starcraft semesa?
Quote:
Originally Posted by semesa
What if we can range villain to a single hand, which is the absolute nuts, then we can assume his calling range is 100%, and bluffing has infinite negative value
In cash game if you bluff $X then your bluff has -$X value.
Quote:
As equity decreases past 50%, bluffing value increases, 0% equity = infinite value
If you have 0% equity, then your bluff has a value modeled by an integral over some appropriate probability mass function.
Define Ω as the sample space/hand range with |Q| as its cardinality.
Define f as the probability mass function that maps an element of the range, ω in Ω, to some 0 ≤ (1-p(ω))q(ω) ≤ 1, where p(ω) is defined as the probability that villain will call with holding ω and q(ω) is the probability that villain is actually holding ω. Constraints are \sum_{i=1}^{|Q|} (q(ω_i)) = 1. So we define f: Ω --> [0,1].
Then the value with 0% equity is the lebesgue integral over Ω that integrates (P+X)*f(ω)*dP - X.
$X is, again, defined as the bet size. $P is the pot size before you bluff.
The solution is bounded in the interval over the reals [0,P].
It'll be easier this way. Consider vectors I and O that have the number of elements equal to the number of ω in Ω. Let each i_ω ∈ I be the chance of folding holding ω, and each o_ω ∈ O be the chance that ω ∈ Ω is the actual holding. Then the E[V] is (P+X)I'O - X.
This could all be wrong (the lebesgue integral, not the matrix algebra). I'm incredibly tired.
Quote:
This also makes semi-bluffing extremely confusing, if semi-bluffing is bluffing with equity, it means we think we behind but not behind by much, so our equity is closer to 50% and we should be less willing to bet and more willing to call/fold.
I have some ideas but they're too early to post.
Last edited by computer1011; 09-23-2012 at 11:29 AM.