Odds - Exposed and Unseen Cards
A lot of you might wonder why we never factor the opponents' cards or the burn cards when figuring out how many cards are left. The reason is that we only consider "unseen cards" as potential outs. If you saw what the burn cards were, or an opponent showed you his hand, you would know that those cards are not going to be drawn and actually could use that information. In texas holdem poker though, we typically do not know what they have, so we don't even think about it when talking about odds.
For instance, take a standard deck of 52 cards, remove two of the Aces and "burn" half of the deck, or 25 cards, without looking at them. If you drew the next card, what are the chances of it being an Ace? It would be 2/50 (2 Aces left out of 50 unseen cards). It would NOT be 2/25 just because you burned half the deck. Okay, do the same thing again, but this time you get to look at the burn cards. Let's say that of all the cards you burned, none were an ace. Now your odds are 2/25 because there are still two Aces and now only 25 "unseen cards".
By that same reasoning, let's play a game of draw poker where you get five cards as usual, but your opponent gets 40. Say you got Ace, King, Queen, Jack all of Spades!, and a Four of Clubs. You get to ditch the Four and draw one from the remaining pile of 7 cards. What are your chances of getting that Ten of Spades? Assuming you don't get to see your opponents hand, your chances of drawing that card would be one out out of 47 unseens. It would NOT be 1 in 7. Let's say your opponent goes to the bathroom, and you cheat and look at his hand while he's away. The cards lose their "unseen" status at that point and we can now factor them in. If he doesn't have that Ten of Spades, you would still have one out and there would be seven unseen cards left (so 1 in 7). If he did have, well...it'd be a 0 in 7 chance.
Some players might also argue that we can have a good idea that an opponent has two certain cards and that should factor into the equation somehow. That could be true. For instance, if you knew and were convinced deep down in your heart that your opponent has an overpair on the flop, you might adjust your open-ended straight draw odds assuming you were convinced that his overpair wasn't two of your outs. Mind you that the probability to make your straight in the turn would change from 8/47 (17.02%) to 8/45 (17.78%). Not a big difference at all. However, the argument against that is that math is based on facts and data. The moment you alter math to accommodate for your intuition is usually the moment before you lose a hand of poker. A player is usually trying to convince himself or herself that he should play a hand or not when that sort of thinking comes into play. Most of the time it's a player's intuition fighting against better judgement. Let is be said though that there are better factors to consider than a difference of a percent when determining whether to call, fold, or raise.
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