Bluffing Theory part deux

Sure everything is situational. Here is something to discuss.
For the stuff below ther are a few conditions.
1.) No tells- You may not say it depends on the read I got. Imagine the guy is in a coma. Tells are overated, a part of the game for sure, but should be used carefully in only marginal situations.


But Im talking about the mathematics of bluffing.

Let's say you only have 2 cards lying around the house 1 ace and 1 king, and a bunch of chips. You shuffle and deal, one guy bets, the other guy folds right?
The ace bets and the king folds.
Now you find a third card. You can now gamble, why because you can bluff, because you have added the element of imperfect information. OK so lets say the third card is a Q.

1.) Ace should always bet, he has the nuts. And if his opponent has the king the king may raise, thinking the guy with the Ace may have the Q, and is trying to bluff.
2.) This is where most of us find ourselves in most situations. The second nuts. there is one hand that can beat us and one that can't.

3.) Should the queen bluff 100 percent of the time? No
should the queen never bluff? NO
so how often should you bluff when you get the queen?

3b) How about bluffing with the king? You must once in a while.. How often?

Bluffing theory part three will be how to defend against bluffing theory.

If you are positive that the three people in the one card per hand game, have A,K, and Q, when would it ever be a good idea for the Q to bluff? Someone holds the Ace, or nuts, and isn't going anywhere, the other holds the King and is folding like a cheap suit to any raise because there's a 100% chance that someone other than him has that Ace. Even if the order of action is Q,A,K, the Queen bluffs, Ace calls or reraises, and the King has the hands determined.

In a normal bluffing situation, one must rely on the fact that they have no opponent, who will be a possible victim to their ploy, holding the nuts. You aren't scaring that guy off of his pot no matter what amount you bet. The success of your bluff is dependant on the fact that you can represent a hand higher than that of your opponent. If you are certain someone has the "nuts" at the table, and you are certain it isn't you, bluffing is a terrible play.

Well, the day has come. I have to admit that I completely agree with diablo. I'm not a really big bluffer (cause I'm still relatively new to the game, so I try to play by the cards). BUT why would someone in that situation EVER bluff their queen. They know that not one, but TWO people have a card that will beat them. And the person with the Ace KNOWS that nothing can beat them. The possibility of scaring them into folding isn't there. I'm sure the example was intended to simplify bluffing, but I'm not quite sure I'm seeing it.

I'm flattered.

He said add extra card, not add extra person

thats true
i was thinking of it the same way that diablo and luna were - that there were 3 cards for 3 people
with 3 cards and 2 people, bluffing the Q isn't a bad idea at all
when you have the Q, your opponent will either have the A or the K
therefore bluffing the Ace when your opponent has the A is not going to work
BUT bluffing the Ace when your opponent has the K is a legit bluff
so i say bluff with the Q %50 of the time
same thing with the K - your opponent is going to have the A %50 of the time, so bluffing %50 of the time will prove effective in my eyes

My excuse: it was early here and I only slept about 3 hrs last night. And in Bills defense I was wondering if he was smokin' something with the way I interprited that question.

I know you don't want to hear "it depends," but it somewhat does. It depends on what type of player your opponent is and what he expects from you.

That being said, I'll try to give you a mathematical answer. If you have the queen you should bluff less than half the time. I figure, there's a 50/50 shot whether he has the ace. If he has the ace, there is a 100% chance he calls or raises; if he has the king, there is a greater than 0% chance he calls or raises. Exactly what is the best amount of time to bluff with the queen depends on your opponents propensity to call with the king.

Bluffing with the king? Seems like you shouldn't ever. If he has an ace he'll pick you off and if he has a queen he'll fold.

It's an interesting post. Bill, would you mind adding a betting structure to this abstract situation. (i.e. Limit betting, with a SB and a BB, we are on the button and acting first.) I think it would make it easier to come to a definitive conlusion.

Is betting the K technically bluffing? You're not representing an A by betting it - if opponent has Q they are beat anyway. Only betting on Q can qualify as a bluff, as it is a losing hand, but can be played to represent a winning one.

Semi-bluff, or as close to that as you can have in this scenario. You have a hand, not the "nuts" but you may very well represent the nuts with the K to push around the Q, or the Q to push around the K. If either one runs into the A, that's yo' aaasssss, Mr. Postman. BTW, sorry I donked this threed up earlier. I am forming a real response to it, please standby...

Nah, a bluff is when you get a better hand to fold (or try too) - cant do that if you've got K, as the only card better is A, and you're not going to get them to fold.

I would suggest that betting the King in this experiment is only a "semi-bluff". I occasionally get accused at the table of "bluffing" when I'm holding a decent drawing hand, like a double-gutshot, open-ended, or four-flush. That's not technically an outright bluff, as I'm betting to build the pot toward the prospect of eventually making my hand and getting a decent pay-off. Representing the Q in your bet as the A or K would be a true bluff, because you know you're holding the worst possible hand with no chance of improvement.

So, given the h2h 3-card scenario here, I think position rules. Whether I'm the first to act or not is going to dictate how I play the A,K, or Q as much as (or more than) the actual card I'm holding.

After actually sitting down and thinking about this, I'm wondering why it even matters. Only bluffing card is the Q, and she only good to represent the A. This question is odd. Too many variables to successful bluffing for it to be simplified in such a manner.

Where I kept donking it up was constantly adding a 3rd player to the equation...

Ya, the question's certainly odd, but I like it. Not so much "when should you bluff" but I like thinking about the strategy of such a game. Hope you don't mind if I take your idea and run with it Bill, but I think I'm gonna invent a simple game like this, and post it in my blog. It will probably be more like 5 cards, and 3 players.... I'll post it on here after I come up with it.

Wow, great stuff everyone Thank you.

Reagarding the king, I concede, the line was supposed to say bet:
How about betting / calling with the king? You must once in a while.. How often?
Sorry, my bad, let's not let it throw us off thread. Kudos to those that caught that.

-Formulas have been eluded to , someone said a bluff attempt should be tried less than 50%. That works
In this case we need to bluff 4 out of the 10 times that we receive the Q.

I'l try to show some math:
2 ouf of 3 times we will receive either, an A or a Q.
When our opponent holds the K he has a 50 50 decision. It is currently a zero sum game. He is correct to call 50% of the time.
We announce that we will bluff 4 out of the 10 times we receive the q.
Now he is forced to call more than 50 percent of the time. we have turned his coin flip into a negative expectation for him.

But wait the king has some options to defend against this, how does he turn this negative ev into a positive one?

Bill

i say bluff the A lol.

I've played A K suited and it has broke me more times than I can tell you. I'm a bit gun shy with them. If either one comes out on flop I'll play,if they don't get to carried away. I've had 2 pairs-A's & K's on table and been beat with 3 duces. It's just pure luck and guts. If it's your time to win and if not it's bye gg.