For me, the main idea in multistreet bluffing is to consider all hands that you'll bet on future streets as value hands, and to choose your bluffing range for the current street appropriately. However, as pointed out before, the theory behind this assumes static hand values. The way I understand it it also assumes that Villain can't raise, but maybe this assumption can be dropped.

Quick idea instead of basining your strategy on MIN-MAX for all reasonable players, your decision tree is based on MIN-MAX with unknown (unreasonable) players who may have a different strategy. One of the awesome challenges with Game and Decision theory is trying to determine the desired outcomes of our challengers. That is why most of Nash theorems state that all players are reasonable. Taking those same basic games and playing them with one reasonable and one unreasonable player, your decision tree changes greatly.

Yeah, I think you have one of two ways of addressing unknown players. Play a GTO strategy as I suggested, since you're not sure how your opponent is going to play. However, if you feel that you can make accurate assumptions on how unknown players play at your level, then you should play an exploitative strategy against this type of player. Is that what you're saying?

Also although all players start off unknown, there's lots of opportunity to begin making assumptions about the player even before we have a reasonable number of hands.

and that is what makes it fun!

I still don't see the difference between Sammy's strategy and exploitive play.

it's probably just lexicon.

I am meeting with my Decision/Game Theorist this afternoon and see what if there are any differences.

I know I have a tiny postcount and no credibility, but please could the OP at some point change the article so that it uses you're/your correctly? As a sticky and an example of content 2+2 posters are capable of generating, I think COTWs should be held to higher grammar nazi standards than usual threads .

EDIT: Actually it's just only one line, nevermind xD.

(MISCONCEPTION 1: Your supposed to lose money with your bluffs)

If villains don't ever slowplay 2pair or sets on coordinated board textures doesn't that mean that I should start overbetting with bluffs and value hands?

I know that overbetting is correct when we can have the effective nuts and villain very rarely has the effective nuts and it allows us to get more value for our big hands and have more bluffs in our range.

just to theory of bluffing.
if you play your bluffs in same way as you play your value hands and if you bluff the same amount of hands as you bet for value then your strategy is unexploitable.. did not see it anywhere, it is interesting theoretical background imho.

sorry it took me a while to get back to your post.

it's nots so much that Villain doesn't slowplay 2pair or sets, it's just whenever his range is capped and your hand is stronger than the top of his range. Similarly, it doesn't matter if the board is coordinated or not, only that the Villain's range is capped (but you're right that people are more likely to slowplay on dry boards).

And so you're correct that when you overbet for value, you'll need to balance that with some bluffs as overbets as well. Do you have a specific question as far as that goes?

do you want to expand upon this? I'm not exactly sure what you're saying. If you're saying that you need to balance your value hands with bluffs, then you're correct. if you're saying that you need to slowplay your worse hands as you do your monsters on dry boards, then I'm not sure that I agree.


I don't think this is correct. But maybe you can explain why you think it is, and we can go from there.

Why do you think that this is true?

If villain can assign the correct probability mass function over your hand range then villain can exploit it. Having a mass function that's uniform over your bluffing range and your value range doesn't exclude you from this.

I could be wrong. Waiting eagerly for your explanation

lunatic fringe: yes, i meant that balance between value hands and bluffs.

why is playing same amount of bluffs as value hands unexploitable?
lets say, that we play 90% of hands for value and 10% as bluffs. then it would be easy for villain to adapt, because if we bet we have it in 90% so it is safe for him to fold.
but now if we play 50% for value and 50% as bluff it is impossible for him to make money from us. why? we win in 50% and lose in 50%. so our income is 0 and his too. btw generaly the entropy of uniformly distributed actions is maximal

i am not in game theory field anymore (moved to fuzzy logic) and i was never expert in it, but as i remembered i should be right.. and one more thing, unexploitable strategy is not the most profitable one

Having the same number of bluffs and value hands is not unexploitable. Since the pot odds are always better than 1:1, you should always have fewer bluffs than value hands.

Edit: It seems like you forgot that there's already money in the pot.

Is your work in machine learning? Or economics?

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Let our hand range be the set O. Let each holding be o ∈ O. |O| is the number of holdings in our range.

Suppose we bluff the river and our range is completely polarized. Let A∪B=O and A∩B={ }, where A is our bluffing range and B is our value range. Let villain have a hand that wins against all a ∈ A and loses to all b ∈ B.
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Consider a probability mass function f(o) over O, where Σ_i f(o_i) = 1. These are the probabilities that villain attributes to us holding some o ∈ O.

Let p_i be the probability that the villain attributes to the hero bluffing some a_i, with i ∈ {1,...,|A|}, and z_i is analogously defined for the value range B.

Then from villain's perspective their objective function (assuming linear utility function, which is best in practice due to ease of estimation) is to maximize (P+X)*(Σ_i p_i f(b_i)) - X , where P is the pre-bluff pot amount and X is the bluff size.

If villain knows the population values of p_i and z_i; namely, p_i = z_i = x% ∈ [0,100] for all i, then we must not use these as our bluff frequency, depending on |A| and |B|. If, for example, |B|\|O| > 0.8, then clearly our bluff frequency should be low because Σ_i p_i f(b_i) will be high, enticing a call from villains very often. If |B|\|O| is very low, then Σ_i p_i f(b_i) will be low and hero should bluff more often because villain is calling rarely.

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I'm still not sure if your outlined strategy is unexploitable. I'll need some more time....