Mathematical Error in SSS

    • Optroot
      Optroot
      Bronze
      Joined: 11.05.2008 Posts: 250
      I was reading over SSS and I saw this question:

      You raised to $0.50 with TT and are left with $1.50. One player behind you re-raises. What do you do?
      **Push all-in

      Pushing all-in is a mistake. Assuming you only get reraised with AA, KK, QQ, JJ, AKs, and AK your win percent would be: (From PokerStove)

      Win 33.654%
      Lose 66.346%

      Which means your EV when calling is (Even with blinds as dead-money)
      EV = $2.15*33.654% - $2.00*66.346%
      = $-.603359
      But when you fold your EV is just.
      EV = $-.50
      Since your EV is higher when you fold, you should fold.

      In Order for this to be a good choice your win percentage would have to be (To make your EV grater than $-.50):

      -.50 < 2.15x-2.00(100-x)
      -.50 < 2.15x-200+2.00x
      -.50 < 4.15x-200
      199.5/4.15 < x
      x > 48.072%

      Which would only happen if you know your opponent holds any comination of jacks and higher (like JQo or AKs) and would reraise you, or you know that it is impossible for them to hold and over pair (somehow...?).

      Additionally to make this a profitable call there would have to be a certain amount of dead money in the pot:

      -.50 < 33.654%*(2.00+x)-66.346%*2.00(100-x)
      -.50 < 67.308%+33.654%*x-13269.2%+132.692%*x
      -.50+13201.892% < 166.346%*x
      131.51892/1.66346 < x
      x > $0.79

      This means that there would have to be more than 79 cents of dead money in the pot to make this profitable.

      So people please if you have TT and get re-raised and have to go all-in
      dont do it unless there is $0.79 of dead money or you know you have at least 48.072% chance of winning or you have $1.19 or less left (or some complicated combination of all of these):

      -0.5 < (x+.15)*33.654% - x*66.346%
      -0.5 < 33.654%x+33.654%.15 - x*66.346%
      -0.5 < -32.692%x + 5.0481%
      0.550481 > 32.692%x
      0.550481/0.32692 > x
      1.69 > x
      (minus the $0.50 you already put in)

      Thanks for reading, hopefully the guide can be changed.
      Please respond if you have found any errors. Thanks again.
  • 12 replies
    • Drakhor
      Drakhor
      Bronze
      Joined: 13.01.2008 Posts: 554
      gah... so much math in the morning isn't healthy... -_-
    • timukasr
      timukasr
      Bronze
      Joined: 26.05.2007 Posts: 1,820
      I think you have to give villain looser re-raising range, because many players don't respect shortstacks and simply play bad. Remember - the SSS is made by professionals over many many many hands and I guess they have made it idiot proof.
    • sismis
      sismis
      Bronze
      Joined: 27.10.2006 Posts: 352
      if he is tight then it is probably really best to fold but agains average opponent this range indeed isnt realistic.
    • xylere
      xylere
      Bronze
      Joined: 27.05.2007 Posts: 2,939
      EV = $2.15*33.654% - $2.00*66.346%
      = $-.603359


      The actual EV is (w/o blinds) $2.50*33.6% - $1.5*66.4%
      Fold has zero EV
      Range can vary from player to player, some players reraise TT+ AQ+, some JJ+ AK
      You can figure it out, if you have some reads or statistics
      otherwise, stick to the strategy and call

      I like your attitude though, keep it up!
    • Optroot
      Optroot
      Bronze
      Joined: 11.05.2008 Posts: 250
      I think you have to give villain looser re-raising range, because many players don't respect shortstacks and simply play bad. Remember - the SSS is made by professionals over many many many hands and I guess they have made it idiot proof.


      It's very important be skeptical of strategies you learn. You cannot just say it was made by math genius' so it's fool proof, there are plays that have to adapt and change, and there can even be mistakes. It's also important to do the research for yourself and change the strategy to your style of play and your strengths. So, for me, I think calling $1.50 is a mistake in this situation. If you like, you can continue doing it all you want, but im just trying to help you save some money, and if I'm wrong, what difference does it make, we understand the principals in the decision better.

      Also, In order for this to be a profitable decision, you would have to put your opponent on any hand containing any combination ok J,Q,K and Aces, that you know they would 3-bet with (even hands like JQ, which some players don't even call with).

      The actual EV is (w/o blinds) $2.50*33.6% - $1.5*66.4%
      Fold has zero EV
      Range can vary from player to player, some players reraise TT+ AQ+, some JJ+ AK
      You can figure it out, if you have some reads or statistics
      otherwise, stick to the strategy and call

      I like your attitude though, keep it up!


      Thanks, I agree with you even if I happen to be wrong, analysis this deep can only be a good learning possibility.

      But I don't understand your EV calculation.
      If you fold you lose a total of $0.50
      If you call and you win, you get $2.00 + blinds (not inc. rake fee) how could you win more than $2.00 (not including dead money) if you only started with $2.00 and there was only one other player?
      If you call and lose, you lose $2.00 total

      And your Fold EV is not 0 because you are giving up your $0.50 which you can still protect, that is why it must be factored into the calculation.
      **(unless you meant $1.50 in which case EV it would be even worse $-0.49 vs $0.00 because the extra $0.50 you save isn't factored in)

      Reads wont really help unless you know that they 3-bet with small suited connectors, but even still, pushing with TT should only be done with extreme caution, and should not be a general rule because re-re-raising is generally done with JJ+, AK+ so it really shouldn't be the standard play.
    • timukasr
      timukasr
      Bronze
      Joined: 26.05.2007 Posts: 1,820
      Originally posted by Optroot
      I think you have to give villain looser re-raising range, because many players don't respect shortstacks and simply play bad. Remember - the SSS is made by professionals over many many many hands and I guess they have made it idiot proof.


      It's very important be skeptical of strategies you learn. You cannot just say it was made by math genius' so it's fool proof, there are plays that have to adapt and change, and there can even be mistakes. It's also important to do the research for yourself and change the strategy to your style of play and your strengths. So, for me, I think calling $1.50 is a mistake in this situation. If you like, you can continue doing it all you want, but im just trying to help you save some money, and if I'm wrong, what difference does it make, we understand the principals in the decision better.
      I agree, seems like you know what you do. Keep it up and you'll be coaching with Xarry2 ;)
    • slikec
      slikec
      Global
      Joined: 04.02.2008 Posts: 1,155
      I play SSS now 10 days on NL0,10/0,20$ and palyed 15k hands. Not much but still i could make some notest about 33% players and if i know is (extremly) TAG is easy fold if i know he is LAG i push if i know he is fish i push aswell. eeven against TAG i push sometimes when i think he holds AQo or AQs or AKo or AKs.
      Basicly even at SSS you have sometimes hard decision but we are only 20BB deep in game so thats why folding is not an option in SSS articles after you raise. I fold maybe 5% hands after reraise even when i hold KK and i have hunch villian have AA i can not fold especially with some dead money in pot(limpers). In 70% cases you are ahead with your range which makes SSS profitable.
    • Yoghi
      Yoghi
      Black
      Joined: 10.09.2007 Posts: 14,387
      I'm not an SSS expert, but I think you are seeing things a bit "wrong" Optroot

      EV fold = 0, this is always the case, because if you fold you will not lose money, neither will you win money. It doesn't matter whether you already invested money in the pot or not. I don't really know how to explain this :(

      The money you invested in the pot is also dead money, it comes from you, but you can't take it back so it's not relevant anymore. You only have 1.50 left and you can win his stack+the blinds+the 0.50 already in the pot.

      And if the player reraises 99+ it changes your equity a lot, a lot more than when he 3-bets QJ. I also think 99 is a lot more likely to 3-bet than QJ or KJ for example.
    • Optroot
      Optroot
      Bronze
      Joined: 11.05.2008 Posts: 250
      Pushing TT is right in some circumstances, but this definately isn't a begginner's play. You must know the hand range of your opponent.

      I'm not an SSS expert, but I think you are seeing things a bit "wrong" Optroot

      EV fold = 0, this is always the case, because if you fold you will not lose money, neither will you win money. It doesn't matter whether you already invested money in the pot or not. I don't really know how to explain this

      The money you invested in the pot is also dead money, it comes from you, but you can't take it back so it's not relevant anymore. You only have 1.50 left and you can win his stack+the blinds+the 0.50 already in the pot.

      And if the player reraises 99+ it changes your equity a lot, a lot more than when he 3-bets QJ. I also think 99 is a lot more likely to 3-bet than QJ or KJ for example.


      Of course you can take the $0.50 raise back, it goes into the pot and you win the pot??? Also they have to call that and they have to put an extra $0.50 in the pot. If you dont count it, the extra $0.50 you win from the pot seems to magically come from nowhere....?????

      If you put your opponent on 99+ AJs+ and AQo+ you still don't have the odds to call, 45.3% win. So, honestly calling here is not something for begginers to do, it is simply more advanced, and should not be the standard play.

      If you discount the $0.50 then you would end up with this:
      WIN = 1.50 + .15 Blinds
      LOSE = -1.50
      FOLD = 0 (and EV = 0)

      EV= 1.65*33.654% - 1.5*66.346%
      EV= -0.439899 (which is still bad since we are comparing it to 0)

      It's still bad unless you have greater than 46.7% chance to win.

      (I hope it doesn't look like I'm arguing, im just confused because this maybe going way over my head, like way over... or not, I really don't know, so I just want to sort this out till it makes sense too me.)
    • xylere
      xylere
      Bronze
      Joined: 27.05.2007 Posts: 2,939
      WIN = 1.50 + .15 Blinds


      WIN = 0.5 (your bet) + $2 (opponent's stack) + 0.15 blinds
    • Optroot
      Optroot
      Bronze
      Joined: 11.05.2008 Posts: 250
      WIN = 1.50 + .15 Blinds

      WIN = 0.5 (your bet) + $2 (opponent's stack) + 0.15 blinds


      You aren't really winning your 0.5 though, you just arn't losing it...
      So in this case the pot is:
      2.00 (mine) + 2.00 (his) + blinds
      but we only win: 2.00(his) + blinds
      the 2.00 stake is just returned to us and we are only up $2.15.

      But, if we discount the $0.50 raise (which I still don't know why that should be done) then you win $1.50 + blinds following the same logic as above.
    • xylere
      xylere
      Bronze
      Joined: 27.05.2007 Posts: 2,939
      Optroot, Yoghi explained it before

      you made a bet, money belong to the pot now
      the fact that you still can act, doesn't make that money yours
      they are in the pot and you can win them as a part of the pot