03- 9-04, LearnTexasHoldem:

Unseen cards and figuring odds...

Question: I was reviewing your site and as i was sifting through the different sections a thought came to me that i cant figure out. when establishing the odds of getting a card on fourth street and then on fifth street you base that on the remaining deck i.e., 47 then 46. This is fairly simple arithmetic. But here is my problem???? If there are nine other players each with two pocket cards does not the probability of catching `your trips/four of a kind, straight, flush etc., become conditional on your need card(s) not sitting in another pocket???. How does one figure out the true statistical probabilities associated with these `conditional' events???? Hope you can help. Thanks.

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Answer: That's a good question Dick. You are absolutely right that if the cards we need to draw to are already said for in other hands or have been mucked, we can't get them. The reason it is 47 and 46 is because we can only accurately account for 5 of the cards on the flop. The rest of the cards out there could just have easily been folded as they are in the rest of the deck.

There isn't any way around this. Sometimes you can rule cards out based on players reactions but this usually doesn't change the odds that much. For example if you see a flop like 443 and you have AA -- a player may make a remark to his neighbor that he folded a 4. I read something once that if you are on the button and everyone has folded, the chance of there still being a lot of good cards in the deck and possibly the blinds having monsters goes up.

Most players, including me, don't think that way. Instead we look at our hand and then figure whether or not the chances of it, coupled with position, are better then two random hands. So the answer basically is that we can't accurately account for other cards being mucked or in players hands so we have to use the unseen total.

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