December 21, 2010

The Fear of Money

"I think maybe the money's what's throwing you off here today."

—Vincent Lauria (Tom Cruise), in "The Color of Money"

During my recent trip to Vegas, I had a hand in a $1/$2 NLHE cash game at Imperial Palace where I folded Kings preflop, making that hand only the second time in my life where I had done so.  The action had been a raise by a tight player, a healthy reraise to $40 by me, followed by an immediate and strong reraise by the tight player, with the two of us looking at playing for ~$450 effective stacks.  The player was so tight, and the reraise was so strong, I open-mucked my Kings, thinking to myself, "He has to have Aces."  The tight player saw my hand and rolled over ... Ace-Eight sooooted.  Oops.

The first time I folded Kings preflop in a cash game was four years ago during my inaugural Festivus trip to Vegas.  I was playing at the Rio in a $1/$2 NLHE cash game, and had recovered from an early downswing to work my stack up above $1,500.  There were several other large stacks at the table and the game was playing loose and crazy.  In one hand, there was a raise to $15, and a reraise to $50.  I was in the small blind and found Kings.  I raised to $150.  First raiser pushed all-in for over $1,000, and the second raiser insta-called for nearly that amount.  Crazy.  I thought forever, and finally folded, figuring one of them had to have Aces.  They rolled over ... Ace-Yak soooted and Ace-King.  Yes, I play badly.

In both cases, I felt there was a good chance I was up against Aces.  My thinking was that it's better to make a small mistake (folding and conceding my initial raise) than to make a big mistake (committing a deep stack with Kings preflop).  Or, as my motto at the bottom of this blog states:  "There's always a better place to get it in bad!"  But in small stakes cash games, it's actually very difficult and highly unusual to be able to put a player on exactly Aces, or even a narrow range like Aces, Kings, Queens, and Ace-King.  Against that larger range, folding a hand like Kings is a major mistake.  So why did I make that mistake, not once, but twice?

Well, my decision-making process in these hands might have been the result of a common psychological aversion to losses, even when the risk of losses can be offset by an identical chance of gain:

... When Kahneman and Tversky framed questions in terms of gains and losses, they immediately realized that people hated losses.   In fact, our dislike of losses was largely responsible for our dislike of risk in general.   Because we felt the disadvantages of risky decisions (losses) more acutely than the advantages (gains), most risks struck us as bad ideas.  This also made options that could be forecast with certainty seem especially alluring, since they were risk-free.  As Kahneman and Tversky put it, “In human decision making, losses loom larger than gains.”  They called this phenomenon “loss aversion”.

—Jonah Lehrer, "The Allais Paradox" (The Frontal Cortex blog, Oct. 21, 2010) (emphasis added).

Now my poor decision to fold Kings preflop in these two hands is a negative expected value (-EV) play against any hand range other than exactly Aces.  The math is rather straightforward, and the decision to fold Kings preflop is—or at least ideally should be—driven entirely by the range of hands I can assign to my opponent(s).  I may have thought I was making a smart laydown by folding Kings, by not putting my deep stack at risk.  But in reality, I was forfeiting more than merely the preflop bet I had placed in the pot; I was also forfeiting my significant expected profits from winning the pot over 2/3 of the time.

However, there are several common poker situations where successful poker players must invest money with some significant degree of risk, and where a straightforward pot odds calculation cannot provide a direct answer as to whether committing chips to the pot is a profitable (+EV) move:
  • Bluffing when it is the only way to win the pot.
  • Semi-bluffing with a draw or marginal hand that is likely behind if called.
  • Calling with a marginal hand that is generally only a bluff-catcher.
  • Value betting the river with a good but not great hand (particularly heads up or when last to act and action has checked around).
In each of these situations, I think many low stakes cash game players err on the side of caution, failing to bet or raise because of a psychological aversion to losses.  In each of these situations, there is often significant value in risking additional chips to win a pot, even without knowing whether one holds the best hand, or even knowing for certain one doesn't hold the best hand.  Yet many players (myself included) will often timidly check and fold in these situations as a default move, rather than analyzing whether a bet or raise is a better expected value play.  In other words, poker players often incorrectly forfeit their interest in a pot out of a fear of losing even more money with a marginal or poor hand, when the more profitable move might in fact be to risk additional chips in an attempt to win the pot.

Even though many low stakes poker players have read books and articles about pot odds and expected value calculations, why do we keep making the error of playing too timidly?  I think an important distinction must be drawn between situations where odds calculations are precise, and situations where the odds are imprecise.  For example, most decent poker players can and do routinely calculate pot odds when they are holding a straight or flush draw; if the pot odds are not favorable, it is a routine fold.  But for situations involving making a bluff or making a call to pick off a bluff, the odds are imprecise, creating doubt and timidity in our analysis of the proper play:
    The first gamble corresponds to the hypothetical ideal:  investors face a set of known risks, and are able to make a decision based upon a few simple mathematical calculations.   We know what we don’t know, and can easily compensate for our uncertainty.  As expected, this wager led to increased activity in the parts of the brain (like the striatum) involved with the expectation of rewards, as subjects computed the odds and calculated their expected earnings.  Unfortunately, this isn’t how the real world works.  In reality, our gambles are clouded by ignorance and ambiguity; we know something about what might happen, but not very much.  When Camerer played this more realistic gambling game, the subjects’ brains reacted very differently.  With less information to go on, the players exhibited substantially more activity in the amygdala, a brain area reliably associated with fear conditioning.  In other words, we filled in the gaps of our knowledge with fear.  And it’s this inexplicable fright—an irrational by-product of not knowing—that keeps us from focusing on the possibility of future rewards.

    —Jonah Lehrer, "The Truth Wears Off" (The Frontal Cortex blog, Dec. 6, 2010) (emphasis added).

    Now the poker literature is rife with examples of expected value calculations for making or picking off bluffs based on estimates of the percentage of times an opponent is calling or making a bluff.  But the problem with these examples is that what is easy on paper is tough to apply in real life.  When was the last time you actually thought, "This player is bluffing in this situation 36.77% of the time"?   Instead, we are forced to deal with more of a gut feeling as to how likely a particular player is to be bluffing or calling our bluff in certain situations.  And that gut feeling leaves us with a feeling of unease, causing our instinct to avoid risk and prevent losses to kick in, making us overly timid in our play.

    Now it's important to understand that our instinct to avoid losses is a hard-wired psychological trait that we must overcome to maximize our success at the poker table.  But our loss avoidance tendency is different from playing with "scared money", which is when we risk money we know is needed for non-poker purposes, or when we put an excessive percentage of our bankroll at risk at one time.  Although both kinds of fear will have a negative impact on our play, the proper remedy for excessive loss avoidance is to be more aggressive, while the proper response to playing with scared money is to drop down in stakes or to quit playing until our dedicated poker bankroll is healthy.

    So, for my first New Year's poker resolution, I shall strive to overcome my fear of losses, and try to analyze hands where I would normally check or fold to determine whether an aggressive play might, in fact, be a better (+EV) play.  I will face my fear of large losses, recognizing there may be a larger reward for aggressive play.  I will push aside that knot of anxiety in my gut, and seek out that rush of joy that comes with stacking chips.  I will not be afraid at the poker table.
    I must not fear.  Fear is the mind-killer.  Fear is the little-death that brings total obliteration.  I will face my fear.  I will permit it to pass over me and through me. And when it has gone past I will turn the inner eye to see its path.  Where the fear has gone there will be nothing.  Only I will remain.

    —Bene Gesserit "Litany Against Fear" from "Dune", by Frank Herbert.

    8 comments:

    1. The best counter to fear is a healthy bankroll. Took me a long time (and an embarrassing amount of money) to learn that lesson.

      I agree with your analysis. The only thing I would have done differently would have been to muck my kings face down.

      -DrC

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    2. Totally off topic, but I tried to assert the Spanish Inquisition twice today and only succeeded in doubling both players up. I think I'm doing it wrong.

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    3. @ CrabblerK3:

      The Spanish Inquisition is never off topic.

      Did you play the hand like Aces? Or Kings? Or 96 sooooted? If so, your opponents may have mistakenly undervalued your hand. You must play the hand strong.

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    4. Interesting linkage. As Grange says, timidity and the inquisition are incompatible. And, oddly enough, someone, every once in a while, actually has a big hand. Odd! :-)

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    5. Excellent post and I think indicative of why a common trait used to describe excellent players is "fearless".

      That's a big part of why I choose to restrict myself almost exclusively to tournament play. For whatever reason, it's easier for me to be more "fearless" when I'm playing with tournament chips in front of me as opposed to "real" chips.

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    6. On the Inquisition:

      Neither hand featured a crub which I believe is half of my problem. And yes, sure enough, one fool rolled up aces on me, not knowing the danger he was facing.

      @ Glenn:

      You've got an interesting idea. I was in a nasty rut over the summer where I was getting steam rolled in cash game play. I played primarily tournaments for the fall and it really helped my play.

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    7. About folding Kings preflop, I've never done it, and I can only assume you are correct that the fear factor plays a big part in why anyone ever would at any kind of normal stakes. In your first example, I do not believe there is ever a scenario in just a heads-up battle preflop where I would ever fold Kings. Perhaps if the stakes got high enough, but those would have to be so high that I don't think I would ever be playing there in the first place. There's just too much of a chance of JJ, QQ, KK or some donkey cripe like Ax sooted (case in point) for me to ever be *that* sure to justify throwing away such a great opportunity to win a lot of cash in that spot.

      Your second example is a stronger case for folding the Kings, though I still think I would not have done it there. You give me a preflop raise from a tightie, and then I reraise, and then the tightie pushes allin *and* another guy calls the allin, that is certainly worth considering laying the Kings there in my book.

      This goes back to a hand I recently commented on on Poker Meister's blog -- I acknowledge that my KK could be behind in these spots, but I have zero fear of losing with them, and if anything what I *do* fear is giving up such a great opportunity to score some dough and then being faced with two Ax type of hands, lower (dominated) pairs, etc. Personally, that possibility scares me much more than calling with the Kings and seeing Aces.

      Nice post. Be stronger in the new year, bro. Never fold Kings preflop.

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    8. I've never folded kings yet preflop, and you simply can't make up too many scenarios where I ever would lay them down in a cash game. And yes, I've lost a 400BB pot in a cash game when the play was short-handed and three of the hands dealt were AA, KK, and QQ. QQ got away relatively unscathed, and I went home lighter in the wallet. But I still don't regret my decision, although it was a relatively close one (villain with AA was capable of putting in the 4th bet with hands other than aces).

      -PL

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