[_D&L_]

Hey Alan, glad to see someone else with some good intuition and thinking.

Here's some thoughts to help you:

1- you already understand that your bet is a hedge, you are sometimes raising for value, and sometimes bluffing.

[ QUOTE ]


If you bet 10 times the pot, your opponent will call with the top 1/11 of his hands to keep you from stealing. You'll win more money if he DOES call and loses, but he's much
less apt to be calling with a losing hand, so you're giving up all those 1 pot size calls where his hand ranged between the top 50% and top 9.09%. In addition, if you DON'T have the nuts, he's much more likely to have the nuts if he DOES call.

[/ QUOTE ]

But you seem worried that your opponent won't be calling you if you bet too much - that your missing out on all the little suck bets you could have made.

You should realize that such a concern contradicts the intuition behind your hedge. You've hedged your value raises and bluffs so that your actually indifferent to whether your opponent calls or folds. Don't worry whether he calls or folds - either way he loses on your turn to bet.

Poker rewards you for your aggression; the opponent being raised suffers a defense penalty. For instance, if the pot is infinite, he has to call you, even if you only bluff one time in a million. He can't afford to have you steal an infinite pot. That's the defense penalty. And if you hedge it right - you gain on average, regardless of whatever bias your opponent has towards calling or folding. Either he calls all your value bets, or he loses the infinite pot to your one-in-a-million bluffs. He's a Loser either way.

2- Our optimization strategy is to increase the frequency with which our opponent encounters our hedge. There are only so many hands capable of being value bet, and lots of potential bluff hands.

The more we raise our value bet hands, the more bluff hands we can hide in their strength. For instance, suppose a pot has $100 in it. If you raise $1, then you can only sneak in 1 bluff for every 99 value raises. But if you bet $100 then you can sneak in 1 bluff for every 2 value raises.

Thus, the more we can raise our value/bluff hands, the better off we are w.r.t everything trapped in the middle, or below.

This is why my original example of a bluff hand that ruled out the nuts, and the nuts, could be raised to an infinite level. (Remember that example was the nut flush, and a bluff hand that ruled out your opponent from having the nut flush, but itself was a worthless hand).

3- The limiting factor: Hands the beat your value hands, and other hands with assymetric information.

This is what constrains our bidding. We weigh the advantage of increasing our hedgning frequency versus the loss we suffer to hands that beat even our value bet cards.

4- Diminishing marginal returns.

The bigger our value bets, the more bluff hands we can sneak through. But as bets grow large in relation to the pot, their growth becomes asymptotic. You can never bluff more than 50% of your hands, even if you raise an infinite amount. If you did, your opponent could gain +EV infinity simply by calling you.

6- Because of diminishing marginal returns there will be an equillibrium point where the value of increasing the frequency of your hedge gives way to losses suffered to hands that beat your value cards (i.e. hands not "trapped in the middle" - my term).

7- Finally, even once you've done all this, you then have to look for sandbagging opportunities. This style of betting shows the strength of your hand. So far Each raise/bluff pair is bet in porportion to its strength.

But this gives away too much information. If we always bet our hands strength, then our opponent would always know to go all in, even if he had a hand just one kicker-notch above us.

Thus, you have to go back through each raise/bluff pair, and look at playing some stronger hands with your weaker ones, to protect the weaker ones from being exploited.

The stronger hands expect to receive enough aggression to justify them being used as sandbags (remember all margins have to be equal). This is by far the hardest part to implement in practice. So many margins... Generally speaking, you sandbag some weak hands with strong hands to severely penalize anyone that comes strongly over-the-top of your weak raises.

p.s. i spent a long time writing a program to do all these things. And it even does a few more things, which is kind of hard to explain, unless you got a firm holding on all the above mentioned concepts. But I have faith in u...


----_Dirty&Litigious_----