Master's degree in Equities

    • Kyyberi
      Kyyberi
      Coach
      Coach
      Joined: 09.07.2010 Posts: 10,511
      As most of the PLO studets are eagerly learning how to count equities, here is your final exam:

      PLO100 with blinds of 1/1

      Hero 100
      Villain 100

      Hero is in button with AAxx.

      Hero raises to 4, villain raises to 12, hero raises to 36, villain calls.

      Now the pot is 72 and both have 64 left in stack.

      Whatever the flop is, villain is going to check. And hero decided to shove any flop. Villain will call if his equity against range of AAxx is good enough to justify that call.

      What is the $EV for hero in this hand when he 4bets? Following things are true:

      Villain will call 100% of time. His range is top 25%, EXCLUDING aces.

      So you need to come up with a $ amount for hero. Please do not post how you calculated that, as it takes away the learning process of others. Just post your answer.

      Hint: http://www.propokertools.com/simulations

      When you can calculate this, you have earned the Master's degree in Equities. :)
  • 13 replies
    • Hortberg
      Hortberg
      Bronze
      Joined: 16.07.2009 Posts: 694
      +24$
    • VisuLatvijai
      VisuLatvijai
      Bronze
      Joined: 15.02.2007 Posts: 255
      Approximately +41.5$ :f_confused:
    • Leito99
      Leito99
      Bronze
      Joined: 27.07.2009 Posts: 754
      +$16
    • Waiboy
      Waiboy
      Bronze
      Joined: 18.09.2008 Posts: 4,877
      I guess this explains the ~1k replies in the skype channel? I'll have to fetch my reading glasses and comfy chair for this catchup.

      Will have to put in some study and answer later.

      Needless to say this thread is pure Finnish rock IMHO.
    • Kyyberi
      Kyyberi
      Coach
      Coach
      Joined: 09.07.2010 Posts: 10,511
      Actually we had big conversation about few hands, equities and pot odds in skype group. It's a looooong conversation, but if someone has problems with those I suggest that discussion. If someone has spare time he could edit it a little, to take all the non-necessary things out. :)
    • Ribbo
      Ribbo
      Bronze
      Joined: 25.06.2010 Posts: 6,157
      about tree fiddy equity.

      GL everyone working it out. :D
    • Jackalof
      Jackalof
      Bronze
      Joined: 08.06.2008 Posts: 1,462
      I call any non paired flop. Easy.
    • Kyyberi
      Kyyberi
      Coach
      Coach
      Joined: 09.07.2010 Posts: 10,511
      Originally posted by Jackalof
      I call any non paired flop. Easy.
      Not what asked :)

      Question was: what is the $EV for hero to make 4bet and shove all flops?
    • Kyyberi
      Kyyberi
      Coach
      Coach
      Joined: 09.07.2010 Posts: 10,511
      Ok, here it is:

      As hero is committing himself to play with his stack in every flop, there are two possible outcomes. Either villain folds the flop or not.

      Let's look at the EV when villain folds the flop:

      Hero is 4betting with 32 more, and he is going to win a pot of 72. So the EV is +$40.

      That was easy. :)

      The trickier part is to determine

      a) how often the villain hits the board
      b) what is his average equity when he hits

      In order to play with his stack villain needs 32% equity on flop (pot odds). Now as we know both player's ranges, we can use propokertools to calculate it. You can play with that PQL stuff, but the easier way is to use Oracle. Here is the thing.

      To get top 25% range, we simply type 25%. To exclude aces, we add ! AA** (these commands/syntax can be found at the website). So villain's range is 25% ! AA**. Hero's range was AA**.


      That shows how easy it is to calculate that for 35% equity. In Oracle you can't calculate for 32%, so I clicked on that "show PQL", copied the text, pasted it to PQL section in propokertools.com and changed the value to 32.

      It gives the answer, 44,5% of time.

      So now we know that hero will win the pot on flop 55,5% of times. 44,5% of times villain will call the shove.

      Now villain will not have 32% equity on flop usually. He has a lot more. So we need to figure out what would be his average equity, when he hits the flop for at least that 32% equity.

      Sounds complicated, but with Oracle and propokertools it's pretty simple.



      Again we have to copy that PQL commands to http://www.propokertools.com/pql and see what the result is.

      The result is average equity of 58%.

      So now we know that those times that hero is called on flop, he has 42% equity.

      Now we need to calculate hero's EV for those situations. Hero 4bets preflop 32, and 64 on flop to win a pot of 200. Now hero's equity share of that pot is 200 x 42% which is 84. Hero bets 96 to win 84. EV is actually -$12.

      So here is the conclusion:

      55,5% of times hero's EV is +$40.
      44,5% of times hero's EV is -$12.

      That gives the total EV of +$16,9.


      Now is this important at all?

      Well, in my opinion it is. Lots of players are wondering in 3bet/4bet pots what to do. Yeah, it is easy to play that QJT9ds when someone 4bets, but what about some more marginal spots? What is the needed SPR to justify a call with KKQT?

      When player calculates that stuff himself, he begins to understand how the game works. Like in this, how many of you would have thought that to 4bet aces that way is actually just +17bb in the long run. I am sure that most of you thought that it would make bigger winnings in the long run. Now comes the question, why are we 4betting aces and risk our stack for such a small winnings? I know it, do you? ;)

      Should I be able to do all this kungfu in the middle of the hand?

      Well, if you can it would be awesome. Although I don't think there are many people in the world who can do it. Let alone some of those freaks would actually play poker. But if you roll these situations and numbers around for a while, you will begin to understand how different hands work in different situations. And how the stack sizes affect the outcome etc. It's like with pot odds and equities. They seem superhard in the beginning. I struggled 6 months with simple pot odds and equities. I tried to learn it from the books, and they all explained it with mathematical terms and formulas. And I thought that I would never understand them. But now, couple of years later, they just pop to my head. Don't even need to calculate and think them that much in most common situations.

      Same thing here. When you do the calculations for different types of hands, you will realize what hands are better in calling and what hands should be folded. And you will see what the SPR should be for certain types of hands to justify preflop call etc.

      And last, but not least. This is pure and boring math. Even if you calculate this sh*t for years, you won't be a good poker player. Sit&go's, tournaments and shallow holdem are coming to a point where it is all about math. 1 table sit&go's are pure math for serious players. They just tune their ranges against other regulars all day long, to get that tiny edge. Like one German pro, he used to play for 3 hours a day and use 6 hours a day to study other players and adjust his ranges. In my mind that is sick stuff.

      PLO is such a game that it won't be mathematically "cracked". So many variables that it's very hard to play game theory optimal in plo. So it's a lot more than math. But still, the game is purely based on math. Even your reads, intuition, feng shui and stuff has mathematical value in your head. When you think "hmm, is he bluffing or not" your mind is comparing the odds in your head. You might just not know it. So the more you understand about math, the better foundation you have.

      I mean, there are winning players in PLO1K that don't really know the math behind situation described here. I have seen them wondering "that guy 4bet me, he has aces. Hmm... Should I call with this hand or not? I don't know if it's profitable or not, maybe I should learn it someday". And this is true story. There are very talented players, who might be even better if they learned the basic math stuff needed in PLO.

      UGH.

      P.S. Another way to get the average equity for villain is to use the graphs in propokertools. But that's too complicated for me :)
    • Kyyberi
      Kyyberi
      Coach
      Coach
      Joined: 09.07.2010 Posts: 10,511
      Interesting thing is that if we calculate the EV for villain, it gives this:

      55,5% of times he loses 24.

      44,5 of times he bets 88 to win 116, so EV is 28.

      His EV for the hand is 13,32 + 12,46 = +$25,8

      So both players have +EV, that means that both players are making profit in the long run. How is this possible?

      We start to calculate things from the point where villain 3bets. This shows that in omaha there are tons of situations where the stacks just go in and no one makes any mistakes. And in the long run this is not where you are making your winnings. In there situations only the house wins in the long run (if we assume that 3bet is always a good play).

      edit: as mentioned later, I made a silly mistake here. 55,5% opponent LOSES, which leads to this:

      His EV for the hand is -13,32 + 12,46 = -$0,86
    • Kyyberi
      Kyyberi
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      Joined: 09.07.2010 Posts: 10,511
      Bumping this up, so it won't get lost in the graveyard.
    • IhasLuck
      IhasLuck
      Bronze
      Joined: 07.05.2010 Posts: 326
      Originally posted by Kyyberi
      Interesting thing is that if we calculate the EV for villain, it gives this:

      55,5% of times he loses 24.

      44,5 of times he bets 88 to win 116, so EV is 28.

      His EV for the hand is 13,32 + 12,46 = +$25,8

      So both players have +EV, that means that both players are making profit in the long run. How is this possible?
      55,5% of times he loses 24. this means its ev is -13.32

      There's a problem actually.. it should be -13,32 + 12,46 = -$0.86
      Op is losing money if he calls the 4bet and calls the shove if he has enough equity on flop. This strategy is unprofitable :f_biggrin:
      he needs a stronger range
    • Kyyberi
      Kyyberi
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      Coach
      Joined: 09.07.2010 Posts: 10,511
      Well mistake is small, but effect on the outcome is big. Thanks for noticing.