Meaningful bluffing

[aliensyndm]

OK quite a nice little piece here from Mike Caro, the mad genius of poker.

Suppose you're playing against a single opponent in a game in which you ante and receive only a single card facedown. You then wager on the strength of that one secret card. Fine. But suppose that you can't find a full deck of cards to play with. How many cards do you need to find for the element of bluffing to be meaningful?

I'll let you have a think and post the answer up in a bit. It's a very good answer and illustrates many important concepts in poker. As well as pasting up his own answer I'll be adding some views and points of my own.

[A.M.P]

Personally I'd think there's what - 14 possible cards you can get. So therefore for me to be in a "good" position I'd like above a ten - 4 cards can beat me with that. So for for me to "bluff" as I think you mean it i'd like 1/4 deck -14 cards.

AMP

[aliensyndm]

OK here's the answer from mike caro....

"You need at least three cards. (And, of course, they can't all be the same rank.) Let's say the "deck" consists of two cards - an ace and a king. If you are dealt the king, you can't bluff because the other player must have the winning ace and must call. There's no reasonable decision to be made.

What if there are three cards - an ace, a king, and a queen? Then, if you're dealt a queen, you might try to bluff. Your opponent would be faced with a meaningful decision about whether to call with a king. He would absolutely call with an ace. (We won't consider raising in this simple hypothetical card game.) If you are dealt the ace, you can bet with impunity, hoping to be called by the king. Or, you might try to check-raise if the rules allow it. The queen, of course, isn't a calling "hand," because whoever has that card knows it's a loser.

But here's where it gets more interesting. If you're dealt the queen, you might decide to bluff. Of course, if your opponent holds the ace, you're dead. But what if he holds the king? Then, he has a rational decision to make. Should he call, hoping you hold the queen? Should he fold, fearing you hold the ace? Now we're seeing the soul of poker.

But, wait! It turns out that this isn't just a curiosity; it isn't just an easy-to-understand mental puzzle. It's more. It means something to poker players, even when they play traditional games for big money.
We saw that you could (and probably should) bet your best card - the ace. And as long as you play poker, you'll make more money simply betting your best hands than doing anything else with them. Sure, we talk a lot about check-raising, about checking to give opponents a chance to bluff. But those are alternative strategies that add to your overall profit if used occasionally. You are unlikely to make much profit in poker if you always seek alternative strategies, if you try to play too fancy. When you have a strong hand, you usually should feel compelled to bet.

And what if you hold the king? In our simple three-card example, you can't justify a bet. You'll always be called when you have the worst card, and never when you have the best one. And that turns out to be a powerful truth about poker. Although there are rare times when you might argue that you should bet a hand that is neither strong nor weak, generally you shouldn't. Medium-strong hands are prime candidates for checking, and if you violate this powerful truth too often, you're certain to suffer.

If you bet your strongest hands, check your medium hands, and bluff with your weakest hands, you'll be walking the right path toward profit. As we get more sophisticated, we learn exceptions, but if we get fancy and use exceptions too often, we'll lose. The three-card example is designed to point serious poker players toward reality. Answer: Three."


Some good lessons there. You don't need to be ultra fancy to make cash from your good hands. Just betting your good hands is a good way to play them. The "theory" of the bluff is also well illustrated. To quote Slansky from The theory of poker (a must read for anyone serious about poker)

Every time you play a hand differently from the way you would have played it if you could see all your opponents' cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you lose.

That's a key thing right there. You bet with the queen and try and make them fold the king, something they would never do if they could see your card. When we play poker there's more cards and more rules but the bare bones of what we are trying to achieve are right there.

[Beanie]

Nice one Alien...a good read

[TheGooner]

Sad anorak that I am ... I knew the answer had to be three ...

But the post answer dialogue was very useful.
Thanks mate.

[aliensyndm]

Knowledge is power gooner. Even having anything to do with the internet made you a sad anorak a few years ago. Now people actively try and learn more about it as they realise just how powerful and useful a tool it can be.
I thought the whole question made some interesting reading.

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