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math for sng push or fold

  • 3 replies
    • gadget51
      Joined: 23.06.2008 Posts: 5,622
      Hi there kantaki, welcome to the forums, Ihope you are well?

      I have moved this to the SnG beginers forum for you, it may get a more appropriate response there ok?


    • pzhon
      Joined: 17.06.2010 Posts: 1,151
      My program ICM Explorer does a lot of the calculations needed to decide whether to push or to fold. It uses the Independent Chip Model (ICM), a commonly used tournament equity model to evaluate the possible results of the hand.

      The easiest decisions are whether to call all-in when you are last to act and there is only one other player in the pot. Use the "Call Push?" button in ICM Explorer. For example, with 4 equal stacks of 3375 on the bubble of a 50-30-20 SNG with blinds of 200/400, if the SB pushes and you are in the big blind, this is the result from ICM Explorer:

      Fold: 2975 chips, 0.2303, SD: $16.36
      Win: 6750 chips, 0.3833
      Lose: 0 chips, 0
      Tie: 3375 chips, 0.25

      Equity needed: 60.07%
      Chip odds: 44.07%
      Risk premium: 16%
      Chips gained by marginal call: 1079.7.
      Ties count as 65.22% of a win.
      SD of marginal call: $18.9.

      You can ignore the standard deviation (SD) information, and the chips won by a marginal call. The most relevant result is that you want 60.07% equity against the pusher's range to call. Although you are getting pot odds of about 5:4, you are really risking about 1.5 times as much as the reward, so you need to be about a 3:2 favorite for calling to gain equity.

      You have to figure out your opponent's rage to determine which hands have 60% equity. That's not just mathematics.

      When you are deciding whether to push, you can use the "Semi-bluff?" button in ICM Explorer. If you set how often you will get called, you can see how much equity you need when you are called. If you set your equity when called, you can see how many calls are acceptable. If you set both, you can see how much equity pushing gains or loses over folding.

      Possible multiway situations are more complicated. There are Nash equilibrium calculators such as ICM Trainer and which use numerical approximations to estimate the game-theoretically optimal strategy, and if you can predict how your opponents deviate then you can use SNG Wizard to estimate what range to push and how much pushing a particular hand gains or loses.
    • kantaki
      Joined: 27.03.2010 Posts: 2
      thanks but iam not sure if i understand everything correctly, lets make an example:

      Ev is calculated with ICM
      1000 $ prizepool
      4 Players left payout strucutre is 50 30 20.
      Player1 2000 chips 202$ EV
      Hero 5000 chips 322 $ EV
      Player2 7000 chips 366$ EV
      Player3 1000 chips 108$ EV

      Player 1 BB Hero SB

      now i calc the EV difference for the BB and SB

      If Hero would push

      and player 1 would win :

      Player1 4000 chips 288 $ EV
      Hero 3000 chips 249 $ EV

      Player2 7000 chips
      Player3 1000 chips

      If hero wins

      Player1 0 chips 0$ EV
      Hero 7000 chips 384 $ EV

      Player2 7000 chips
      Player3 1000 chips

      this would give each player a EV difference of :

      If hero would push and BB would call (co bu fold)
      Hero -73$ / + 63$ (SB)
      Player1 -202 $ / + 86$ (BB)

      so Player1 needs atleast (202/288) 70% win to make a profitable call.

      but 70% win against what range ?

      if i (hero) would push with 100% (any two cards) he could only call with : 99+ AKs (0.8% Range)

      But this is only against 100% range. so if i want an accurate result i need to give my enemy my pushing range. but to calculate my pushing range i need to get his calling range :/

      maybe u can give me an example based on my example.

      How would you set the villains calling range ?
      How would you set the hero's pushing range ?

      my idea is that i could use some existing handcharts as a base for my calculations, but iam not sure how accurate this will be.


      i think i have a pretty good idea how to calc the pushing range.
      i just set my Pushing range to 100% than i calc the calling range for my villains based on the 100%, than i could calc my pushing range because i have the calling ranges from my villains. and i do this as often as my pushing range ~ epsilon.

      i think this could be a relativ exact aproximation. ill compare my results in sng wiz very soon and let you know.