[PairTheBoard]

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It seems your point is "probability only applies to future events; events that have already occurred (such as a girl getting a haircut) cannot have probability assigned to them." This is perhaps semantically true, but useless. My contention is that we can equally use probability to apply to events that have happened in the past but that we do not know the outcome of, and that this is just as valid as using probability on future events.

Case in point:
You have the A[img]/images/graemlins/spade.gif[/img]K[img]/images/graemlins/spade.gif[/img]. The board comes Q[img]/images/graemlins/spade.gif[/img]J[img]/images/graemlins/spade.gif[/img]2[img]/images/graemlins/heart.gif[/img]. What is the probability your flush will hit?
We use probabilty in poker all the time. But the deck is already shuffled; if you have perfect information about the state of the deck, you *know* that the flush either will come (100%) or won't come (0%). The randomizing event has happened. But we don't know the outcome yet; it's hidden. Therefore we use probability to analyze the problem. I can say "the repeatable part of the experiment is flipping the cards over; I'm not going to reorganize the deck" all I want - the use of probability is still valid.

Clearly you disagree with this, but you aren't convincing me that your point is valid very easily.

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One difference here is that the known cards, AsKsQsJs2h do not DETERMINE what the next card to be dealt will be. However they DO EFFECT the probabilty for the next card. Suppose this hand is heads up with no burn cards. Prior to seeing the AsKs in your hand and the QsJs2h on the board you would have said that the probabilty that the 8th card in the deck is a spade is 13/52. The other difference with the Twins is that in this case you know how the probabilty for the 8th card has been affected by what's been revealed. Seeing the AsKsQsJs2h has changed the probabilty for the 8th card to a known 9/47. That's the conditional probabilty for the 8th card Given your hand and the flop cards. The twin with the tony is the same idea only the original 50% probabilty is changed to an Unknown conditional probabilty when the Tony twin is revealed. In fact the Tony twin completely Determines which twin is behind door 2, we just don't know what the determination is.

Also, as far as the past future thing. What exactly do you mean when you say the probabilty is 9/47 that the 8th card will be a spade? I believe you mean that if you arrived in this same situation - a randomly shuffled deck and cards dealt as they are - repeatedly over numerous trials you would then see a spade on average 9/47 ths of the time. Whether or not this is actually done doesn't really matter. But that's what you Mean when you state the probabilty.

However, what if I told you this. We are going to keep the cards just as they are and shuffle in numerous players to sit in your seat to have the fixed 8th card revealed to them. Let the random Suit S denote the outcome of the revealing of the fixed but unknown 8th card to a random player put in your seat. Would you still insist the probabilty that (S is a spade) is 9/47?

PairTheBoard