Hold 'em Poker for Advanced Players - Ebook written by David Sklansky, Mason Malmuth. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Hold 'em Poker for Advanced Players.
A level 3 hand would have suited hands down to KJ, QJ, and the 9-9 pair. Level 2 hands have suited hands down to Q's (AQ and KQ), and the pairs J-J and T-T. Level 1 hands have the three top pairs and the top suited hand, A-K. This standard was based on Sklansky's principles, and is a model of how 'Sklansky' is SUPPOSED to work. Sklansky hand groups was formulated by David Sklansky and Mason Malmuth. Both of these old school poker players understand the math very well. It is no surprise that our hand rankings aligns very well with their proposed hand groups. Sklansky hand group proposes that Tier 1 group consists of pair A, pair K, pair Q, pair J and suited AK. Editor’s Note: This article was first published in the March, 2014 issue. In part one, we looked at Norman Zadeh’s approximate game theory optimal solution to a heads up, pot-limit, one round poker game.Both players ante $1, the first player checks or bets $2 and if he.
David Sklansky Starting Hands Book
Two Plus Two Magazine, Vol. 17, No. 2Editor’s Note: This article was first published in the March, 2014 issue.
In part one, we looked at Norman Zadeh’s approximate game theory optimal solution to a heads up, pot-limit, one round poker game. Both players ante $1, the first player checks or bets $2 and if he checks, the second player bets either $2 or checks also. There are no raises.
Zadeh worked out that the first player should bet his top 14% and bluff with his bottom 7%. He should check and call with hands between 14 and 50 and check and fold with hands between 50 and 93. The second player should call with the top half of his hands and if checked to bet the top 30% and bluff with the bottom 15%. He would fold hands 50-85.
When both players use Zadeh’s strategy, the first player has an EV of about -8.5 cents.
What if one of the players differs substantially from this approximant game theory optimal strategy? To give you an idea of what happens, take a look at the following example. Suppose the first player uses the strategy where he bets the top 40% and the bottom 32% of his hands and checks and calls with the remaining hands, which are between 40 and 68. Against him, would player two’s GTO strategy, as specified by Zadeh, still work? Certainly, that strategy is far from the best when facing player one. For instance, player two should never bluff against player one since he will always be called. Secondly, when player one bets, the Zadeh strategy for player two will have him folding far too often. Finally, if player one checks, player two should value bet way more than his top 30%.
In spite of all these flaws, mathematicians contend that GTO does at least as well against bad players as it does against other GTO players. Thus, they would predict that sticking with Zadeh’s strategy will win player two at least 8.5 cents per hand. We will see if that’s right in part three of this essay.
For now, however, I think it would be a good exercise to come up with the perfect counter strategy to player one given that you know his strategy. Again, his strategy is to bet hand 0-40 and 68-100 and to check and call with the rest. Before reading further, see if you can do this yourself.
Suppose player one checks, how many hands can player two bet for value? Well certainly, he can bet 0-40, as they are all certain to win. But, he can also bet another 14% and still be the favorite. Do you see why? Player two will be calling from 40-68. If player one bets, we need to call with hands that have a better than 1/3 chance of winning since we are getting 2:1 odds. Notice that hand 68 is an easy call since it loses to hands 0-40, but beats the bottom 32% that he also bets. The fact is that player two can call with hands all the way down to 76. With that hand, he will lose to all of player one’s value bets and even to some of player one’s “bluffs”. Still though, he is only a 48:24 underdog.
We will now use the method I showed you in part one to calculate the EV of player one when facing the perfect counter strategy.
● If player one has hand 0-40 and player two has hand 0-40, there will be a bet and a call and they will break even. This happens 16% of the time and the EV is 0.
● If player one has hand 0-40 and player two has hand 40-76, there will be a bet and a call and player one will win $3. This will happen 14.4% of the time and the EV is 43.2 cents.
● If player one has hand 0-40 and player two has hand 76-100, there will be a bet and a fold and player one will win $1. This will happen 9.6% of the time and the EV is 9.6 cents.
● If player one has hand 40-54 and player two has hand 0-40, there will be a check and a call and player one will lose $3. This will happen 5.6% of the time and the EV is -16.8 cents.
● If player one has hand 40-54 and player two has hand 40-54, there will be a check and a call and they will break out even. This will happen 1.96% of the time and the EV is 0.
● If player one has hand 40-54 and player two has hand 54-100, it will go check-check and player one will win $1. This will happen 6.44% of the time and the EV is 6.44 cents.
● If player one has hand 54-68 and player two has hand 0-54, it will go check-call and player one will lose $3. This will happen 7.56% of the time and player one will lose 22.68 cents.
● If player one has hand 54-68 and player two has hand 54-68, it will go check-check and they will break even. This will happen 1.96% of the time and the EV is 0.
● If player one has 54-68 and player two has 68-100, it will go check-check and player one will win $1. This will happen 4.48% of the time and the EV is 4.48 cents.
● If player one has hand 68-76 and player two has hand 0-68, it will go bluff-call and player one will lose $3. This will happen 5.44% of the time and the EV is -16.32 cents.
● If player one has 68-76 and player two has 68-76, it will go bluff-call and they will break even. This will happen .64% of the time and the EV is 0.
● If player one has 68-76 and player two has 76-100, it will go bluff-fold and player one will win $1. This will happen 1.92% of the time and the EV is 1.92 cents.
● If player one has 76-100 and player two has 0-76, it will go bluff-call and player one will lose $3. This will happen 18.24% of the time and the EV is -54.72 cents.
● If player one has 76-100 and player two has 76-100, it will go bluff-fold and player one will win $1. This will happen 5.76% of the time and the EV is 5.76 cents.
When you add up player one’s EVs, it comes to -39.12 cents, much worse than how he would do if he stuck to his GTO strategy, even against a world class player.
To be continued…..
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