Lets draw some conclusions here....
At first I saw this and didn't like it. I thought it was a slightly veiled brag post. Then I looked at it and realized it wasn't.
What this move essentially does is force your opponent off the same hand. After looking at the action of the BB it seems clear that you he has an Ace. He check/raises you on the flop and you call and then he bets right into you on the turn. I guess he could have a King here but I don't think a lot of micro opponents do this and the thinking behind betting a King like so has to be a lot different from the way micro opponents are thinking. There is also the possibility that he could flip over a better hand.
But then I thought about it some more and said to myself "Well even though this push is meant to move my opponent off the same hand, those times I get called I am always a dog." If called your opponent is going to show you a better hand or a hand you are splitting with right now. But those times that your splitting with him you can still lose in the sense that if he pairs his kicker he is going to beat you. That’s because most likely his kicker is higher than a 6 and when he pairs it, he makes a higher two pair. But also when the K pairs you are also losing more often than not, because his kicker is higher than a 6 more often than not.
So I Stoved up some results on this hand. I gave my opponent AQo-A7o (without him having the Ad of course) and AQs-A7s (without him having the clubs or diamond combo suits) and found that your equity was only 43.128%. His equity was 56.818%. That’s because 43.128% of the time BOTH of you will win when he calls and you guys see a showdown. The other 13.64% of the time he wins all of the money when he calls.
So lets assign some probabilities to the frequency of your opponent calling with a hand you are tied with (these are the hands that your opponent will call with but can still beat you come the river). Lets say he calls 40% of the time not believing or thinking he is splitting the pot with you. The other 60% he folds. So your expected value from your push versus these hands is:
(.60)($29.25)+(.40)[(.8636)($0)+(.1364)(-$31.50)]=$15.83
A note - .8636 combines the probabilities that you both tie on the river and win nothing.
But lets also touch a little on the hands that have you beaten at this moment already. Those cases apply when he has a set of aces, kings, AK for two pair and a 6 holding. One could make the case that the way this hand played your opponent may have one of these holdings. If we assign him probabilities to the chance of flipping over a hand that beats you or a hand that you are tied with, again we can look at your expected value. Lets say that your opponent will have a hand that beats you 30% of the time and a hand you are tied with 70% of the time. So:
(.30)(-$31.50)+(.70){(.60)($29.25)+(.40)[(.8636)($0)+(.1364)(-$31.50)]}=$1.63
So the expected value of your push versus the opponent who is going to flip over a hand that you are behind to or a hand you are tied with but can lose to on the river is $1.63. Lets tweak those numbers a little and see what happens. Lets say you know your opponent is more TAGgy. Maybe you expect him to only bet this way with a hand that is beating you say 40% of the time. So your expected value is:
(.40)(-$31.50)+(.60){(.60)($29.25)+(.40)[(.8636)($0)+(.1364)(-$31.50)]}=-$3.10
Lets tweak it to 50% and see what happens:
(.50) (-$31.50)+(.50){(.60)($29.25)+(.40)[(.8636)($0)+(.1364)(-$31.50)]}=-$7.84
Wow!!! Look at our EV drop the tighter we think our opponent is. Tighter in the sense that he will only behave the way he did with a hand that will beat us. So lets draw a conclusion from this part of the post so far.
Conclusion
Looking at your opponent and his proclivities, the more we believe our opponent will behave this way with a hand that is beating us at this moment, the less inclined we should be to push.
Lets go back to the drawing boards one more time and look at an opponent who could behave like this very often with a hand we are tied with at the moment.
So we once again assign the probability that our opponent will have a hand that beats us 30% of the time and a hand we are tied with (but that could beat us by the river) 70% of the time. We know the expected value of this call is $1.63. But lets go back and look one more time at our opponent and see if we can get any reads on him. If we know that our opponent has a hard time getting away form hands and big bets don’t scare him then we can maybe adjust the frequency that he will call with these hands we are tied with. Lets make them bigger. Lets now say he calls 70% of the time not believing or thinking he is splitting the pot with you. The other 30% he folds.
(.30)($29.25)+(.70)[(.8636)($0)+(.1364)(-$31.50)]=$5.78
We see that just looking at the hands that we tie with our expected value actually decreased by him calling us more often. Lets see what happens when we plug it into our equation where he has a hand that beats us 30% of the time and a hand that we are tied with 70% of the time.
(.30)(-$31.50)+(.70){(.30)($29.25)+(.70)[(.8636)($0)+(.1364)(-$31.50)]}=-$5.40
Again our EV dropped the more often we thought our opponent would call with a hand that ties us!!! Lets draw one more conclusion and then tie them together.
Conclusion
Looking at your opponent and his proclivities, the more we believe our opponent will call our push with a hand we are tied with, the less inclined we should be to push.
So there we have it. Maybe we can take this information and formulate it into some theorem or something. Something that brings it all together.
Also check my math! I am 90% sure it is right but maybe Pokey wants to check it too!!! Also let me know if you agree or disagree with what I am saying! I love this hand and it was a blast to think about. [img]/images/graemlins/smile.gif[/img]
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