of my range including lots of flush draws and figuring the best way for him to get value from me is by bluff-catching.

With two flush draws and a straight draw after the turn – 8d 7h 5d – Kh – surely I would bet for value again if I had a 2-pair or better hand.  Doesn’t my turn check look more like I’m on a draw (which would be true) and taking the free card?

I’m having trouble narrowing Rick’s range here.  What do you think it is?

One axiom of poker says that in order to bluff, my range should not be too polarized (i.e., only very strong hands or bluffs).  What does my range look like here?  Should I turn my Ten-high nothing-at-all busted combo-draw hand into a bluff here?  If so, how much should I bet?

Please leave replies in comments, and check back in a few days for the spoiler.

The Butterfly Effect

The Butterfly Effect, a phrase coined by American mathematician Edward Lorenz (an early pioneer in the field of chaos theory) is a concept that states that “small causes can have larger effects.”

From Wikipedia:  “The phrase refers to the idea that a butterfly’s wings might create tiny changes in the atmosphere that may ultimately alter the path of a tornado or delay, accelerate or even prevent the occurrence of a tornado in another location. The butterfly does not power or directly create the tornado, but the term is intended to imply that the flap of the butterfly’s wings can cause the tornado: in the sense that the flap of the wings is a part of the initial conditions; one set of conditions leads to a tornado while the other set of conditions doesn’t. The flapping wing represents a small change in the initial condition of the system, which cascades to large-scale alterations of events (compare: domino effect). Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different—but it’s also equally possible that the set of conditions without the butterfly flapping its wings is the set that leads to a tornado.”

It is a popular metaphor in science writing, in describing how sensitivity to some set of initial conditions can have a very large impact on some later state of things.

Last night a butterfly flapped its dainty wings at the poker table, and the resulting tornado cost me some money.

We were at a private house game.  It’s late.  The host has announced that at the end of the current orbit, he is breaking up the game and sending us all home.  Consequently, the play has loosened up in an already loose poker game, as some of the players want to be sure not to miss out on one last opportunity to smash the flop and recoup some losses or add to their gains.

I’m in the small blind, when the player on the button posts a live straddle of 4 BBs.  For purposes of this blog, I’ll refer to him as “Chris.”  Chris is not one of those players who always straddles every time he has the button, but this time he does.  I don’t really care whether other players straddle or not; it requires some adjustments and I generally feel confident that I can make these adjustments better than most players.  (Then again, maybe not.)

Anyway, I look down at pocket kings.  There were eight players at the table and I briefly considered just calling the straddle in hopes that one of the seven players to act after me would raise.  If Chris were known to frequently make big raises from the straddle position even with random card strength, as a stealing strategy, I might have done that.  But it seems unwise to risk a cascade of callers, so I raise to 11 BBs.  In hindsight, I could and should make a larger raise and still expect a caller or two.  I don’t want to run off all of my customers with such a strong hand.  Despite Chris’ straddle, 11 BBs is a large opening raise for this game, but I’ll be first to act on all subsequent betting rounds so a multi-way field is not very desirable.

The next player, in the big blind, very quickly calls.  Given the size of my raise and the speed of his call, this indicates strength.  For purposes of this blog, I’ll call him “Jeff.”

One other player calls, and Chris also calls, which given his positional advantage post-flop and the great pot odds he is getting (7 BBs to call with 37 BBs already in the pot gives him approx. 5.3-to-1 pot odds), he can call with a very wide range.

The flop is 887.  “Danger Will Robinson, Danger!” goes the voice in the back of my head, and I check.  Jeff bets 20 BBs, and consistent with my earlier thoughts when he called my pre-flop bet so quickly, I think his range is dominated by pocket pairs 99-QQ.  One player folds, but Chris calls on the button.  I call as well.  I’m not ready to put all of my chips at risk, but folding at this point would be way too nitty.  For perspective, Chris started the hand with about 95 BBs, Jeff started with around 175 BBs, and I have both of them well covered.

The turn is a 4.  I check again, hoping to keep the pot small.  Jeff bets again, this time 45 BBs.  So much for pot control. Chris pauses briefly, then takes a deep breath and goes all-in for his last 63 BBs.  I would have called Jeff’s bet, and still feel good about my read on him.  Chris, on the other hand, isn’t risking his entire stack with a drawing hand like T9, nor a middling strength hand like A7 or even 99 on this board.  He doesn’t seem afraid of either of us and has no real fold equity here.  Does he think Jeff might fold for 18 more BBs, with 212 BBs now in the pot?  Hardly.  I fold my kings, and Jeff makes a crying call, declaring that he knows he’s never good here unless he hits a 2-outer.

The minor surprise is that Chris doesn’t have an 8 in his hand, but 65, for a turned straight.  This actually gives Jeff 4 outs, as he flips over pocket queens.  Another queen or 8 would make him a full house.  The river misses, however, and Chris scoops up a nice pot.  I silently congratulate myself on sensing danger and releasing my hand, and tell Jeff and Chris what I was holding as I’m pondering the dynamic of what just happened and wondering how I might have played this differently or whether I simply lost the minimum.

After the hand is over, Chris comments about the impact of his straddle, saying that if he had not straddled, the entire hand would have gone down differently.  He might have called whatever action occurred prior to him on the button, but surely with pocket kings in the small blind I would raise enough to make it impossible for him to continue.  Not only that, but with pocket queens in the big blind, Jeff might put in a big re-raise over the top of my bet, especially if he thinks I’m just trying to steal the dead money in the pot.

Not only all of that, but Chris also notes that the only reason he straddled is because the game is about to break up, so this would be his final hand on the button and he straddled just in case he might get a good situation for leveraging his positional advantage.  15 or 30 minutes earlier he would not have straddled.

As played, I was first to act, so my raise communicated enough strength to make Jeff cautious about re-raising with six more players yet to act pre-flop.

It is tempting to describe Chris’ straddle as the flap of the butterfly’s wings that altered this hand.  But it is more subtle than that.  The initial small change in conditions that led to other changes ultimately shifting chips from Jeff’s and my stacks to Chris was the clock, and our host’s need for sleep.  Our host was the butterfly, fluttering his wings by announcing the game would end soon.

Imagine this hand without a button straddle.  There might be multiple limpers or a raise to around 6-8 BBs.  Chris would over-limp, and may or may not call a modest raise.  From the small blind with pocket kings, I’m definitely going to re-raise.  I cannot say for sure how much, as it would depend on the action in front, but it would likely be more than Chris would call with 65.

With Jeff being the big blind, last to act with pocket queens, he and I could have ended up in a pre-flop raising and re-raising war.  That would have turned out good for me.  If we didn’t get all-in pre-flop but were heads up, I would have been more likely to take a bet/bet/bet line post flop.

Alternatively, what if I had just called Chris’ straddle, as I briefly considered, hoping to trap a raiser and subsequent callers?  Another flap of the butterfly’s wings.  Then Jeff likely raises with pocket queens.  I’m not sure how much, but likely more than 11 BBs given that there would already be one caller of the straddle.  When it got back around to me, I would still re-pop it, having the effect of driving Chris out of the pot if Jeff’s raise didn’t already do that.  Again, this scenario is probably very good for me.

Damn butterfly!

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Hanging with D-Wade and Queen Bey

NOTE:  This entry was originally posted on a different site on September 3, 2016 and has been slightly edited prior to re-posting here.

It’s poker night.

I show up at a private house game where I’m one of the regulars.  We play in our host’s garage.

Shortly after the game starts, a new player arrives, a young black man who resembles NBA star Dwyane Wade.  I know this because later, on the TV, I can see ABC News’ George Stephanopolous interviewing Dwyane Wade in the aftermath of the tragic shooting death of his cousin in Chicago.  The TV is right above this new player and I notice a strong resemblance, so for purposes of this blog, I’ll call him “Dwyane.”

When he first arrived, Dwyane looked familiar and I thought I might have played poker with him one or two times previously, but now I’m not so sure.  He’s wearing shorts that hang down below his knees and look like they are two sizes too large in the waist.  I just don’t get that look, but seriously, I try not to judge.  Once I even tried wearing my pants positioned where the belt loops are just below the fattest part of my butt cheeks (only at home, alone).  It was not comfortable.  The slightest breeze, movement or bump into something could collapse my pants down around my ankles before I would have time to react.  If there is something about that style of dress that I was missing, I’m still missing it.

The other thing noteworthy about Dwyane’s appearance is his cap, which at first glance appears to be a military reference, but actually says “STRIPCLUB VETERAN” across the front.

I try not to judge.

The thing is, Dwyane has brought a female friend with him, and we can only assume this to be his girlfriend.  She was strikingly attractive, with longer, curly, well-coiffed hair that reminded me of Beyonce, only with darker skin and wearing yoga pants.  I’m not one to know these things, but if someone told me Dwyane’s girlfriend had undertaken some artificial booty enhancement, I would believe it to be true.  Whoever started the trend of women wearing yoga pants as everyday apparel deserves to be rich and famous, with a special place in heaven.

Lacking any other name to use, for purposes of this blog, I’ll call her “Bey.”

Bey sits very quietly behind Dwyane and watches him play poker.  Occasionally she moves from the back of his left shoulder to the right side.  For about 59 out of every 60 seconds, she is pulling or rearranging a couple of strands of hair in the front, rubbing off the hair product holding her beautiful curls in place.  She is left with a few strands of frizz among a sea of curls.  I wish I had a time-lapse video.

No introductions are made, so perhaps this isn’t Bey’s first appearance here and I’m the one who is slightly out of the loop.  That would be normal.

Nevertheless, here we are.  Bey is the only female present, not playing poker but just watching, not talking other than some infrequent and inaudible words with Dwyane, smoking hot, and Dwyane is still wearing his STRIPCLUB VETERAN cap and has to grab his shorts every time he stands up.

He gets a run of good hands and after an hour or so, Dwyane is up approximately $250.  I feel this very strong urge to say something.  Like:  “Hey ‘Dwyane,’ why don’t you take your winnings and buy ‘Bey’ a very nice dinner, then see if y’all can find something else to do?  Oh yeah, and lose the hat!”  With a wink and extra emphasis on the word something.

But I try not to judge, and keep quiet.

Our host always provides something for the players to eat, and tonight it is chicken stir fry from a Japanese takeout place.  Dwyane brings a full plate over to the table, and a few minutes later I hear him encouraging Bey to have some too.  I had dinner before arriving, so I passed on the food.  It might have been delicious.  Although our host insisted that it was a medium-priced Japanese chicken stir-fry, from a distance is looked like the stuff you get when you have to search for coins in the sofa cushions so you can afford the cheapest Chinese takeout in town.

I need to learn not to judge.

Mrs. is probably right when she observes that I’m not so great at dating anymore (nor was I ever).  But tonight, I’m feeling pretty darn confident in my “what not to do on a date” reads at this poker game.

Around 1:00 a.m. I am leaving.  Dwyane and Bey are still there.  His winnings have turned into a loss.  Rather than top off his stack, he continues to play with a single, short stack of chips in front.  Bey looks bored with everything other than those strands of hair she keeps stroking, determined to get the last bit of hair product out of there.

I consider offering Bey a ride home, but it occurs to me that at least one of them may have some major insecurities about their relationship.  Besides, how would I start a conversation:  “Do you know about Beyonce?  My step-mother calls her “BEE-yonce” but my father calls her “Be-YON-see.”

Nah, that would never work.  I make a mental note to say something nice to Mrs. tomorrow morning.

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Math, Combinatorics and Frequencies

NOTE:  This entry was originally posted on a different site on June 16, 2016 and has been slightly edited prior to re-posting here.

I played this hand at a private cash game a few days ago.  On the river, it was obvious that I needed to fold.  Then again, maybe not.

With QQ in middle position, I raised to 8 BBs following a single limper.  This is a bit more than normal for me, however at this game there were frequently multiple callers pre-flop so I decided to let them pay me a little extra.  Or thin the field.  Either would be fine.

There were 3 callers, making the pot 34 BBs, already a bit bloated.

On a flop of K54 with two spades, I bet 16 BBs and the button called.  For purposes of this blog, I’ll call him “Adam.”  Adam is a 23-year-old loose/aggressive thinking player.  He likes to play mixed games and finds Texas Hold’em a bit boring, but plays it because that’s what’s available around here.  Although I’ve only played with Adam a few times, he is willing to mix it up, gamble and be aggressive if he senses an opportunity to steal a pot.

One the one hand, I’m targeting a hand that will call my slightly less-than-half-pot bet like 66-JJ, A5s, A4s or 56s.  On the other hand, I’m concerned about Adam holding either a King or a flush draw with two spades in his hand.  If he does have a King, it’s probably not AK as he would be more likely to re-raise pre-flop on the button.  But it could be KQ or KJ, maybe as weak as KTs.

The turn is an off-suit deuce.  I bet 20BB more and he calls.  My bet is deliberately small, hoping he will call with weaker pocket pairs or other non-flush draw / non-Kx hands that might fold to a larger bet.  He will definitely call with a flush draw and that’s a risk I’m willing to take.  If he has a King with a strong enough kicker, he might raise just in case I am the one chasing a flush.  I know he’s capable of playing his draws aggressively, but not 100% of the time.

The river is the 8 of spades, which completes the flush (if that’s what he’s chasing).  Now I’m faced with a situation that Bart Hanson at Crush Live Poker calls “5th Street Chicken.”  This is where I’m out-of-position, and don’t want to put any more money in the pot.  But if I check, I’m opening the door for Adam to bluff if he actually has one of the hands I’m targeting.

Quick recap:  The board is Ks 5h 4s – 2d – 8s.  I have QQ.  Adam is on the button and called my pre-flop raise, and called my flop and turn bets.  There is now 106 BBs in the pot.

The pot is really too big for my 1-pair hand.  I don’t even have top pair.  If I bet on this river, am I essentially turning a hand with showdown value into a bluff?  Yes.  Is that a good idea?  No.

I check.  Adam bets 32 BBs.

Clearly I have to fold.  He either has the King, or he hit his flush draw, and he’s betting for value.  His bet is small, which it has to be after I waved a white flag by checking the river, all but announcing that I don’t have a flush, nor a hand that is strong enough to bet/fold (for value).

What would you do?  Leave a comment below…

Math

I decided to fold, but before relinquishing my cards started doing the math.  There are 106 BBs in the pot.  Adding his bet of 32 BBs makes it 138 BBs.  By calling, I’d be risking 32 BBs to win 138 BBs means I’m getting pot odds of 4.3-to-1.  I would have to win 1 out of 5.3 times for calling to be profitable, in the purest poker mathematics sense.  That’s slightly less than 19%, a pretty low threshold.  I was recently reading a limit Hold’em strategy book, and recalled some commentary about calling on the river.  Often you will be getting pot odds of 10-to-1 or more in a limit game due to the constraints on bet sizing.  The author’s point was that while most players should fold much more often pre-flop and on the flop, they should call on the river when they have showdown value and there is any chance they are good as little as 8-10% of the time.  That’s just how the math works.

So I ponder this for another minute.  Adam is capable of turning a weaker hand into a bluff here.  What does he think I have?  I went bet-bet-bet-check.  My range can easily be 99-QQ, AK, KQ, KJ, and is probably pretty transparent at this point that I have a 1-pair type of hand.  After I checked the river, the 3rd spade coming in is a great bluffing card for him.  With a King, he’s more likely to check back after the scare card arrives.  But I think he’s figured out that I can fold when it’s obvious that I’m beat.  And he’s got the stones to take advantage of my discipline and tight image.

Combinatorics

I don’t do the combinatorics at the table, but there are far fewer flush draw combos in his range than other combos.  If I include literally any two spades that include an Ace or have two gaps or fewer, that is about 24 combinations.  Plus 3 combinations of pocket 88’s that binked the river for a total of 27 value combos.  I’ll assume that he always bets with these hands.

His non-flush draw, non-Kx calling range for the flop & turn (66-JJ, A5s, A4s, 65s)  has about 39 combinations.  These are the hands that I beat and was targeting with my small bet-sizing.

Frequencies

Now the questions is how frequently will Adam turn one of these 39 hands that I beat into a bluff on the river?  If the answer is 7 or more out of 39, then the mathematically theoretically correct response for me is to call.  Add 7 bluffs to the 27 value combos, and I win 7-out-of-34 times, or 20.6%.  If I do call his river bet, I’m probably going to lose this pot, but poker theory tells me I’ll lose less over the long run by calling in this spot than by folding.  It feels really messed up to have to think this way.  Nevertheless, I think his bluffing frequency with this set of facts is greater than 7-out-of-39, probably closer to 13-out-of-39 (33.3%) or more.  I feel like I’m about to throw away 32 more BBs because of poker math.

To succeed at no limit Texas Hold’em, however, you have to trust your reads.  My read on Adam says his bluffing frequency is high enough for me to call.  And my read on this situation overall is that the most important question right now is the one about his bluffing frequency.

So I call.

He says “I have a pair of fives.”  With 6-5, the turn card gave him a gutshot straight draw to go along with his weak pair… just enough for my small bet to keep him in.

When he sees my cards, he says he figured it was something like that.  “What do I have to do to get you to fold?”

I start to say “Math” but shrug my shoulders instead.

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