Game Theory

[Demiparadigm]

Wondering if anyone has any thoughts on Game theory as it relates to Hold'em? I play a very math-oriented game which a lot of players here don't seem to care too much for.

Here's an example:
I'll call it the "semi-bluff check raise" A play I haven't ever seen in a book.

In a NL ring game, bilnds are $5/$10

Let's say you bring it in in for $30 holding AQh. 2 players behind you call along with the big blind. There is now $125 in the pot

The flop comes Kh, 8c, 3h giving you the nut flush draw.

The BB checks, you check, the next player bets $60 (1/2 pot) the button calls and the big blind folds.
There is now $245 in the pot.

You now have more than great odds to chase your flush and call.
(your odds are 2:1 of making the flush by the river and the pot is laying you 4:1)

but instead, given the size of the pot to your bet, you raise to $180 making the odds about 2:1 if called(245+180=425/180-or2.36:1,which theoretically, is a positive-expectation play.
if re-raised to $360 you still have implied odds to call. (fold if raised more)

You now have taken control of the pot, and could win if your opponent folds.
You have effectively disguised your hand and may get called even if you make the nuts.
If you check the turn, you may get a free card when your opponent checks behind you.
You may win by betting the turn (following this theory- $200 in to the now $605 pot to match your 4:1 odds of making the flush on the river)

I would only make this play maybe 1 in 9 times that it comes up,(I'd rather take the odds than lay them) but it is an interesting element to mix up my game.

I would love to hear thoughts.

[Demiparadigm]

Game theory and bluffing:

First you determine the chance that you have the best hand
Add that to the percentage of the time you will have the best hand at the river
Add the percentage chance your opponent will fold if you bet
Subtract the percentage chance that your opponent will raise if you bet
use that as your chance of bluffing

For example in the above $5/$10 NL game my opponent raises on the button to $30
I call in the BB with j/10 offsuit
the flop comes 389

I probably don't have the best hand, but I have an OESD with 2:1 chance of hitting, and 2 over cards
My opponent could have been trying to steal the blinds
so I will assume that there is a 10% chance that I have the best hand
and a 33% chance of having the best hand (not including the 6 outs from my over cards)
I think there is a 30% chance that my opponent will fold to my bet,
and a 10% chance that he will reraise (you have to gauge this on how your opponent has played up to this point)
so 10+33+30-10= 63%
so, I should actually bet this flop more than half the time.

You need also, however, to take into account the pot odds that your opponent is getting to call your bluff.
so, you take the pot size ($65) and consider your chances of making your hand (33%) then bet an amount where your odds from the pot- if your opponent calls- are equal to the odds of making your hand.

So, going back to the above example, I would bet the pot, hoping my opponent folds, but if he called, I would have bet $65 to win $130 (his call, plus the pot amount)

NOTE: This would not be a winning play, in general, except the amount of times that your opponent folds, more than makes up for the times you lose the hand.

[Wet_DreaMer]

Very nicely written post. Well explained, and good examples for newer players.

Im pretty sure most people around here use this already tho, to varying degrees.

[johnnyawe]

Demiparadigm, awesome post and explanation.

The semi-bluff check/raise is in fact a well known strategy, especially when you flop the nut flush draw, like in your example. You appear to have "independantly discovered" this play, which says a lot for your understanding of the game. Your explanation of the strategy is as good as any I've ever read. Good stuff.

[johnnyawe]

Game theory and bluffing:

First you determine the chance that you have the best hand
Add that to the percentage of the time you will have the best hand at the river
Add the percentage chance your opponent will fold if you bet
Subtract the percentage chance that your opponent will raise if you bet
use that as your chance of bluffing

For example in the above $5/$10 NL game my opponent raises on the button to $30
I call in the BB with j/10 offsuit
the flop comes 389

I probably don't have the best hand, but I have an OESD with 2:1 chance of hitting, and 2 over cards
My opponent could have been trying to steal the blinds
so I will assume that there is a 10% chance that I have the best hand
and a 33% chance of having the best hand (not including the 6 outs from my over cards)
I think there is a 30% chance that my opponent will fold to my bet,
and a 10% chance that he will reraise (you have to gauge this on how your opponent has played up to this point)
so 10+33+30-10= 63%
so, I should actually bet this flop more than half the time.

You need also, however, to take into account the pot odds that your opponent is getting to call your bluff.
so, you take the pot size ($65) and consider your chances of making your hand (33%) then bet an amount where your odds from the pot- if your opponent calls- are equal to the odds of making your hand.

So, going back to the above example, I would bet the pot, hoping my opponent folds, but if he called, I would have bet $65 to win $130 (his call, plus the pot amount)

NOTE: This would not be a winning play, in general, except the amount of times that your opponent folds, more than makes up for the times you lose the hand.

Demi, have you read Texas Hold 'Em for Advanced Players by David Sklansky? He has a chapter on game theory that reads exactly like this post.

EDIT: I meant to say Theory of Poker by Sklanksy, not Hold 'Em for Advanced Players.

[BL Mike]

The other nice thing about the semi-bluff check raise is when you show down your hand, you then subsequently get a little more action on your check raises when you have the goods.

[dsaxton]

I think that game theory is really only useful in poker in the most basic situations, where the numbers are already given (e.g., in determing pot odds and things like that). But, for most decisions in this game, the numbers will not even be known, and therefore you will have to rely on your own intuition in order approximate just how likely you believe something to be. These situations include, the chances that your opponent is bluffing given past tendencies, the board cards, your pocket cards (as seen cards), and any other important information; the probability that your opponent is holding a certain kind of hand, given similar information. These are situations where you won't be presented with precise probabilities, but rather will have to approximate them for yourself using some crude form of intuitive statistics.

I feel that the crux of poker is not knowing numbers and doing math, because the numbers generally aren't even known, but instead it's on relying on your own rational judgement to decide for yourself just how likely something is.

[FlyingSaucy]

I don't see the connection to game theory in your example. I like the idea in terms of mixing up they way you play draws, and taking some aggressive steps that will get people to fold to you. However if you do it more than a couple times people will be on to you.

Demi, have you read Texas Hold 'Em for Advanced Players by David Sklansky? He has a chapter on game theory that reads exactly like this post.

The Theory of Holdem also has a chaper for it. I haven't read a better application of game theory to holdem. It however is incredibly weak and oversimplified. Game theory as it is today is a field that is not nearly developed enough to describe any real application to holdem. Holdem is far too complex to make it worth worrying about.

Put it this way, if game theory offered any actual strategic solutions, there would be software out there that can kick the crap out of the best human players. However at this point there is no such program. Knowing game theory may be remotely useful in that it will help you to understand what factors to consider when developing a sound strategy. Other than that, it's not worth concerning yourself with much.

IMO, artificial neural networks is a field that offers the best chance at developing a winning system. Of course I know about 1 lecture's worth of 4 year old material about that.

[johnnyawe]

Actually it is the Theory of Poker, not Hold 'Em for Advanced Players, that has the Game Theory chapter.

[FyrFytr998]

Man I envy all you math geniuses. I just play the cards as they come. I wonder how many pots I may have lost by not knowing my odds. Stoopid numbers.