Random Math / Theory Question
 

Assume a situation where my opponent must hold either a set or a specific pair. Assume that the odds of him being dealt the specific cards for the pair or the specific cards for the set are equal. Under these circumstances is it much more likely for my opponent to have a set than a pair if his actions are equally indicitive of either?

Edit: See my third post, it makes much more sense [img]/images/graemlins/frown.gif[/img]

Re: Random Math / Theory Question
 

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Assume a situation where my opponent must hold either a set or a specific pair. Assume that the odds of him being dealt the specific cards for the pair or the specific cards for the set are equal. Under these circumstances is it much more likely for my opponent to have a set than a pair if his actions are equally indicitive of either?

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You have to count the combos of different hands your opponent could have. Then, if you want to, weigh down some of the possibilities if you don't think he always plays like that.

Re: Random Math / Theory Question
 

The entire point of the question is that it's made under the assumption that all permutations and other outstanding factors aside from the difference in odds to flop either hand type are equal.

Re: Random Math / Theory Question
 

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The entire point of the question is that it's made under the assumption that all permutations and other outstanding factors are equal.

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I think your post is too general, and it depends. Please give an example that uses your assumptions, and we can figure out what is most likely.

Re: Random Math / Theory Question
 

"Does how likely my opponent is to have flopped a certain type of hand affect how likely he is to have that hand when he represents either it or another hand equally, all other factors withstanding?"

Edit: Adding an example I gave to a friend over MSN:

Like, if somone stuck a gun to your head and said "your opponent must have either 77 for a set or AK for a pair, he's equally likely to be dealt either 77 or AK (not the case in reality, but assume)" you'd choose AK and expect to be correct by a large margin?

Re: Random Math / Theory Question
 

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"Does how likely my opponent is to have flopped a certain hand affect how likely he is to have that hand when he represents either it or another hand equally, all other factors withstanding?"

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I don't think this makes sense, although I kind of see what you're getting at.

The point is that we can see the flop, and we can see his betting. The unknown information is his hole cards. If the flop is K 7 3 and you tell us that it's equally likely he has a pair of kings or a set of 7s, then guess what? Under those assumptions, it's equally likely he has a pair of kings or a set of 7s.

This is just because you've given us the distribution of his hole cards as being 50% 77 and 50% Kx.

The reason there's a skewing of likelihood between the set and the pair in real life is precisely because there are fewer 77 combinations that Kx combinations.

Guy.

Re: Random Math / Theory Question
 

Right, you've almost got it. The only factor left over is that it's far more unlikely to flop a set than a pair. Does this affect our results? Or is it independent when his actions represent either hand equally?

Re: Random Math / Theory Question
 

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Right, you've almost got it. The only factor left over is that it's far more unlikely to flop a set than a pair. Does this affect our results? Or is it independent when his actions represent either hand equally?

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That part doesn't matter. Once the cards are out, the likelyhoods of things change from how likely it was to happen before it happend.

Once again... see what hands they could be playing the way they are, and count the combos...

Either that, or phrase your question in an easier to understand way.

Re: Random Math / Theory Question
 

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That part doesn't matter. Once the cards are out, the likelyhoods of things change from how likely it was to happen before it happend.

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That actually answers my question, and gives me enough of an explanation that it makes sense to me now. Sorry this was worded so awkwardly, but the whole question was conjecture (I don't know [censored] about math). Thanks for being patient.

Re: Random Math / Theory Question
 

Here is an example of how to do this:

Board = KQ52
Your hand = AQ

Our estimate of the probability that he would play his hand the way he actually played if he holds:

55 = 10%
KK = 100%
QQ = 100%
AK = 50%
Everything else: 0%

55 = 3 possible hands * 10% = 30
KK = 3 possible hands * 100% = 300
QQ = 1 possible hand * 100% = 100
AK = 9 possible hands * 50% = 450

There is only one possible QQ hand because you can already see two queens.

There are nine possible AK hands because there are three unseen aces and three unseen kings.

P(55) = 30 / (30+300+100+450) = 30/880
P(KK) = 300 / (30+300+100+450) = 300/880
P(QQ) = 100 / (30+300+100+450) = 100/880
P(AK) = 450 / (30+300+100+450) = 450/880