Equity question - need calc help

    • gavinonymous
      gavinonymous
      Bronze
      Joined: 18.12.2008 Posts: 1,146
      Hi, I'm trying to figure out a general equation for how much I should bet X when opponent folds Y% times and I have Z% equity on the flop. I also want to solve this equation for all X and Y and see what a graph looks like.


      First, is it even possible to do, and second what is the math for the first part. Not sure if I have this right.

      Suppose I have K Q in BB against a BU open range, I call pf and flop comes 4 9 J

      Now I decide to donkbet semibluff my two overs and I estimate my opponent will fold 50% of his hands - so I should bet pot if I only considered fold equity - to make a better hand fold (maybe small pockets or missed AK with no hearts) or take down the pot right away.

      I also have a fair bit of equity on the flop maybe 41% according to Equilab, so I don't need to bet full pot, my semi bluff is part value, part bluff?

      so I have

      EV(folds) + EV(calls)

      say the pot is P$ and my bet is X$

      my equity if folds is 100%

      my equity if calls is 41%

      if folds I win $P? or $1/2P??

      if calls I win P$ + X$ (or 1/2P$ +X$?) profit 41% of the time and lose same amount 59% of the time (assuming no turn and river action - maybe this is where the math breaks down..)

      so my EV on flop (no turn and river)

      50% X (P$) + 41% X (P$ + X$) - 59%(P$+X$+)

      = 0.5P + 0.41P + 0.41X - 0.59P - 0.59X

      = 0.32P - 0.18X

      for a pot of $16 and a bet of 10$

      P= $10.00 ($16 minus my say 6$ contribution)

      = $3.20 - $1.80 = $1.40

      so with 50% fold equity and 41% equity a 2/3 pot bet is worth $1.40

      if my fold equity was instead 30% and my bet was the same my bet would be worth

      = 0.12P - 0.18X

      = $1.20 - $1.80 = - $0.60, not a great bet equity wise, but our EV could improve or worsen on the turn and we might get more action - so maybe it's not even worth doing the math and plotting the surfaces?

      thanks for reading even if you don't respond. thinking on a thread helps me figure this stuff out.
  • 6 replies
    • gavinonymous
      gavinonymous
      Bronze
      Joined: 18.12.2008 Posts: 1,146
      I guess to start my range is off, since they are folding 50% of hands they open raise - their range of called hands tightens and my equity is less..so how to figure this in the equation!
    • MatejM47
      MatejM47
      Black
      Joined: 21.01.2010 Posts: 1,193
      The problem is that whenever you get called here your equity will be around 25% not 41%. Other then that your calculations seem to be fine.

      If the pot on the flop is 10$ and you bet pot into it assuming he folds 50% of the time you will win 10$ half the time. Half the time you do get called you will lose 7.5$ considering you have 25% equity. So on avreage you will win 2.5$ doing this move if there is no more action on turn and river.

      Generally gutshots and stuff like that are better to bluff with then air type hands or stronger hands like OESD since you can easily fold it if you get raised, and if he is slowplaying something then your implied odds are great when ever you do hit your gutter that gives you extra 10% equity to your bluff. How ever you can't go crazy when ever you hit a K or a Q since you might eaisly be dominated by AK,AQ, KJ QJ type of hands and it will be hard to pot control OOP. Personally i prefer to C/R this type of hands since many players consider donks weak and will raise you more often then not.
    • Kruppe
      Kruppe
      Black
      Joined: 20.02.2008 Posts: 2,144
      why would you want to do that?

      i'm afraid pretty much every statement or assumption you make is full of holes, i don't even know where to start
    • alexgeor
      alexgeor
      Bronze
      Joined: 22.01.2010 Posts: 56
      Before engaging in ev calc:

      You dont bluff on this board
    • gavinonymous
      gavinonymous
      Bronze
      Joined: 18.12.2008 Posts: 1,146
      Originally posted by Kruppe
      why would you want to do that?

      i'm afraid pretty much every statement or assumption you make is full of holes, i don't even know where to start
      Ok, this is a good start - the hand is just an example. It could be anything. Can you offer anything constructive?

      Basically I want to know how to calculate equity including fold equity and board equity. The assumptions are arbitrary, and probably wrong, but it's just for illustration.

      The equation eludes me.

      You have fold equity and equity on the board (in that example I used Equilab, so is Equilab wrong.. anyway it's immaterial) It is variable - I want to see how the variables changing affects bet size.

      Thanks if you can help, if not I'll keep working on it.
    • Kruppe
      Kruppe
      Black
      Joined: 20.02.2008 Posts: 2,144
      there's no equation, as the flop isn't the final betting round

      you just have to think about all the possible lines for you and villain on all possible turns and rivers...