KKing David

Ruminations on poker

Archive for the tag “bluffing”

Rope-a-Dope

Most poker experts will describe two reasons for betting:  Value Betting and Bluffing.

Betting for value happens when you think you have the best hand, and want to get called by someone with a worse hand.  When they call, you make money.  When you make a good hand, one that is likely or certain to win at a showdown, you want to get as much money as possible in the pot and the way to accomplish that is by betting.

Bluffing happens when you think the other player has a better hand than yours, but will fold it if you make a strong enough bet.  Maybe both of you have weak hands.  Or the board fits with a narrative you can tell that represents a very strong hand.  When they fold the best hand, you make money.

In this hand from last night, however, the best line turned out to be checking for value.

This is poker’s version of the rope-a-dope, made famous by Muhammad Ali in the 1974 heavyweight boxing title match against George Forman.  Boxing in Zaire (now Congo), Ali backed up against the ropes in a protective stance and let Foreman flail away at him.  With a defensive posture designed to deflect Foreman’s power, combined with letting his body bounce against the ropes, Ali’s body absorbed very little pain.  After five rounds, Foreman began to look worn out.  After seven rounds, Foreman was spent.  Ali won the fight with an eighth round knockout over the younger and heavily favored Foreman.

In a casino game last night, I had KJo in middle position.  Not great, not terrible.  I put in a raise to 5 BBs and got two callers.  One will act before me on future betting rounds; the other will be after me.

The flop was K43, rainbow.  This is a really good flop for me, but probably terrible for the other players.  The first guy checks.  This is what makes a hand like KJ difficult to play for value.  What hands can be in my opponents likely ranges that will call if I bet again here, and I can beat?  KT?  Kx with weaker kickers?  Pocket pairs 55-QQ?  The player who will act last is a younger, somewhat aggressive player.  For purposes of this blog, I’ll call him “George.”  This is my first trip to this casino, and he’s only been at the table for an hour or so, so I have no history and very limited information.

I also check, and George bets 8 BBs.  The first player folds.  I definitely think I have the best hand here.  If that’s true, raising will only get him to fold.  I fiddle with my chips to try to look uncertain, and call.

Turn (31 BBs):  5d.  This puts two diamonds on the board (including the king).  I check again.  George looks like he’s trying to size me up.  I would like for him to think I have a hand like QQ, JJ, TT or 99 that will have to acknowledge that he has a king in his hand for a better pair.  I would like for him to think he can bluff me.  He bets 15 BBs.  I shuffle my chips again as if I might call but I might fold.  The only hands he can have that beat me (other than something very deceptively played) are KQ, 44 or 33.  There are three combinations of 44 and 33, and eight combinations of KQ that he can have, for a total of 14 combinations out of his entire pre-flop calling range (which might have 100-200 combinations (7.5 – 15% of all possible hands).

Let’s assume his flop bet was just a simple stab at the pot leveraging his favorable position.  If he has nothing, but the first player and I both seemed to miss this flop, or are scared of the king, that’s a reasonable play.  In fact, it is one of the benefits of being last to act – you get to take down small pots like this that nobody else seems to want.  Then I called his flop bet.  That makes the pot larger and worth fighting for.  How frequently will George fire a multi-barrel bluff?  Given my image as a middle-aged white guy (MAWG), and the way I’ve played during his time at the table suggesting a fit-or-fold style, I think his bluffing frequency is high enough to warrant calling again, and so I do.

River (61 BBs):  7d.  At first this looks like a scary card.  Now there are three diamonds on the board, making a flush possible.  And there is a 345-7, so any 6 makes a straight.  I check again, knowing this looks scary enough for many aggressive players to take a final stab.  In my mind, I’m Ali and he is Foreman.  (Friends, just let me have my moment here, OK?)  I’m backed up against the ropes, with my (muscular?) forearms in a vertical position protecting my upper body and face.

George fires out a much larger bet of 43 BBs.  Let’s assume he actually has a hand that is better than mine.  Would he bet that much?  After I’ve shown (or tried to…) hesitancy in calling his flop and turn bets, and a scary looking card falls on the river, what can I possibly have that would call again.  I raised pre-flop, then turned passive on a king-high board.  Would I play this way with AA, AK, or KQ?  Or KK?  If so, would I call a bet that is nearly triple the previous bet when the river card cannot possibly have helped me?

At the table, I don’t need any time to process this.  George’s bet is begging me to go away, so I quickly flip a single chip onto the felt and announce “call.”  Ryan sheepishly turns over As Ts.  He was bluffing with total air the entire time.

Had I made the more straightforward continuation bet on the flop, George has an easy fold and I would have won a very small pot.  Rope-a-dope for value!

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Winning by Leading

You want to win more often than you lose, right?

In team sports, two teams compete head-to-head.  When each contest starts, the score is tied, 0-0.  The scoreboard doesn’t confer any advantage to one team or the other.  Whether it is football, basketball, baseball, hockey or soccer, the winning team is the one with the most points, runs or goals at the end of the game.

What matters is the final score.  One team can be losing throughout the game, only to pull ahead on the final play.  Or the score can remain tied for most of the contest until one team scores to take a late lead.  Or a team can be dominated early, only to have momentum shift in their favor for a come-from-behind win.  Or the lead can shift back and forth multiple times.  Or a team can score first, extend their lead, and never be threatened.  Under every scenario, the winner is whoever has the lead at the end of the game.  It seems silly to have to say that, doesn’t it?

Yet in every sport, the team that scores first ends up winning a majority of the time.  At any time during the game, the team in the lead is most likely to win.

In baseball, hockey and soccer, the team scoring the first run or goal will win about 2/3 of the time.  In football, the team scoring first will win more than 60% of the time.  In basketball, with NBA teams averaging 100 or more possessions per game, the edge is not as great.  The first team to score wins approximately 54% of all games.

Having an early lead doesn’t guarantee victory, but it improves your chances.

In Texas Holdem poker, some of the dynamics are fundamentally different from team sports.  You aren’t a team.  It isn’t a head-to-head competition.  You can opt-out, by folding.  Yet we can still think of each hand of poker like a team sports contest.

Here is the fundamental rule:  The best starting hand is more likely to be the best hand at showdown.

I know, call me Captain Obvious, but bear with me just a bit.

One of the biggest flaws of poker players is playing too many hands.  This post started with a simple question:  You want to win more often than you lose, right?

Before the cards are dealt, the score is tied.  Are the conditions favorable?  Sports teams prefer to play at home.  If professional sports teams played all of their games at home, they would win 5-10% more games.  In poker, the equivalent of the home field advantage is having good position (button or cutoff seat), plus a deep chip stack, winning image and calm emotional state.  Are you giving yourself the poker equivalent of home field advantage?

After the cards are dealt, the score is no longer tied.  Although you can’t look at a scoreboard to see who has the best cards, somebody is in the lead.  Everybody’s betting actions provide us with clues.  If you have the best hand pre-flop, this is the equivalent of scoring first in a team sport.  It doesn’t guarantee victory, but does make you the favorite.  If you have the best hand plus home field advantage (good position, deep stack, winning image, calm emotional state), you are an even bigger favorite.

The amazing thing here is that in each hand of poker, you can opt-in by betting, raising or calling, or you can opt-out by folding.  Professional sports teams don’t have the luxury of opting out when the other team has home field advantage and scores first.  You do.  So why in the world do so many poker players voluntarily put themselves at a probabilistic disadvantage by opting in with hands that are already losing?  Jeez, another hand will start in just a minute or two.

There are 169 possible combinations of two cards.  We can rank them in order of their probability of winning against a full table of opponents.  AA will rank highest; before the flop, this is the nuts.  Next is KK.  There are plenty of poker equity calculators that will show the projected win percentage of each hand vs. any number of unknown hands.

What do you have?  Is it likely to be the best hand at this point – before the flop – in the contest?  Possibly?  Unlikely, but with a reasonable chance of improvement?  Never?  Since poker is a multi-player contest, winning more than anyone else might still be less than 50% of the time.

For example, suppose you are dealt Kh Jh.  King-jack suited is a good hand.  It ranks in the top 7% of all hands.  Out of 169 possible combinations, my Poker Cruncher app ranks it as #15 in strength.  It is possible that you have the best hand at the table.  Kh Jh is projected to win 46% of the time against two random hands, while each random hand is projected to win 27% of the time.  Even though you probably have the lead, the multi-player aspect of poker forces you to acknowledge that most of the time, another player will win the pot.

Limp / call range

But the other players don’t have random hands.  Let’s take this a step further.  Suppose one other player limps in from middle position, you raise with Kh Jh in the cutoff seat, the big blind calls and the limper also calls.  You are 3-handed going to the flop, but now you can eliminate many of the 169 combinations from each villain’s range.  You can eliminate the strongest hands, with which they would raise instead of calling.  And you can eliminate the weakest hands, which they would simply fold.

For this example, let’s assume the limper would have raised rather than limped with all 14 hands that rank stronger than Kh Jh.  These are:  AA, KK, QQ, JJ, TT, 99, 88, AKs, AQs, AJs, ATs, KQs, AKo, AQo.  We’ll eliminate those from his or her range.  Also let’s assume he or she would fold the weakest 50% of all hands, instead of limping or in response to our raise.  We’ll eliminate those too.

BB call range

The big blind was responding to our raise.  We’ll assume that he or she would re-raise only with a top 10 hand:  AA, KK, QQ, JJ, TT, 99, AKs, AQs, AJs, AKo.  Since we only got called, we can eliminate these.  We’ll also assume the big blind folds the weakest 60% of all hands to our raise.  We’ll eliminate those too.

Now we can recalculate our equity.  Kh Jh is projected to win 41% of the time, vs. 28% for the limp / call hand in middle position and 31% for the big blind.  You are still the favorite, just less so than against two completely random hands.

If your raise was a little bit larger, maybe the big blind would fold and the limper would fold the weakest 60% rather than 50%.  Now you would be heads up, and project to win 58% of the time at showdown (in all cases, these win rates assume there is no further betting), switching the outcome from ‘lose most of the time’ to ‘win most of the time.’  See how powerful raising is?

Suppose, instead, that you had made the same raise with Th 8h and gotten the same two calls.  Now you would be projected to win 30% of the time. vs. 33% for the limp / caller and 37% for the big blind.  Instead of starting with the lead, you’ve opted in despite being an underdog, and done so via a raise.  Why would you want to do that?  Have you forgotten the original question:  You want to win more often than you lose, right?

It is possible to win a pot without having the best hand.  There is even a technical term for this:  bluffing.  Sports teams don’t have this weapon.  Imagine a Little League baseball team yelling in a menacing tone at the other team, “we are beating y’all by more than 10 runs, so you should quit and go home under the mercy rule!” even though the other team is actually ahead by one or two runs.  That would never work.  I’ll return to bluffing in a later post.

There are other reasons you might want to opt-in with starting cards that won’t enjoy the early lead.  This involves pot odds and implied odds.  I’ll return to this in a later post as well.

For now, if you want to win more often than you lose (right?), the easiest place to start is by playing hands that are more likely to be in the lead already and raise enough to shrink the number of remaining villains.  Before you starting bluffing or calculating pot odds and implied odds, just practice playing poker with the lead.  Develop the habit of opting in with the lead and opting out whenever another player is more likely to have the lead.  Opting out eliminates your disadvantage, with no penalty.

Imagine a professional sports coach being able to withdraw from a game after the other team scores first with no penalty, no impact on the team’s win/loss record.  The coach would simply say he’s decided to reset the scoreboard and start over.  In team sports, that would never work.  In poker, you have that option every hand.

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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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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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No More Free Beer

Last night I played in a home cash game.  I’ve played 4 times previously with this group, lots of fun, and won some decent amounts of money each time.

So I decided to be a nice guest, and buy an extra 6-pack for the host.  I emailed to inquire as to his favorite brew, bought some (and another 6-pack for myself with intention of leaving behind the extras in hopes that some would survive until the next game or two there).  When I arrived and handed him the gift, I smiled broadly and explained this was just a small show of appreciation for being invited to join the game, he and his friends are lots of fun to play with and besides they keep giving me their money.

We had a good laugh.

Then started playing poker.  Not too deep into the night, I got AA, raised to $5 (blinds are $1 and $1) and 3 callers.  The flop was 3h 5h 7h.  I have the Ah, so this is not a terrible flop for me.  Everybody checks and I bet $11.  One caller.

Turn:  Jh.  Bingo!  Now I have an Ace-high flush and the only remaining issue is how to extract the most value.  The remaining villain checks, and I’m concerned he might just go away too easily.  By checking behind, I can represent weakness and hopefully induce a bluff on the river.

River:  5d.  Sure, this pairs the board, bringing full houses into the realm of possibility, but I’m really not so worried about that.  He leads out with a bet of $22.  Looks like the bluff I was hoping for.  I don’t want to re-pop him too hard, so I make a barely min-raise to $45.

Now he tanks for awhile, and says the river cards worries him.  I find this a little odd, as if he’s somehow representing the Ah, which I have securely in front of me.  He tanks some more, and looks to be leaning towards folding.

Then he re-raises all-in.  Huh?  My best guess is that he  has convinced himself that I’m the one bluffing here.  I feel pretty pot committed.  Let’s see… there’s about $180 in the pot and I have about $45 behind.  I’m getting 4-to-1 to call.  Gotta call here, and I do.

He says, “Sorry, but I have the nuts!” and turns over 6h 4h for a flopped straight flush.

About an hour later, I get into a hand with Ks Tc, and the board runs out As Js 6s Ac 2s, again giving me the top flush on a paired board.  The same villain leads out on the river, and again I raise – not seeing any possible straight flushes out there.

This time he calls, and says “I suppose you have Ace-Jack.”  Nope, nut flush.  He turns over A-6 for a full house, and takes most of my second $100 buy-in.

Is there a lesson to be learned here?  Probably so.  I tend to think many players are too tight in playing a flush on a paired board.  The percentage of the time that a paired board actually results in someone having a full house (note that in hand #1 above it wasn’t a full house, but a straight flush that did me in, but I digress) is fairly low.  On the other hand, both of my flushes involved 4 same-suit cards on the board, and I had the top possible flush both times.  It is much more likely that someone has a lesser flush than a full house (or quads, or a straight flush).

According to my math, a single player with a random hand will make a full house less than 3% of the time when the board is paired.  Of course, by the river his hand is no longer random.  With about the widest range I can imagine for hand #1, he makes a full house less than 8% of the time.  I’m not going to calculate for hand #2 but it should be higher due to the paired card being an Ace.  Many aces in his range.

I guess in hindsight, I have no issues with the way I played the first hand.  It was just a cooler, my AA turned into an A-high flush and lost to a flopped straight flush.  I’ll enjoy telling and re-telling that story.  The second hand warrants a call and not a raise on the river.  Much easier for the villain to have AJ, A6 or A3 and hit a full house, although I’m pretty sure he checked the turn.

Both times I could have called and not raised on the river, and saved about $120 +/-.

Is that actually the higher EV play?  I’m really not sure.

Please add your thoughts in the comments section.

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