When and if should we deviate from correct icm play?

    • Luupainaja
      Luupainaja
      Bronze
      Joined: 16.03.2010 Posts: 1,148
      Hi!

      Most of us use SNGWizard to see if we can call an all in or push in push-or-fold-mode. We adjust the ranges and see if the edge we got is neg or pos. But should we sometimes deviate from the wizard suggestions, that is, should we sometimes deviate from "correct" icm play, i. e make an -ev play or skip an +ev move in that certain situation. The main argument is that sometimes its better to make such plays because those deviations from icm open up opportunities in future situations which compensate the lost or missed equity.

      One of those theories is presented by 2+2 superstar Gigabet in his Gigabet Dilemma or Gigablock Theory (a post from Gigabet himself: http://archives1.twoplustwo.com/showflat.php?Cat=0&Number=2610396&page=0&fpart=1&vc=1, this post is pretty hard to grasp, but he def has something). The theory basically claims that sometimes its good to make -ev play to get a chance to have a greater edge on future hands. For example, when you're one of the bigstack with other 2-3 players (belonging to the same stacksize "block" with those players), then you cannot benefit from the situation as much as you could when you'd have enough more chips than they to haul yourself up to higher stacksize block. So it might be profitable to take an -ev shot against shortstacks in case when losing that confrontation doesnt increase the stacks difference between you and other bigstacks significantly, but winning that confrontation opens you to an opportunity to get a runaway chiplead.

      I think it's a valid point, but is there some more solid justifications for deviating from "correct" icm play and for giving up an edge sometimes? Some claim that you should never give up an edge, that you should take every +ev move you can. In what follows, I'll try to show mathematically, that sometimes you should skip +ev play.

      Here's a situation from 9-man 10$+1$ hyper turbo stt with 10bb starting stacks. Its a first hand, everyone folds to BU who pushes exactly 30%.



      It seems that hero should call here with A7s. Hero's edge is 0.18%, which means that calling should increase expected winnings by 0.162$ (90$*0.0018) on average. So should hero make this call?

      Let's see, what's the A7s equity vs wiz 30% range (22+, Ax+, K4s+, K8+, Q9s+, K8+, QJ, JTs):
      %win = 49.73%, %lose = 50.27% (ignoring ties)

      50.27% of times hero busts for 0.162$ and 49.73% of times hero doubles with expected winnings of X$ + 0.162$ where X$ is expected winnings after doubling up. Lets take hero's ROI 10% and lets assume for now that doubling up doesnt increase hero's ROI. So X$ = 11$*0.1 = 1.1$

      So the expected winnings if hero makes the call:
      0.5027*0.162$ + 0.4973*(1.1$+0.162$) = 0.70903$

      BUT if hero does NOT make the call, his expected winnings with 10% ROI are 1.1$ (!)

      In order to this call to be profitable we must assume that hero's ROI is not the same after calling, but has increased due to bigger stacksize which gives him advantage in future situations. Exactly how much hero's ROI has to increase to make this call?

      We simply have to solve the following equation:
      0.5027*0.162$ + 0.4973*(X$+0.162) = 1.1$
      X$ = 1.886

      So hero's ROI has to increase around 1.7 (1.886/1.1) times. If hero is a good player and he feels that his edge increases at least that much over the field, then he should make this call. Otherwise it should be a fold.

      Its plausible that hero's ROI increases after doubling up, but that kind of a supports the argument in the beginning of this post: we cannot only take into account hero's direct expected value in a given situation provided by SNGWizard, but we have to consider future opportunities aswell (for example, believing that bigger stack will increase our edge in future hands (i e our ROI)). Those considerations should make us sometimes skip +ev play or take a -ev shot. Now, the real question is, how to recognize those spots in a game?

      Some good reading on the subject:

      http://forumserver.twoplustwo.com/36/stt-strategy/3-5k-post-edge-really-edge-743669/

      http://forumserver.twoplustwo.com/36/stt-strategy/minimum-edge-theory-100959/

      So what do you think, if and when should we deviate from wizard suggestions (assuming that we manage to insert correct ranges obv)?

      Any comments are much appreciated.
  • 3 replies
    • pzhon
      pzhon
      Bronze
      Joined: 17.06.2010 Posts: 1,151
      I was a critic of Gigabet's theory when he came out with it. You should know that Gigabet at that time was viewed by many as a poker guru or genius, but he later ran into a lot of trouble. He backed out of a big prop bet and went negative according to Sharkscope (while games were still much softer than they are now). Now, this doesn't mean he is definitely a losing player, or that he is wrong about his very controversial theory. However, you should be more skeptical than many of the people responding in those very old threads.

      Getting knocked out of a tournament is very vivid. The difference between your starting stack and a double stack is not as vivid. As a result, there are many people who greatly underestimate the value of doubling up early, just because it isn't obvious how much that improves your chance to make it into the money or to win the tournament. (According to the ICM, doubling up in a 9-player 50-30-20 tournament increases your equity by about 82%, ignoring dead money. In a MTT, doubling up early usually adds over 90% to the value of your stack.) I think Gigabet makes a similar mistake when he says that in some situations, there is no difference between having 3000 and 4000 chips, so he feels free to waste 1000 chips on very bad gambles trying to get more. There are a lot of times when you gain or lose a few chips at a time, or you double up against a big stack or lose to a short stack, and those extra 1000 chips will come into play.

      The ICM is not the end of the story, but it's a great model which has made a lot of professional poker players their livings for years. If you change it, you need to be confident that you are improving it, not just changing it for the sake of change.

      ------------

      Now, about your specific calculation: I don't know why you are assuming your ROI is 10% in a hyper turbo, but it shouldn't still be 10% after you lose the big blind and have 270 chips instead of the starting 300. Folding is not worth 1.1 buy-ins.

      I have no idea where you are getting the 0.18% edge. This is highly questionable and seems to be leading you to very strange conclusions... you need to be very confident of it, then. Where do you get this?

      How are you getting that busting out is worth $0.162 instead of $0? Are you giving some value to getting knocked out of the tournament early or something? You gain an advantage by making good decisions in the tournament, not by turning down larger and larger edges.

      lets assume for now that doubling up doesnt increase hero's ROI
      This strikes me as a terrible assumption. You have to have a huge advantage over your opponents to have a 10% ROI in a hyper turbo despite the rake. Doubling up should not end your incredibly large skill advantage. Why would calling now force you to play so much worse later?

      At this point I'll just wait for you to clarify what you mean because your calculations don't make sense to me.
    • Luupainaja
      Luupainaja
      Bronze
      Joined: 16.03.2010 Posts: 1,148
      Originally posted by pzhon
      Now, about your specific calculation: I don't know why you are assuming your ROI is 10% in a hyper turbo, but it shouldn't still be 10% after you lose the big blind and have 270 chips instead of the starting 300. Folding is not worth 1.1 buy-ins.

      I have no idea where you are getting the 0.18% edge. This is highly questionable and seems to be leading you to very strange conclusions... you need to be very confident of it, then. Where do you get this?

      How are you getting that busting out is worth $0.162 instead of $0? Are you giving some value to getting knocked out of the tournament early or something? You gain an advantage by making good decisions in the tournament, not by turning down larger and larger edges.

      lets assume for now that doubling up doesnt increase hero's ROI
      This strikes me as a terrible assumption. You have to have a huge advantage over your opponents to have a 10% ROI in a hyper turbo despite the rake. Doubling up should not end your incredibly large skill advantage. Why would calling now force you to play so much worse later?

      At this point I'll just wait for you to clarify what you mean because your calculations don't make sense to me.
      Thank you for your answer.

      By 0.18% i just meant how much should hero's expected winnings increase according to icm if hero makes the call. Thats basically wizard's Diff%. I calculated it manually aswell:

      ICM calculator:
      EVfold = 0.1011
      EVwin = 0.2068
      EVlose = 0
      %edge = %win*EVwin + %lose*EVlose - EVfold = 0.00174164 = 0.17%

      0.01% difference is probably due to rounding off.

      Yes, your're right, ROI will not remain the same after losing BB, but we might aswell assume that our ROI will be 10% after losing 1BB and its not important what it was before.

      And you're also right that giving some value for busting out is dubious. Hence, the expected winnings if hero makes the call are probably even less.

      However, that doesnt change my core point. Of course i dont think that doubling up doesnt increase ROI, i was just making this assumption to illustrate the point that not only that ROI increases after doubling up but ROI increasing to a certain amount is NECESSARY CONDITION to make this call. So, the question was how much SHOULD MY ROI INCREASE IN CASE OF DOUBLING UP FOR THIS CALL TO BE PROFITABLE (for this necessary condition to be met). I made the same calculations again, this time taking busting out worth 0$ and ROI after folding (and losing 1bb) 5% (which is just an example, i dont have a clue whats a good ROI in hyper turbos, i dont play those):

      0$ + 0.4973*(X$+0.162) = 11$*0.05 = 0.55$
      X$ = 0.94397

      So hero's ROI should increase around 0.94/0.55=1.7 times after doubling up to make this call compared to folding. And my point with that was and is we cannot just look at the wizards diff% and make a decision, we have to think about future opportunities which different options open to us. If you think that your bigger stack advantage is big enough, make the call, but you should fold if you think that winning this coinflip doesnt increase your edge enough which might be quite big already due to the extremly soft field and thus forces you to wait better spots.
    • pzhon
      pzhon
      Bronze
      Joined: 17.06.2010 Posts: 1,151
      Originally posted by Luupainaja
      By 0.18% i just meant how much should hero's expected winnings increase according to icm if hero makes the call. Thats basically wizard's Diff%.
      Ah, I thought it was something like the minimum edge %. So, your 0.18% value is based on the particular hand against this particular range, A7s vs a 30% range, and you would have a different value if you gave yourself a different hand. You can't take this edge % to make a general statement about the equity you need with other hands.

      Suppose I have KQo in the big blind and am considering calling all-in aginst a 40% button push. How much equity do I need? You have calculated one number with A7s vs a 30% range. You would get another number with A5o vs a 15% range, and another with 88 vs. a 50% range. Do I need 3 different equities with KQo against the same 40% range, depending on which hand you chose to evaluate first?

      You used the edge% to evaluate busting out of the tournament as worth $0.162 instead of $0. This still makes no sense to me. You are going to get a different value if you give the hero AKs. Is busting out on the first hand with AKs worth much more than busting out with A7s? Not to me.

      Yes, your're right, ROI will not remain the same after losing BB, but we might aswell assume that our ROI will be 10% after losing 1BB and its not important what it was before.
      We often push 10 bb to try to steal 1.5 bb because 1.5 bb is worth risking our stack. You can't neglect the value of 1 bb. If you assume that losing 10% of your stack doesn't hurt, you are not doing a serious or careful analysis. It is a very strange assumption that you can expect to win 1.1 buy-ins in a hyper turbo when the ICM says your fair share of the prize pool is about 0.83 buy-ins.

      By the way, it's not at all clear what you mean by your ROI after doubling up. ROI means return on investment, and it's not clear what to take as your investment or return when you are evaluating a possibility which doesn't happen 100% of the time. Nevertheless, if you assume that you are one of the best poker players in the world with an astoundingly large advantage in a hyper turbo with equal stacks, you should also assume that you have at least some skill advantage over your opponents after you double up. If you don't, then of course you will require a huge edge in this hand in order to risk giving up your amazingly large skill advantage. This can be used to rationalize all sorts of bad plays which decrease or eliminate any advantage you might have had.