Sklansky-Chubukov numbers

    • Tim64
      Tim64
      Black
      Joined: 02.11.2008 Posts: 7,401
      I've just read this Gold article and have a qn for you fellow shortstackers.

      The article says that it makes sense to use the Sklansky-Chubukov on the higher limits when our edge against the average low-limit player is no longer sufficient. The original numbers were based on NL200 but are mathematically valid for all limits, I believe.

      My qn is: at what limit should we begin to incorporate these pushes into our strategy? Only once we hit NL200 (not anytime soon for me :) ) or earlier?

      Second, does it not make you rather readable?

      TIA
  • 18 replies
    • xponentx
      xponentx
      Bronze
      Joined: 10.02.2008 Posts: 341
      In my experience of NL25 and NL50, I don't believe they are profitable on these limits. You'll just find that big stacks will call your push, especially when you're <13ish BB. My understanding of these numbers is that they assume a certain amount of fold equity, which I just don't think you get on these limits. I have seen a decent amount of solid players on NL50, but it's still about 50/50 with random fish. I think once you start to see a higher proportion of decent players, these pushes will become profitable. In fact, I would say if you keep an eye on the stats, you could probably use these on any limit provided the table has a low VPIP.
    • cyzo
      cyzo
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      Joined: 19.07.2008 Posts: 117
      Originally posted by xponentx
      In my experience of NL25 and NL50, I don't believe they are profitable on these limits. You'll just find that big stacks will call your push, especially when you're <13ish BB. My understanding of these numbers is that they assume a certain amount of fold equity, which I just don't think you get on these limits. I have seen a decent amount of solid players on NL50, but it's still about 50/50 with random fish. I think once you start to see a higher proportion of decent players, these pushes will become profitable. In fact, I would say if you keep an eye on the stats, you could probably use these on any limit provided the table has a low VPIP.
      The numbers assume a perfect opponent who can calculate equity instantly and, more importantly, knows your cards. Any hand that is a push according to the Sklansky-Chubukov numbers should be pushed rather than folded on every occasion at any limit. It is always +$EV. However, sometimes another more is more +$EV, such as raising with aces rather than shoving directly.

      That is my understanding of the article.
    • Tim64
      Tim64
      Black
      Joined: 02.11.2008 Posts: 7,401
      Thanks cyzo, my understanding also. Article did not seem to refer to fold equity. (Although of course, in practice, you will sometimes get the better hand to fold pf, because you do have fold equity sometimes.)

      The main change seems to be remembering not to rebuy when you hit 15BB - which I have been doing instinctively up til now...

      Cheers both of you - any other thoughts out there?
    • burek2000
      burek2000
      Bronze
      Joined: 16.11.2007 Posts: 3,105
      Hey guys,

      Originally posted by cyzo
      The numbers assume a perfect opponent who can calculate equity instantly and, more importantly, knows your cards. Any hand that is a push according to the Sklansky-Chubukov numbers should be pushed rather than folded on every occasion at any limit. It is always +$EV. However, sometimes another more is more +$EV, such as raising with aces rather than shoving directly.

      That is my understanding of the article.
      ...perfect understanding of the articles, cyzo. :f_thumbsup:

      Sklansky-Chubukov pushes are based on equity against random hand ranges of the players behind us and our stack size(from which we determine our odds to push). So, actually those pushes are +EV even if we show our hand to the opponent behind us and he can make a perfect play against us, meaning those pushes are profitable against any opponent on any limit, even more because most opponents won't play "perfect" against us.

      So, those pushes are good for some extra money, but not necessary on low limits, because you can get enough $$$ even without them, but would increase your profit if you did use them.

      Also, I like to use them against unknown opponents and against very loose opponents with hands that have bad playability postflop, because against known (tight) opponents or hands with good playability postflop it's better to make a standard raise, because that way you can extract more value than with Sklansky pushes themselves alone.

      And about being readable... ...of course opponents who know Sklansky pushing ranges can adjust their play to almost perfect against us, but since those pushes are +EV even against opponent who plays perfect you don't have to worry about being readable.

      In case I forgot something just ask away...

      Regards,
      burek2000
    • TheBu11d0g
      TheBu11d0g
      Bronze
      Joined: 25.07.2008 Posts: 2,019
      Moved to No Limit Strategy Discussion

      Kind Regards,
      -Steve
    • Tim64
      Tim64
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      Joined: 02.11.2008 Posts: 7,401
      Great - thanks for all the responses, guys.

      Tim
    • dextart
      dextart
      Bronze
      Joined: 03.10.2008 Posts: 22
      Just my 2 cents:

      Everything that has been said above is indeed very true (except for the pushes assuming fold equity to be profitable, which is not the case of course)...

      However, I was also wondering about the way different limits and players could influence the amount of +EV one can extract by utilizing purely Sklansky-Chubukov based pushes, so I did some calculations, assuming 20BB as well as sitting in SB:

      1. Our hand range for S-CH push with 20BB is ~25%.
      2. Our EV for the push, as well as variance, depends solely on the percentage of times our opponent will choose to call us.
      3. If opponent in BB never calls, our EV = 1.5BB with zero variance, which is ideal.
      4. With BB calling with a wider range, our EV decreases, but only down to 0.8BB at 15% calling range. Up from there, it only increases at the expense of our opposition.
      5. If our opponent perfectly adapts to our range, however, he should only call us with a range of up to 9%, depending on his preference for variance. After that, only the poker room profits. His EV @ 9% calling range is a meager 3.43BB, resulting in a total EV when facing the push of 3.43BB * 9% = 0.31BB
      6. Our EV at 9% calling range from BB is 0.9BB. If we were to employ the whole range (i.e. including playable hands) only for pushing, our EV for SB position would be = 25%*0.9 - 75%*0.5 = -0.15BB. If that's a lot, is up to you to decide.

      Now, from above also follows:

      1. Perfect opposition can only bring our S-CH push EV down to 0.9BB, no less. At higher limits, I believe this might eventually be the case if you stick to the book.
      2. At lower limits, our EV can vary between 0.8BB and 1.5BB against reasonable players, which is ok I guess.
      3. Extreme fish and maniacs that are likely to call with 15%+ are probably better avoided though, as potential increase in EV would come at a price of huge increase in variance. After all, even with a calling range of 100% they have 37.6% equity against our range...
    • xponentx
      xponentx
      Bronze
      Joined: 10.02.2008 Posts: 341
      Well, I thought fold equity was a factor in the calculations, guess I was wrong. I guess i've just been unlucky, as every time a Sklansky-Chubukov push of mine is called, it's a flip or a bad beat, and the occasional win. Because of how little i've won with this move I assumed that a fold would be a good outcome for a lot of the hands in the range.
    • Tim64
      Tim64
      Black
      Joined: 02.11.2008 Posts: 7,401
      Well I sympathise with this. It seems to me that an average/decent opponent will not call a 10BB+ push from the SB without a good hand. Since you are not pushing with your v good hands (because you get more value by raising instead) it seems to me that you can assume if you're called by a good player, you're probably behind.

      So, when they don't call you only win 1.5BB, and when they do you (usually) lose 10BB.

      This doesn't mean that it's -EV to employ the push; just that if you pushed 6 times and were called once, you'd probably have lost money overall. So it's hard to assess profitability after only a few pushes and it only takes one push of 3,3 and getting called by 4,4 and losing, to make a person very nervous about doing it again.
    • Nunki
      Nunki
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      Joined: 25.10.2006 Posts: 865
      Originally posted by dextart
      Just my 2 cents:

      Everything that has been said above is indeed very true (except for the pushes assuming fold equity to be profitable, which is not the case of course)...

      However, I was also wondering about the way different limits and players could influence the amount of +EV one can extract by utilizing purely Sklansky-Chubukov based pushes, so I did some calculations, assuming 20BB as well as sitting in SB:

      1. Our hand range for S-CH push with 20BB is ~25%.
      2. Our EV for the push, as well as variance, depends solely on the percentage of times our opponent will choose to call us.
      3. If opponent in BB never calls, our EV = 1.5BB with zero variance, which is ideal.
      4. With BB calling with a wider range, our EV decreases, but only down to 0.8BB at 15% calling range. Up from there, it only increases at the expense of our opposition.
      5. If our opponent perfectly adapts to our range, however, he should only call us with a range of up to 9%, depending on his preference for variance. After that, only the poker room profits. His EV @ 9% calling range is a meager 3.43BB, resulting in a total EV when facing the push of 3.43BB * 9% = 0.31BB
      6. Our EV at 9% calling range from BB is 0.9BB. If we were to employ the whole range (i.e. including playable hands) only for pushing, our EV for SB position would be = 25%*0.9 - 75%*0.5 = -0.15BB. If that's a lot, is up to you to decide.

      Now, from above also follows:

      1. Perfect opposition can only bring our S-CH push EV down to 0.9BB, no less. At higher limits, I believe this might eventually be the case if you stick to the book.
      2. At lower limits, our EV can vary between 0.8BB and 1.5BB against reasonable players, which is ok I guess.
      3. Extreme fish and maniacs that are likely to call with 15%+ are probably better avoided though, as potential increase in EV would come at a price of huge increase in variance. After all, even with a calling range of 100% they have 37.6% equity against our range...
      I'm sorry dex, but quantitively at least, most of what you have written is very misleading.

      eg. A sb optimal open-shove versus a very good opponent is only worth about 1/3 of a BB (not taking into account the lost-value of our bigger hands) in NL100 or less. This assumes a 5% rake up to a $3 maximum.

      In fact the rake has an impact on the SB's shoving range. ie. The SB's shoving range DOES NOT precisely correlate to the S-C ranking. Versus looser players you need to take care since a whole bunch of -EV calls will also be -EV for the aggressor (a bit like how a loose-player may spoil your EV on the bubble in a tournament if you shove too wide).
    • cyzo
      cyzo
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      Joined: 19.07.2008 Posts: 117
      Originally posted by Nunki

      I'm sorry dex, but quantitively at least, most of what you have written is very misleading.

      eg. A sb optimal open-shove versus a very good opponent is only worth about 1/3 of a BB (not taking into account the lost-value of our bigger hands) in NL100 or less. This assumes a 5% rake up to a $3 maximum.

      In fact the rake has an impact on the SB's shoving range. ie. The SB's shoving range DOES NOT precisely correlate to the S-C ranking. Versus looser players you need to take care since a whole bunch of -EV calls will also be -EV for the aggressor (a bit like how a loose-player may spoil your EV on the bubble in a tournament if you shove too wide).
      This is a cash game. The net EV between both players = -rake. In a tournament, both can be -$EV since all players not involved in the hand get +$EV for someone being knocked out. It is true that rake could potentially make both players in -EV positions (This happens to all-in EV every time you see AA vs AA, AK vs AK, even AKs vs 22, etc).

      Regarding the player who is calling your cash games S-C shoves, if they are calling too loosely, that means that they are calling with hands that are BEHIND your hand. This will hardly result in you losing money...

      Basically, you are saying that an playing against imperfect opposition is more -EV than playing against perfect opposition, correct?

      Also, because that players are imperfect, they will sometimes call when they are behind and fold when they are ahead, giving you still more EV. Following the S-C SB shoving range is +EV. In fact, due to the mistakes opponents make, shoving an even wider range is more +EV (See the page in the article after the table with the pure S-C shoves).
    • dextart
      dextart
      Bronze
      Joined: 03.10.2008 Posts: 22
      Originally posted by Nunki

      I'm sorry dex, but quantitively at least, most of what you have written is very misleading.

      eg. A sb optimal open-shove versus a very good opponent is only worth about 1/3 of a BB (not taking into account the lost-value of our bigger hands) in NL100 or less. This assumes a 5% rake up to a $3 maximum.

      In fact the rake has an impact on the SB's shoving range. ie. The SB's shoving range DOES NOT precisely correlate to the S-C ranking. Versus looser players you need to take care since a whole bunch of -EV calls will also be -EV for the aggressor (a bit like how a loose-player may spoil your EV on the bubble in a tournament if you shove too wide).
      Appology accepted :)

      Seriously though, what exactly do you find misleading? My calculations include 5% rake, and the results are exactly as I mentioned, perhaps I just wasn't able to express myself clearly enough. But the minimal open-shove EV from SB using S-CH range (not the modified one) is actually 0.8 big blinds, not 1/3. If you want, I can post the formulas I used for calculations, and the excel table values I got?..

      Ah, and I also thought about the value lost through pushing playable hands, so I did another calculation, excluding 99+, AJ+, KQ+ from the range, and recalculated our expected EV only for the remaining pushes. Turns out that it's still quite profitable, 0.42 big blinds to be exact. So if you want to compensate for the EV difference, you have to be able to extract at least an EV of 1.7 big blinds for the "playble range". My hand sample at NL100 is not exactly sufficient (20K), but with this handrange in SB I'm only up 1.64 big blinds, so go figure... Yeah, and don't bother pointing out I'm a loser :f_biggrin:
    • Nunki
      Nunki
      Bronze
      Joined: 25.10.2006 Posts: 865
      Originally posted by cyzo

      Regarding the player who is calling your cash games S-C shoves, if they are calling too loosely, that means that they are calling with hands that are BEHIND your hand. This will hardly result in you losing money...

      EG. 20BB starting stack, 5% rake and hero open-shoves from SB. Hero is open-shoving AA-22,AKs-A2s,KQs-K8s,QJs-QTs,AKo-A2o,KQo-KTo and villain is calling the same range. As a result of villain's crappy strategy K8s becomes a losing hand for us to include in our shoving range. Versus a good player K8s is fine to open-shove with. (Villain loses 4.4 BB's, Hero 0.1BB's).

      Originally posted by cyzo


      Basically, you are saying that an playing against imperfect opposition is more -EV than playing against perfect opposition, correct?

      I didn't say this at all but as the above example shows this can indeed be the case for specific parts of your range if you neglect to make the correct opponent-specific adjustments.


      Originally posted by dextart


      Seriously though, what exactly do you find misleading? My calculations include 5% rake, and the results are exactly as I mentioned, perhaps I just wasn't able to express myself clearly enough. But the minimal open-shove EV from SB using S-CH range (not the modified one) is actually 0.8 big blinds, not 1/3. If you want, I can post the formulas I used for calculations, and the excel table values I got?..

      My calculations differ from yours. In the example I quoted above should the BB be playing perfectly then he would call with AA-55,AKs-A9s,AKo-ATo giving hero an EV of 0.24BB's for his shove. If the BB always calls then we win 1.1 BB's (and we should have open-folded 22).



      Originally posted by dextart

      Ah, and I also thought about the value lost through pushing playable hands, so I did another calculation, excluding 99+, AJ+, KQ+ from the range, and recalculated our expected EV only for the remaining pushes. Turns out that it's still quite profitable, 0.42 big blinds to be exact. So if you want to compensate for the EV difference, you have to be able to extract at least an EV of 1.7 big blinds for the "playble range". My hand sample at NL100 is not exactly sufficient (20K), but with this handrange in SB I'm only up 1.64 big blinds, so go figure... Yeah, and don't bother pointing out I'm a loser :f_biggrin:
      Sounds interesting.
    • cyzo
      cyzo
      Bronze
      Joined: 19.07.2008 Posts: 117
      Originally posted by Nunki
      Originally posted by cyzo

      Regarding the player who is calling your cash games S-C shoves, if they are calling too loosely, that means that they are calling with hands that are BEHIND your hand. This will hardly result in you losing money...

      EG. 20BB starting stack, 5% rake and hero open-shoves from SB. Hero is open-shoving AA-22,AKs-A2s,KQs-K8s,QJs-QTs,AKo-A2o,KQo-KTo and villain is calling the same range. As a result of villain's crappy strategy K8s becomes a losing hand for us to include in our shoving range. Versus a good player K8s is fine to open-shove with. (Villain loses 4.4 BB's, Hero 0.1BB's).

      Originally posted by cyzo


      Basically, you are saying that an playing against imperfect opposition is more -EV than playing against perfect opposition, correct?

      I didn't say this at all but as the above example shows this can indeed be the case for specific parts of your range if you neglect to make the correct opponent-specific adjustments.


      Originally posted by dextart


      Seriously though, what exactly do you find misleading? My calculations include 5% rake, and the results are exactly as I mentioned, perhaps I just wasn't able to express myself clearly enough. But the minimal open-shove EV from SB using S-CH range (not the modified one) is actually 0.8 big blinds, not 1/3. If you want, I can post the formulas I used for calculations, and the excel table values I got?..

      My calculations differ from yours. In the example I quoted above should the BB be playing perfectly then he would call with AA-55,AKs-A9s,AKo-ATo giving hero an EV of 0.24BB's for his shove. If the BB always calls then we win 1.1 BB's (and we should have open-folded 22).



      Originally posted by dextart

      Ah, and I also thought about the value lost through pushing playable hands, so I did another calculation, excluding 99+, AJ+, KQ+ from the range, and recalculated our expected EV only for the remaining pushes. Turns out that it's still quite profitable, 0.42 big blinds to be exact. So if you want to compensate for the EV difference, you have to be able to extract at least an EV of 1.7 big blinds for the "playble range". My hand sample at NL100 is not exactly sufficient (20K), but with this handrange in SB I'm only up 1.64 big blinds, so go figure... Yeah, and don't bother pointing out I'm a loser :f_biggrin:
      Sounds interesting.
      First of all, that range does not follow the S-C numbers at all, so you will not generate enough equity from folding with some of the hands in that range. I doubt that I even need to argue this, as I was under the assumption that this thread was about Sklansky-Chubukov numbers. I had no idea that you were arguing that pushing hands that were not in this range would not be profitable. If you extended your range arbitrarily to 23o, that would again be unprofitable.

      Also, you can beat an opponent who makes perfect calls. The closest your opposition can get to this in actuality is calling with hands that are ahead of your range, not the individual hands in it. Therefore, their calling range will never be your shoving range. If it is, they will be losing a lot of money. In fact, they will never gain from you by calling, and you will still gain when they fold.

      To quote dextart "1. Perfect opposition can only bring our S-CH push EV down to 0.9BB, no less. At higher limits, I believe this might eventually be the case if you stick to the book."

      In practice we will be pushing with a wider range the actual S-C numbers, and this range will not include premium hands and hands with high post-flop playability. These will be raised. If anything an opponent does makes even a single hand you are pushing or raising with -EV, this is your fault; you should not be making that play; it is not consistent with the numbers.

      Returning to this: "My calculations differ from yours. In the example I quoted above should the BB be playing perfectly then he would call with AA-55,AKs-A9s,AKo-ATo giving hero an EV of 0.24BB's for his shove. If the BB always calls then we win 1.1 BB's (and we should have open-folded 22)."

      An opponent playing perfect will not call your handrange with another handrange. He will call your hand with a handrange. I do not this that you understand this very well.
    • Tim64
      Tim64
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      Joined: 02.11.2008 Posts: 7,401
      *Tim64 wonders why he ever asked the question in the first place since he doesn't understand any of the answers and wishes he was a lot better at mathematics :( *
    • dextart
      dextart
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      Joined: 03.10.2008 Posts: 22
      Nunki, I think you are looking at the S-CH shove from a little bit different perspective than it's supposed to be viewed.

      It's true that perfect opposition can make any particular hand close to 0 EV (but still slightly positive), but it would require playing exactly against that hand! Unfortunately for BB, we don't reveal our hand, so if he assumes that every time we shove, we do it with K8s, he can indeed adjust his calling range to the degree of making it -EV for us to shove K8s (and that's only because K8s has a S-CH number of 39 and strictly speaking should not be pushed with 20BB stack size, only 19BB).

      Now, let's think of what our opponent achieved with doing the above adjustment. Well, he made it unprofitable for us to shove K8s, let's credit him with that. He also made sure his EV is -0.5BB every time he is calling our pushing range in general. Did he make our pushes less profitable? Not in the slightest. Also, his calling range will increase our variance. Not that S-CH numbers promise you low variance to start with.

      So, in practice, our opposition sitting in the BB has to take into account the whole range of our pushes and adjust accordingly, perhaps to the degree of being perfect. They can never perfectly adjust to every hand, because they can't know what we have. Hence questioning the profitability of individual hands is jus redundant.
    • cyzo
      cyzo
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      Joined: 19.07.2008 Posts: 117
      Originally posted by dextart
      Nunki, I think you are looking at the S-CH shove from a little bit different perspective than it's supposed to be viewed.

      It's true that perfect opposition can make any particular hand close to 0 EV (but still slightly positive), but it would require playing exactly against that hand! Unfortunately for BB, we don't reveal our hand, so if he assumes that every time we shove, we do it with K8s, he can indeed adjust his calling range to the degree of making it -EV for us to shove K8s (and that's only because K8s has a S-CH number of 39 and strictly speaking should not be pushed with 20BB stack size, only 19BB).

      Now, let's think of what our opponent achieved with doing the above adjustment. Well, he made it unprofitable for us to shove K8s, let's credit him with that. He also made sure his EV is -0.5BB every time he is calling our pushing range in general. Did he make our pushes less profitable? Not in the slightest. Also, his calling range will increase our variance. Not that S-CH numbers promise you low variance to start with.

      So, in practice, our opposition sitting in the BB has to take into account the whole range of our pushes and adjust accordingly, perhaps to the degree of being perfect. They can never perfectly adjust to every hand, because they can't know what we have. Hence questioning the profitability of individual hands is jus redundant.
      quoted for truth
    • Nunki
      Nunki
      Bronze
      Joined: 25.10.2006 Posts: 865
      Originally posted by dextart
      Nunki, I think you are looking at the S-CH shove from a little bit different perspective than it's supposed to be viewed.

      I'm not sure how SC-shoves are supposed to be viewed but the "mini-game" SB vs BB shove/call is a trivial one to be sure. SC-rankings don't ordinarily give optimium shoving ranges either.

      Originally posted by dextart

      It's true that perfect opposition can make any particular hand close to 0 EV (but still slightly positive), but it would require playing exactly against that hand! Unfortunately for BB, we don't reveal our hand, so if he assumes that every time we shove, we do it with K8s, he can indeed adjust his calling range to the degree of making it -EV for us to shove K8s (and that's only because K8s has a S-CH number of 39 and strictly speaking should not be pushed with 20BB stack size, only 19BB).

      SC-hand rankings do not account for rake. BTW, we start with 20BB's and shove 19.5BB's after posting in my earlier example.

      Originally posted by dextart


      So, in practice, our opposition sitting in the BB has to take into account the whole range of our pushes and adjust accordingly, perhaps to the degree of being perfect. They can never perfectly adjust to every hand, because they can't know what we have. Hence questioning the profitability of individual hands is jus redundant.
      I only mentioned individual hands in the context of part of a range. Questioning the profitability of individual hands versus a range is one of the key steps in developing an optimum strategy.


      Originally posted by dextart

      1. Our hand range for S-CH push with 20BB is ~25%.
      2. Our EV for the push, as well as variance, depends solely on the percentage of times our opponent will choose to call us.
      3. If opponent in BB never calls, our EV = 1.5BB with zero variance, which is ideal.

      Anyway, all I wanted to point out in this thread is that the figures quoted by Dex for profitability of a SB vs BB shove/call strategy are not correct.

      Referring to the above quoted example: EV=0 when we fold and EV=1.5 when we get a hand and shove. EV for this strategy is therefore 1.5/4 unless we always get a hand. This is not the only mistake.