maths/variance question

    • adasko99
      Joined: 13.02.2011 Posts: 1,994
      Hello everyone :)

      I'm trying to sort one of my mindset problems out by running a variance simulation.
      I know there are some kind of variance simulators but i decided that the best proof would be actually physically running it myself step by step.

      In order to do it i created an empty EV graph which i will be filling with results of throwing dice.

      I decided to start with using three dice. Each containing the digits from 1 to 6
      That means the results can vary from minimum #3 to maximum #15 = 13 combinations.

      I decided that 7 chosen numbers will give me a +EV result, while the other 6 chosen numbers will give me a -EV result

      I would like to know if my assumptions below are correct:

      if 13 numbers = 100%
      is 7 numbers = 65% ?
      and is 6 numbers = 35% ?

      is EV EDGE = +15% ?
  • 9 replies
    • VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 9,207
      First off, I think that the maximum would be 18.

      Then only looking at the totals, there would be 16 combinations 3 to 18.
      Some totals can be made far more ways than others.

      3 for example has only 1 combination, as does 18

      For each combination where the numbers on the 3 dice are all different there are 6 different ways to roll that combo.

      For each combination where two dice are the same, there are 3 ways to roll that combination

      12 for example could be:
      6,5,1 - 6 combinations
      6,4,2 - 6 combinations
      6,3,3 - 3 combinations
      5,5,2 - 3 combinations
      5,4,3 - 6 combinations
      So 12 has 24 combinations

      So just picking 7 numbers "at random" to be your +EV totals isn't the whole story.

      There are 6^3 or 216 ways to roll 3 dice.
      Make a table for each of the numbers and their combinations like so:
      3: 1 combo
      4: 3 combos
      5: 3 Combos
      6: 9 combos

      When you have your table built, you will be able to select sets of numbers that give you different percentages. I'm guessing that 12 will have the most combos.

      Interesting exercise. I'd be interested in seeing the table.

      I think perhaps writing a simple script -- perhaps in Excel or similar -- would give a faster result.

      All the best,
    • adasko99
      Joined: 13.02.2011 Posts: 1,994
      that's right it's 18 so 16 combos :f_biggrin: thanks :f_thumbsup:

      i see yes, good point, hm i will try to work it out somehow, thanks :)

      ps. script would probably be good, but i really really want to do it manually to see with my own eyes the process of lets say a downswing of 20 rolls when the chances were like 65% vs 35% :f_biggrin:
    • adasko99
      Joined: 13.02.2011 Posts: 1,994
      i found some help but it's hard for me to wrap my head around it :(

    • 3prswins
      Joined: 27.07.2011 Posts: 204

      from your diagram of dice combos and odds.... you can take a score of 5-9 inclusive to be your ~65% edge. (this is actually 66.67% but close enough).

      Then you could say hitting between 5-9 would give you +1 and anything else would be -1.

      I've drafted up an simple excel sheet that can run these simulations + graph + max drawdown etc. However this doesn't need to be done with the dice.... simple numbers would work just as well.

      PM your Skype and i can send it over :) .
    • adasko99
      Joined: 13.02.2011 Posts: 1,994
      So i managed to come up with a way to run an EV simulation on paper to witness the variance with my own eyes :)
      I was using Backgammon percentages to either hit a certain number or avoid getting hit by a certain number - using two dice and Backgammon rules (doubles)

      * 6 different rolls with different chances (positive and negative but +EV altogether) - randomized every time

      * for 6 different "big blinds" amounts - also randomized every time as well

      the general EV of my chances was +EV 54.63% if not I'm not mistaken

      depending on the outcome of the randomness, I was playing for either:
      50bbs, 100bbs, 150bbs or 200bbs

      So after exactly 74 rolls i hit a -1700 (900bbs below EV) downswing and ran out of space on my chart that is almost A2 size lol :f_cool:

      Will have to expand the chart and will carryon to see when i will finally be above my 0EV line lol :P

      Or maybe i should increase my edge a bit ehehe.

      It's a pretty cool exercise i must admit :P It makes it a lot easier to realise that the soft is not rigged and that is actually quite possible to get your AAxx fucked in 400bbs pots in PLO like 5 times in a row :f_cool:

      It's also eazier to believe it's possible and accept it, when you actually physically do it yourself instead of having to believe that EV simulations software is right :P

    • Happa2
      Joined: 14.08.2010 Posts: 3,638
      AAxx is a strong hand preflop but will get you in trouble in big pots :O
    • adasko99
      Joined: 13.02.2011 Posts: 1,994
      erm, that is correct yes :)
    • martinemem
      Joined: 05.07.2011 Posts: 596
      No offense, but it almost makes me laugh you use omaha as a comparison to 3 1-6 dices.

      I know you wanna do something that seems possible to wrap the head around.
      I know nothing about PLO though, i do know that "naked aces" is useless in multiway pots. Even if you are more than 200bb deep they start to become very useless, unless you play hu. Even in hu they actually also lose value if they are naked, and you start to become deep (200bb+).

      If you play 6m i would almost go as far as saying you are toying with thin value spots if you open, somone flats, bb pots it. Already here you deffinately either need double suited, or atleast 1 suited with connectors (not connectors like A :heart: A :diamond: 7 :heart: 8 :spade: - but like A :heart: A :diamond: K :heart: Q :club:
      Unless ofc if you play Hi/lo
      Does the lowest low exceed 8 to 9, or it that low too high? Is the lowest low 8?

      Just because im curious, and dont understand SHIT about plo, do you openfold UTG 6m A :heart: A :spade: A :diamond: K :club: - if not, do you openfold A :spade: A :heart: A :diamond: 6 :club:

      This is what happens when you compare backgammon to PLO/FLO/8-game:
    • adasko99
      Joined: 13.02.2011 Posts: 1,994
      haha yeah, Gus Hansen, what a degen :P

      no offence taken bro :)

      I was not trying to compare dice rolls to playing PLO, I was just using dice equities to simulate PLO stackoffs in different spots :)

      You sometimes stackoff with ~70%, sometimes with ~60% , sometimes with ~55% sometimes with ~50%, sometimes with ~45% , sometimes with ~40% (i was not taking any pot odds into consideration , just pure equities)
      Sometimes for effective ~50bbs , sometimes for ~100bbs , sometimes ~150bbs, sometimes ~200bbs.

      So dice rolls just helped randomise those and simulate different spots :)

      Obviously there is no way to simulate the whole actual game of PLO when there are thousands of other things involved :)

      About AAxx in PLO:

      #1 You always have to open any AAxx, you cannot openfold AAxx ever

      #2 If you are effective ~100bbs, you open AA96 rainbow and someone 3Bet pots it - you have to 4bet / jam :) Even with AAAx :)

      They either have AA themselves or they have like very strong rundowns or double paired hands but altogether vs that range even the shittiest AAxx are good to jam preflop
      You will never be a lot ahead, usually like 55% or literally flipping but in a 3bet/4bet situation you've got more then enough good pot odds to jam :)

      #3 Yes, in Hi/Lo the highest (worst) low card is an 8. But Hi/Lo is a different story regarding playing AAxx :P Especially No Limit Hi/Lo hyhy :D

      that is all preflop of course.
      postflop, like you guys said, a lot of the times even the greatest AAKKds is sometimes just cbet/fold or even check/fold on a lot of Flops :)