Need help, advice and thoughts on Game Theory in Limit HE.

[Sasnak]

Doing some rereading of TOP and became interested in the section on Game Theory. Sklansky discusses a couple of examples which one was the odd/even finger game. You know, "Once, twice.... SHOOT!" and you stick out one or two fingers after you decide whom is calling odds or evens. He cited the use of a tossing coin to determine and randomize your choice of one or two fingers. Heads/odds and tails/evens. This way your opponent couldn't out think you or "put you on a hand" so to speak.

The other example was using certain cards to bluff at a pot in Razz or Lowball. (I forget which but not important). With the use of bluffing cards your expected winrate would increase. With each additional bluffing card added your expected winrate would increase as well. As your opponent really wouldn't know if you had a hand - or were just bluffing. Again more "randomization".

In Limit, I'm a fairly mechanical player with PT stats which are hovering around 17/8/2.5 with a 2BB/100 WR. Not that it matters but I'm still learning and do have a TAGistic approach, let's just say I'm above the ABC style (learning every day) and not yet an aggro 2+2er with a 6BB/100 sustained WR. I will raise for value preflop and post flop. Push my draws. Reraise for info, to buy the button, buy myself outs, get someone fold a weak Ace, etc.

Now, I would like to utilize and experiment with some Game Theory but don't have a good enough grasp of what I need to begin with. How would one "randomize" their actions say on the Turn or River? Does anyone use some type of Game Theory in their preflop actions? Are you using specific cards, etc? I recall reading in one book about picking either a black or red AK and limping in with that specific hand just to throw off your opponents, I'm assuming this works better in a live game rather than online, but you get the gist of it.

Would CRing a scare card on the Turn if it happened to be a A[img]/images/graemlins/spade.gif[/img] or K[img]/images/graemlins/spade.gif[/img] with two or less others in the hand be considered a legitimate GT tactic?

Any advice or links to good threads?

[AaronBrown]

Game theory is interesting to analyze poker, but you don't need to understand it to play. For example, you can use it to compute the optimal bluffing frequency against a single opponent who knows your frequency and plays perfectly. That's nice, but in real poker you adjust your bluffing frequency depending on whether or not you're getting called with your good hands. If you are, don't bother to bluff. If you're not, bluff until you get some calls. If you never get calls, bluff all the time.

It's nice to make your bluffs perfectly random, but the main point is to make sure your opponents don't know when you're bluffing. The first mistake people make isn't to bluff at predictable times, it's to represent their hand inconsistently.

A good game theoretic way to bluff is to pick some specific hands, then pretend to yourself you have a different specific hand. Make the same mental calculations as if you did have the pretend hand, and the same bets. A common mistake of bluffers is not to give opponents the same scrutiny as when they care how strong that hand is. Of course, you can't completely fool yourself, you don't want to call a showdown bet, but it helps you stay consistent to pretend.

The two troubles with that approach, in my experience, is you can't pick your bluffing times or situations. I bluff when I think the table is ripe for it, generally based on people folding too much, but also on feel. That's dangerous, because if I have reasons for deciding when to bluff, other players might guess them. But I think I make more than I lose by trying.

Situations are even more important to me. It's not that I want my opponents to call more in general, I want them to call more in specific situations. So those are the situations I want to bluff in. Maybe players are already too eager to bet before the flop, so there's no point in starting out a hand bluffing. But they fold quickly if they don't improve. So I want to run bluffs when a start with a good hand and don't improve even though there are scare cards on the table. In the game I described, that will be profitable, and if I get called, I'll make more money when I hit the flop.

That's triply dangerous. Not only might my bluffing get predictable, but I will be bluffing in exactly the same situations other people are likely to be bluffing (another common mistake is to spend all your time thinking about your play, none about how your opponents are reacting to the same data) and, since I'm changing horses in midstream, I may act inconsistently.

I don't think game theory will help you much with any of this. It's nice to know, and it deepens your appreciation of the game. It can help protect you if you're playing against much better players. But if you're already winning, I don't think it will make you richer.

[Cincy Peach]

this raised an interesting question about my game . . the OP talks about his humble 2BB/HR but that is much better than I do online. (For some reason I do better at B&M)

How often do you do a pure bluff (as opposed to a semi-bluff, where you have something or some draw to fall back on)?

I mean, I almost NEVER pure bluff, except occassionally on the river when I have completely missed and then it is a simple math exercise comparing the pot odds to the chance I estimate he will fold. And ussually I will only try this on hands where I was betting a strong draw aggressively, represtenting a made hand all along.

In limit hold'em, how much pure bluffing is really effective? If I do it as seldom as once per hour is that a major hole in my game?

[Arnfinn Madsen]

Depends on the leve. At .25/.50 I would never almost bluff. At 2/4 a lot of bets are +EV regardless of what you have, i.e. some BBs are so tight that when folded around to you, raising any 2 from SB with follow up bet on flop is +EV. This is IMO a pure bluff.

[NMcNasty]

Against one or two opponents, flops with one high card and a low pair A33, J66, etc. are great for pure bluffing in an unraised pot.

[AaronBrown]

Pure bluffs should be reserved for good players. The only reason to do a pure bluff against bad players is a pure advertising play, when you hope to get called. The only thing bad players will remember enough to affect their play is if you showdown a large pot holding 7 2 offsuit, with no pairs, against a guy who had three Kings. That will earn you a lot of money, but you don't need anything this fancy to take money from bad players.

Among good players, the proper ratio is about half as often as your good hands win without showdown. Looking at it another way, when you win without showing your hand, you want to have nothing to show about a third of the time. You have to be careful not to get to mechanical about that, some players fall into a pattern of two wins-by-fold in a row means a bluff at the next opportunity.

Also, there are a wide range of styles, all of which work. I recommend changing among them frequently. If you semi-bluff a lot, you don't have to bluff at all. If you play a lot of hands, bluffing is less important. If other players bluff a lot, you should reduce your bluffing. Some players react very badly to being bluffed, against these players you want to bluff.

Another factor is to run your bluffs in streaks. In some games it makes sense to establish a tight reputation, then bluff the rest of the night. In others you want to run a bluff or two early, then never again. Keep everyone guessing.