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Wednesday, February 10, 2010

Mathematics of NLHE Ep 3

Covered in this episode:

  • Revisiting Pot Odds
  • Implied Odds and Reverse Implied odds math
  • Tools to help us determine Pot Equity
  • Mental shortcuts

Pot Odds let us determine whether or not we can profitably continue in the hand based on the amount of money we stand to win vs the amount of money we must risk. So basically a risk to reward ratio, risk:reward.

Reverse Implied Odds is the term used to describe the amount you may lose by hitting your hand and still not having it be the best (and subsequently losing more money).

  • Ex. UTG opens to 35 and you call w/ 98s OTB at 1000nl. Flop comes 7T4r and our assumption is that the villain is TAG and if he has a good hand, we are going to stack him. UTG cbets 60 into 80 and we call due to implied odds. Turn is 4x and UTG fires 140 into 200. Do we have the odds to call if he is stacking w/ a range of only TT-AA?
    • If our plan is to get all in when we hit our straight against this player. There are 6 ways to make AA-JJ (24 combos) and only 3 ways to make TT which makes 27 combos, 3/27 giving him a set of tens or 11%.
    • JJ being 6/27 or 22% of his range, now we only have 6 cards to improve to a straight... which means we need 6.7:1 to call however we only have 4 clean outs as the 2 jacks give him a boat. We'll hit those 2 outs about 4.5% of the time.
    • (TT) 11% of the time we'll be drawing dead and "improve our hand 18.2% of the time
    • (JJ) 22% of the time he'll make 2 of our outs dirty and we'll hit one of those 4.5% of the time
    • (QQ-AA) 66% of the time we'll hit our draw 18.2% of the time and win the pot, 81.8% of the time we'll lose our $140
    • EV(TT) = 11%[18.2%(-140+(-765)) + 81.8%(-140)] = -$30.73
    • EV(JJ) = 22%[8.75%(140+200+765) + 4.5%(-140+(-765)) + 86.75%(-140)] = -$14.41
    • EV(QQ-AA) = 66%[18.2%(140+200+765) + 81.7%(-140)] = +$57.15
    • EV(TT-AA) = $12.01. This is barely positive considering this tight range, if we add 77 and 44 into UTG's range, this will become -EV and even more so if we take out QQ or JJ since he will not always stack with those.
      • EV(TT), (-140+(-765)) is what we lose if we hit our hand
      • EV(JJ), 8.75% is how often we will hit our 4 clean straight outs. 4.5% is how often we will hit our dirty straight outs and lose our call + stack. 86.75% is how often we miss

Multiway Pots

  • Multiway pots can affect pot odds and implied odds decisions in a few ways
  • When making a pot odds decision in a multiway pot, our position will matter greatly whether or not we can continue in a hand even if we're getting good immediate odds and implied odds

More on Implied Odds

  • Don't fall into the trap of overestimating implied odds
  • Implied odds vs a good LAG player is often bad and implied odds vs a TAG is often good but what about vs a 40/10 calling station? Our implied odds stands to be pretty good vs a station, especially one that plays 40/10. He has a tight preflop raising range and often is not willing to give up w/ weak one pair hands or draws.
  • If your implied odds is not good but you have a hand that you want to play, it is better to 3bet the hand and take control.
  • Board texture can greatly affect implied odds and thats why straight draws play better than flush draws and 1 gappers have a lot of implied odds

Mental Shortcuts

  • Fudge the numbers so that it is easier to calculate it in your head
  • Ex. 1 - We have 30% equity. Vil bets 265 into 490. Call or Fold?
    • 30% equity is close to 33% equity which we know is 2:1 so we need slightly better than 2:1
    • pot odds = 265+490:265. This can be fudged so we can do it quicker. 265 is close to 250 and 490 is close to 500 so we are getting 250+500:250 odds which is 3:1. much easier
  • Ex. 2 - We have 20% equity. pot is 725 and Vil bets 365. do we have pot odds?
    • 725 is close to 700 and 365 can be round down to 300. 300+700 = 100 and 25+65 = 90 or roughly 100. So we know our odds are 1100:365. We need 20% or 4:1. 4x300 = 1200 and we only have 1100. So no.

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