[NL2-NL10] Trouble understanding bluff equation

    • Tim64
      Tim64
      Black
      Joined: 02.11.2008 Posts: 7,401
      Hi,

      This is taken from the SSS article on Donk Bets and Bluffs in gold:

      Opponents' bluffs

      Every opponent has his own way of bluffing and semi-bluffing. A tight opponent will rarely bluff, whereas looser and more aggressive opponents will certainly do so often.

      If you can figure out when your opponent bluffs you'll be in a dream come true. You can play according to hand ranges without running into any big problems. If not, you will have to use average values.

      In general you can assume that an opponent will bluff 10% of the time. Tight opponents, and those who have you under observation, will bluff less. You can give aggressive opponents the full 10% and, with the right read, even more.

      To take bluff frequency into account you simply determine your average winnings against bluffs (you will usually be ahead 3:1) and put it into the formula.

      EV = FE * Pot + (100% - FE + Bluffs) * [Equity * Total Pot - Costs] + Bluff * [Equity * Total Pot - Costs]

      Your call range is reduced by the same amount you believe to be your opponent's bluff frequency. ***


      I'm having a bit of trouble understanding this and wonder if anyone can shed some light?

      So far, 'translating' the equation, I have somthing like this:

      "EV = (percentage of time our opponent folds and we win the pot outright) plus percentage of time our opponent doesn’t fold plus [amount of times he bluffs] X chance of winning pot less costs PLUS percentage of times he bluffs X chance of winning pot less costs

      My first question is: shouldn't one of these be "percentage of times he 'DOESNT' bluff"? If so, which?

      Second, if our opponent doesn't fold and we have to contest the pot, presumably we have much better equity (chance of winnng) in those cases (10% or whatever) that he is bluffing than where he isn't? Where is this dealt with in the equation, please?

      Finally, I don't understand why it says our call range is 'reduced' by the amount of opponent's bet frquency. If we believe our opponent bluffs 10% of the time, shouldn't we be calling 10% more often. If it's refering to hand range, then shouldn't we call 10% wider to account for that bluff percentage?

      Any help greatly appreciated,
      Tim
  • 8 replies
    • Nunki
      Nunki
      Bronze
      Joined: 25.10.2006 Posts: 865
      Originally posted by Tim64

      Opponents' bluffs


      EV = FE * Pot + (100% - FE + Bluffs) * [Equity * Total Pot - Costs] + Bluff * [Equity * Total Pot - Costs]




      I'm having a bit of trouble understanding this and wonder if anyone can shed some light?



      EV = FE * Pot + (100% - FE - Bluffs) * [Equity1 * Total Pot - Costs] + Bluff * [Equity2 * Total Pot - Costs]

      where Equity2 = 25%. Note the change of sign of the second "+" in the original equation.
    • dandycal
      dandycal
      Bronze
      Joined: 10.10.2008 Posts: 1,711
      Hi there Tim,

      The change of the second + sign that nunki mentioned I think relates to this:

      EV = FE*Pot + (100% - FE + bluffs) <<< this is actually miswritten - I reported the mistake already.

      It should be (100% - FE - bluffs) or [100% - (FE+bluffs)]. As it means the % of times you are called by the opponent when he is not bluffing. I believe that was your first question.

      Second. This is dealt with in the last part of the equation, if I'm not wrong: Bluff * [Equity * Total Pot - Costs]. That's your profit in the % of times your opponent is bluffing. There your equity will surely be higher.

      The third one also got me a bit confused. I'll take the opportunity to read the article again and see if I understand it.

      Hope this is helpful.


      EDIT: It also seems to me that our calling range should be increased by the same amount we believe to be our opponent's bluff frequency.

      Perhaps another mistake? Let's see if someone else can help us out.
    • burek2000
      burek2000
      Bronze
      Joined: 16.11.2007 Posts: 3,105
      Hey Tim64,

      I'll try to unchain the equation.

      EV=

      FE*Pot

      ...this are the winnings you win every time your opponent folds due to fold equity.

      +(100% - [FE + Bluffs])*(Equity*Total Pot - Costs)

      ...I've bold the brackets that are missing in the original equation. The first part here tells us what are our winnings when our opponent doesn't fold and doesn't bluff. Therefore the Equity here is Equity against his non-bluff hand range. And Total Pot is the pot we can win and Costs is the money we need to invest in order to stay in the pot.

      +Bluffs*(Equity*Total Pot - Costs)

      ...this last part deals with the times our opponent bluffs us. Bluffs here mean actually bluffing frequency which should be ~10% according to the article. Equity is not the same equity as in the last part, but this equity is the equity we have against our opponent's bluffing range which should be ~25% according to the articles. And Total Pot and Costs are same as in previous part.

      Another thing... ..."Your call range is reduced by the same amount you believe to be your opponent's bluff frequency."... ...this actually means:"Your call range is reduced by the same amount you believe to be your opponent's bluff frequency reduced." ...meaning your calling range and opponent's bluff frequency increase/decrease linear.

      I hope this helps.

      Regards,
      burek2000
    • Tim64
      Tim64
      Black
      Joined: 02.11.2008 Posts: 7,401
      Hi all and thanks to Nunki, Dandycal and Burek2000 for the helpful responses.

      I understand the first part of the equation now: what's needed is either brackets around the 'FE + Bluffs' or for it to be written '100% - FE - bluffs'.

      I assume someone can arrange for the article to be fixed?

      And I think I understand the last part of the equation now, which sets out that small additional amount we can add on where opponent is bluffing and we are therefore ahead.

      But I'm still not clear on the last point.
      Another thing... ..."Your call range is reduced by the same amount you believe to be your opponent's bluff frequency."... ...this actually means:"Your call range is reduced by the same amount you believe to be your opponent's bluff frequency reduced." ...meaning your calling range and opponent's bluff frequency increase/decrease linear.


      It seems to me the following must be true: the less often your opponent bluffs, the better hand you need to call his donkbet/reraise. So, for example, if you raise with A :heart: Q :diamond: from BU and get called by MP3 and flop is K :club: 4 :spade: 8 :diamond: and MP3 re-raises your c-bet you have to ask yourself how often your opponent bluffs. If he rarely bluffs then in most cases he will hold a K and you can comfortably fold. If he often bluffs then you may well still be ahead and can consider pushing over the top.

      But I'm not sure how this relates to our 'call range', since we have an actual hand and don't need to think about our range. To put it another way, how would it help me to know that this particular opponents bluffs approximately 10% of the time?

      If you know he bluffs 10% of the time, are you saying that our call range reduces to 10% (i.e. the top 10% of hands)? or that it reduces by 10% from what it otherwise would have been? Can you give me a practical example to help me understand how it works?

      Finally, just to make sure I understand, what exactly do we mean by a bluff in this article? In my example, if villain has
      3 :spade: 4 :spade: he also has us beat here since he has a pair. But I'm not sure if this counts as a bluff? So, is a bluff: a) where opponent has complete air and is merely representing some better hand (e.g. K,J in our example); or b) where he has a part of the flop but would be beaten by many better hands which he is trying to get to fold by betting?

      TIA
      Tim
    • dandycal
      dandycal
      Bronze
      Joined: 10.10.2008 Posts: 1,711
      Hi Tim,

      I think Burek said pretty much the same thing that you are saying about the bluff frequency.

      Our call range is reduced by the same amount you believe your opponent's bluff frequency to be reduced - or rather, to have been reduced.

      So I understand that if we believe our opponent has reduced his bluff frequency, then we reduce our calling range. Whereas if he increases his bluff frequency, we can increase our calling range. It is as you said, the less often he bluffs, the better our hand must be. The article apparently need some editing. I already submited a report about the first equation (though they haven't fixed it yet) and will submit a report about the sentence we are talking about.

      Regarding the bluff, I think both options A and B you mentioned could qualify as a bluff, but mainly the situations when he has air or when he is betting draws (semi-bluff).
    • Tim64
      Tim64
      Black
      Joined: 02.11.2008 Posts: 7,401
      Ahhhhhhhh.

      Great - that makes much more sense. So we are saying that, if the same opponent, after 1000 more hands seems to be bluffing 10% less than he used to, we now need a 10% better hand - on average - to call with.

      This makes sense in principle though in practice it's hard to imagine how we can assess whether someone bluffs more frequently or less frequently than before. The only way to catch someone in a bluff is to call them and see their cards, after which it's too late...

      I suppose you can watch their play against other opponents but even this isn't perfect since a thinking player will probably bluff more often against a tight opponent than against a calling station so villain may well bluff more against tight SSS'ers like us than against looser players. ;(

      In any case, many thanks all for clarifying this tricky article for me :f_grin:
    • burek2000
      burek2000
      Bronze
      Joined: 16.11.2007 Posts: 3,105
      Thank you, dandycal, for clarifying my post. I hope everything is clear now.

      Considering what bluff is, bluff is a bet with intention to make better hands than yours fold, no matter what you have.

      Regards,
      burek2000
    • Tim64
      Tim64
      Black
      Joined: 02.11.2008 Posts: 7,401
      Cheers Burek2000,

      Nice and clear now - thanks for explaining about the nature of a bluff.

      Tim