How to get Ahead in Advertising

A breakthrough I’m having right now is the benefit of fold equity.  As discussed before, about 10-15% of the time my opponents will be drawing and brick off or have a some other hand with dubious showdown value.  In these hands if I’ve show strength preflop and the pot is laying 9 or 10:1 by the river it makes sense to just keep firing bets, particularly when there are few draws available (aka a “dry” board).  The reason is if the pot is that large the chance opponents will fold on the river just makes it worthwhile to keep firing.  Also, with good hole cards I’m not simply just plowing bets in cold bluffing.  With six outs to a good pair I’m getting a good 20% equity or so by the river.  Missing the flop it’s 2.5 big bets to bluff out the hand but with that fold and drawing out equity it’s more like a functional 1.5-2 big bets.  At that price I can hit my card and win or my opponent will have to fold only about 1 time in 8 to make this betting line profitable.  Here’s an example from a hand I played last night:

I was in early position with A-10 off suit.  One player limped in; I raised and three players all together called.  The flop came 8s-9h-2s.  Checked to me; I bet and everyone called. The turn was the Qd.  It checked to me and I bet again.  Only the player to my left called.  There are now 8 big bets and will probably be 10 on the river.  So, I’m getting about 9:1 on my river bet, no matter what card comes.  The chance that my A is good along with the 15% or so chance my opponents draw bricks off and he’ll fold make it clearly worthwhile to just stick a bet out there.

The river turned out to be a 10.  Of course I bet, got called and my opponent turned over 7-9 off suit.  He wasn’t too happy but the lady to his left teased him about the several hands he had earlier when he made his hand on the river and won.

These small post-hand events do have some value.  It draws the attention of players to the hand.  My opponents all see that I bet down with only A high.  This all serves to create some doubt in their minds about what I’m holding when I show strength early in the hand.  Did I make my hand on the flop?  I only seem to be playing big cards.  What will my opponent think of his 8-7 on a K-2-8-5-2 board?  With 10 big bets in the pot, he’ll only have to fold 1 time in 8 for my raise-bet-bet-bet line to be profitable.  If he calls and I turn over KK, how valuable was my earlier hand when I bet down with only A high, even if I hadn’t caught my card and lost?

The final benefit of playing hands out like this is that it balances my play and makes me much less vulnerable to exploitation.  If better players are sitting at my table they will take note if I raise preflop and check-call the flop and check-fold the turn.  These players will assume this "one and done" pattern is a habit for me and will almost always bet the turn and river, confident I will fold.  Or, they will notice I bet the flop and turn, put me on a value hand and not pay off.  If I'm always just betting, they don't know what I have and can't react to me with much confidence.  Players freeze up and make mistakes.  It's true that they will end up with strong hands played passively and beat me.  It's also true they will draw out.  But, when pots get as large as 8:1 I don't have to win all that often to make up for those loses and make a profit.

Bluffing and Fold Equity

The romantic story about bluffing in poker is that the sly shark senses weakness in his opponent.  A sweaty brow, dilated pupils, shaky hands all clues to the expert player that his rival doesn’t have as strong a hand as he is representing.  Acting on this sixth sense our hero makes a big raise at a critical point in the hand holding perhaps only 8 high and his pray folds.

The truth about bluffing is much more mundane and is, of course, embedded in very simple math.  A successful bluff is not trying to outsmart an opponent holding top pair or getting players to make bad lay downs.  Bluffing is simply determining the range of possible hands an opponent won’t showdown with, figuring out what percentage of those hands are among all the possible hands he could have and if the pot is laying me good enough odds given that percentage to make my bluffing bet worthwhile.

Another conventional piece of thinking about bluffing is that it’s just not possible in limit hold’em given the small size of the bets relative to the pot.  As I’ve talked about before, hard and fast rules in poker lead to habits that less talented players fall into that cost them a lot of money in the long run.  Using the above analysis bluffing is absolutely possible in limit hold’em.  In fact, if players aren’t incorporating bluffing into their play the results will ultimately be devastating to their bankroll.  Here’s an example:

Hero is in the cutoff seat with A-J off suit.

UTG + 2 limps

Highjack limps

Hero raises

Button calls

Big Blind calls

UTG + 2 calls

Highjack calls

Five players 10 small bets.

Flop 9d-8d-2c

Checks to Hero who bets

Button and BB fold

UTG calls

Highjack calls

Three players 13 small bets

Turn Ks

Checks to Hero

At this point there are 6 ½ big bets in the pot.  Assuming at least one opponent will call there will be nearly eight big bets by the end of the hand.  To bluff out the hand it will cost me only two big bets at this point, so I’m getting 4:1.  I may be up against a pair an 8 or 9x up to a king or ace.  Also very likely is a straight or flush draw that threatens to brick off since a disconnected K rolled off.  So, probably around 30% or so of the one opponent who call’s range he is unlikely to show down with (assuming the flush or straight draw doesn’t come in).

Another element of this analysis is the idea of fold equity.  On top of the 30% or so of hands an opponent won’t show down with in the example above is the 10 or 15% chance that he could fold.  Keep in mind I raised preflop, C-bet and a king rolled off on the turn.  Let’s say my opponent has 8-10 and peeled the flop.  What happens if a Q comes off on the river?  What is he going to think of his pair of 8’s?  Now getting close to 40% that my opponent either won’t show down or will fold, my 4:1 to bluff out my hand has become the mathematically correct play.

It’s important to note that 40% is not 100%.  I’m still loosing more than half the time in a spot like this.  But, the math shows that I don’t have to win that often to make my betting correct.  If this situation was played out over and over 100 times with the same flop, my same cards and random cards making up my opponent’s hands, I will come out very far ahead because of the size of the pot.  I will only win 2 times in five but the amount of those wins will more than compensate for the times I lose.

An Expert in Value City

One of the things that separates the good from the expert players in poker is finding extra value bets.  Conventional wisdom is with a medium strength hand when checked to on the river a check behind is the best play because you will only be called by a better hand.  Experts understand that hard and fast rules are seldom applicable at the table and in the long run forming habits can cost a player a lot of money.  Reading board texture and understanding your opponent’s range of hands should always guide decisions about betting.  A hand I played recently went like this:

Hero in Highjack with Jc-10c

UTG +2 limps

Hero raises

SB calls

BB calls

UTG +2 calls

Four players, 8 small bets

Flop Js-10d-2h

SB checks

BB bets

UTG + 2calls

Hero raises

SB folds

BB calls

UTG + 2 calls

Three players, 14 small bets

Turn 9c

BB checks

UTG + 2 checks

Hero bets

BB folds

UTG + 2 calls

Two players 9 big bets

River 3h

UTG + 2 checks

Read on UTG + 2 is an older retiree, beyond a regular and more of a fixture at this room; a weak-tight player who seldom bets unless very strong. He is capable of check-raising with the nuts. He often calls down with top pair, which is what I had him on; top pair strong kicker or possibly a straight draw.

Hands that are beating me here are K-Q, Q-8, 7-8, J’s, 10’s, 2’s or 9’s.  Hands I’m beating are any J-x, 10-x, A-K, A-Q, 9-x, Q-x, K-x, A-x all are within the realm of possibilities my opponent might call down with.  The majority of the hands I’m beating are also likely hands he would (and should) call on the river with.

Two pair is the average winning hand in poker.  Over and over again I’ve seen players (including myself) check behind in this spot and be content to win the pot and forego a value bet.  The thinking being that with a possible straight on board and the inherent averageness of 2-pair, “I’m only getting called by a better hand.”  An expert player will be able to do the above analysis of the range of hands my opponent could have and will call with.  Heads up on the river the criteria for betting is I need to be ahead of a little better than half my opponent's range (better than half because I could get raised).  I am beating well above 50% of my opponent's range so it is correct to bet on the river expecting to get called by a worse hand.

If you are curious, I in fact did not bet the river and checked behind.  I turned over my top two pair and my opponent did indeed show A-J.

What are My Chances?

Here is a graph generated by a slick little program I ran across on a site called ev++.  They have a page with a number of tools including a variance simulator.  This graph shows the frequency and size of downswings I can expect given my current win rate and sample size.

What it shows is that EVERYONE winning at the rate I am right now can expect to have a 180 big bet downswing at some point.  At 4/8 that's around $1400, about half my bankroll.  Isn't that amazing?  So, basically it's inevitable that I will loose half my bank roll at some point in one sustained losing streak.  Want to know something else?

About half the time I can expect a downswing twice as large!

Bottom line is it's about 50/50 that I'll go broke.

Here's something really scary:

I've got a 20% chance of a downswing as large as 700 big bets.  1 time in 5 I will just keep losing and losing, no matter how much money I put in, until I've lost $5700!

Depressing and fascinating at the same time!