KKing David

Ruminations on poker

Archive for the tag “implied odds”

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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Daily Debacle – Low Flush

This hand occurred in a $0.50 / $1.00 no limit game online.

I have the button, and dealt 3d 2d.  Yes, I know these are really low cards, but there is one limper in front of me so I limp in to see a cheap flop, in position.  A guy I play with in some local live games says he always plays deuce-trey suited because you can win a really big pot with a well disguised hand when it hits.  I think about him as I click the ‘call’ button.  The small blind folds and the big blind checks, so I got what I wanted.  The original limper has been at the table for 18 hands, with stats of VPIP = 50, PFR = 22.

The flop is Kh 7d 5d.  A flush draw.  Woo-hoooo.  Both players check, so I bet $2 into a pot of $3.50.  BB folds and the limper calls.

What I should do now is estimate a range for this player.  Given his stats and pre-flop lime, it will be a pretty wide range but won’t include many premium hands that would have open-raised.  Let’s go with this:

Pairs:  99, 88, 77, 66, 55, 44

Suited:  Almost any 2 diamonds, including any Ad, any Kd, Qd Jd-8d, Jd Td-8d, Td 9d-8d, 9d 8d, 9d 6d, 8d 6d, 6d 4d

Unsuited:  KQ-K5 (including suited but not diamonds), 7T-75, and maybe some random 5’s like A5, 65, 54.

The turn card is 3s, giving me a low pair to go with my flush draw.  While a pair of 3’s is pretty weak, this  creates 5 more outs for me with the remaining 2’s and 3’s.

The original limper checks and I get $6 into a pot of $13.50.  In hindsight, this bet is too weak, about 44% of the pot.  If I’m trying to say “Dude, I’ve got this one” a larger bet is needed, somewhere around $10 or $11.  Now the villain check-raises to $15.


Did the 3 help him?  Or was he setting up for this all along?  If the 3 helped, he could have 33 for a set (only one combination of 3’s is now possible) or 64 to make a straight (any 64 suited might have limped in) or K3 (I suppose a very loose player could limp with K3 suited, but much more of a long-shot.

Otherwise he might have flopped a set of 777 or 555 and been waiting to ambush me.  KKK less likely as he would have raised pre-flop.  Or flopped two pair with K7 or K5.

I have a hard time seeing this check-raise with a single pair of K’s or anything weaker.  His pre-flop limp rules out AK and probably KQ (both should have raised pre), and the check-raise represents too much strength.

Should I call or should I fold?  The pot is now $28.50 and it will cost $9 to call.  I’m getting 3.2 – to – 1 odds to call.  The odds of making my flush, assuming all 9 outs are live, are 3.9 – to – 1 against.  Not good enough. If he has a set, then two of my outs are likely counterfeited, leaving me with odds of 5.3 – to – 1 against.  On the other hand, if he has something weaker that I can bet by hitting another 3 or a 2 on the river card, I may have as many as 14 outs (9 diamonds, 3 deuces, 2 treys).  Then my odds are 2.1 – to – 1 and I should call.

One last consideration.  I have position and get to act last.  This helps me to have a better chance of getting more of his chips into the pot.  I can assume I have some implied odds here so I decide to call.

The river is Ad.  Ba-da-bing!  My flush comes home to pappa.

He leads with a bet of $20 into a pot that is now $37.50.

Do I need to consider the possibility that he has a stronger flush?  Methinks not.  If he’s also chasing a flush, his check-raise on the turn makes no sense.  That was clearly a value bet, the board isn’t paired, and it’s time for me to take him to Value-Town.

How much to raise?  I consider a minimum raise, to $40.  No, too conservative and too transparent.  That just screams “I HAVE A FLUSH.”  Shove all-in?  No, too aggressive.  I want to win a bigger pot and justify the implied odds on which my turn call was based, not blow him off the pot now that my draw has arrived.  I decide to raise to $50, leaving me with $34 behind.

In hindsight, this was not a good size for my raise.  I’m pot-committed.  The pot is $107.50 and will grow to $137.50 if he calls.  If he re-raises all-in, the pot will be $171.50 and cost me $34 to call, giving me odds of slightly more than 5 – to – 1 to call.  There’s no way I’m going to fold me flush with those odds.  Instead I should simply call here – if I think he might also have a flush – or go ahead and shove, hoping he will interpret that as a bluff.

He rather quickly re-raises all-in, and I think the pot odds make my call mandatory.

He shows Kd Jd for the nut flush.  Jeez.  It turns out he had flopped top pair, decent kicker and 2nd to nut flush draw, and the river card being the Ad made his hand the absolute nuts.  He wins a $207.50 pot.

Year-to-date online results:  (- $814)

Month-to-date online results:  +$391

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