KKing David

Ruminations on poker

Archive for the tag “bluffing”

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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