Quote Originally Posted by Sci Fi
Gingerwizard,

A more practical way of deciding the likelyhood that the six callers held an ace or king would be to compare the activity in this hand to the activity in prior hands. If the button is often facing six callers then my notion that aces and kings are likely to be held by the callers is questionable. However, if this is far from the norm then I don't think it unreasonable to think a high probability exists that one or two of your outs are gone. Think about it. Six callers have paid money to play their cards. That's twelve cards out of the thirteen available. Does it seem unreasonable to you that the two highest cards would have each been played?

I don't mean to detract from your thread but that other thread got out of hand. I'm still curious about the calculation of the AK call given X outs are gone. Anyone?
The point is that your beliefs must be specified and then used to form a judgement about your hand. It is quite easy to put a probability on so many of your outs being dead and then work out your probability to win the hand conditioned on so many outs being dead.

E.g. Let D= "The event that 3 of your outs are dead"
Let W = "Probability you win the showdown with 99"

First you make your own subjective judgement about P(D)
Then P(W | D) is easy to calculate in PokerStove (provided you don't believe in external forces such as luck driving the outcome)

Then P(W&D) = P(W | D)P(D).

Then to get deeper we could specifiy Di = "The event that i of our outs are gone"
and use

P(W) = sum_i {P(W | Di)P(Di)}

what you must understand is that by doing this you must coherently express your beliefs of the liklihood that he limps all of the other types of hands too. E.g. PP's, SC's, connectors, junk, Qx, Jx, so that all your beliefs specify a coherent distribution, and that the sum of all of these probabilities is 1.

if You can do that then you can come up with a new expected value to win and then you must base your decision of whether to call or fold on that and that alone.

I argued above however that you cannot express with confidence probabilities for the Di and for all other hands, different from those specified in the assumption that "all hands are equally likely."

If you can and you want to then go ahead, but know that experienced posters on this site cannot help you with these judgements as they are purely personal and understand that by doing this you will make a lot more mistakes by calculating the wrong probabilities and thus lose more money than posters on this forum.