Hi Everyone.

I'm a beginning poker player, and most of my playing experience has been through online play, although I am now starting to play more live games. I'm hoping you can help me with a basic question about calculating the strength of your hand.

Why do you count your probability of making a good hand by taking the number of outs and dividing this by the total number of unseen cards? Doesn't the total number of unseen cards include the cards held by the other players?

An example:

Say you are holding K-Q, and the flop comes:

10-9-2

You're pretty sure the one other player in the pot is carrying either pocket aces, or has made a set, meaning that you really need to hit the straight by getting a jack.

Most of the literature I've read on calculating odds instruct you to count your number of possible outs. In this case, there are four jacks probably remaining in the deck. So far, so good.

The next step is where I'm getting stuck: dividing your outs by the number of unseen cards. Most sources say you should count all unseen cards-- both in the deck (45) as well as the number held by the other players (2), for a total of 47 unseen cards.

But why count the cards held by the other players? If you're trying to evaluate the probability that you're going to get a jack, it's never going to be the case that the other player will take a card from his own hand and place it on the turn or river for you.

In my example above, doesn't it make more sense to count the total number of unseen cards as 45, not 47? It may not make a huge difference when you're playing against only one other person, but if you're in a hand against a large number of other players, it seems that you are greatly overstating your odds of making the straight if you count all the cards held by the other players as being within the realm of possibility.

I hope that makes sense. Thanks for your help!

True-- but what if you've got a total of 5 other players in the pot? Then your odds change to--

8/37 = 21.6%

I guess what really impacts your probabilities is if you think one of the cards you need is held by another player. If you figure that at least one of the cards is already dealt, then your odds become--

7/37 = 19%

Maybe I'm overthinking this; all variations are pretty close to the original calculation of 17.02%.

Barry Greenstein talks about this in his book. He uses x/45, but it looks like it doesn't make a difference.

Why bother memorizing x/47 when you can use the rule of 2 and 4. Of course, the rule of 2 and 4 is a bit jumbled too. I've heard it said several ways, but too me it makes more sense to calculate outs on each street. Outsx2 turn, outsx2 river and outsx4 if your all-in on the flop.

Just realized there's a simpler way to think about it. Bluescreen, your same logic can be applied to all the cards in the deck except the top card. You can't be dealt the bottom card, so why count that in the denominator? You can't be dealt any of the cards except the top card. So let's make the denominator 1! Probability = 4/1 = 400%! That's another reason you have to count all the unseen cards, not just the ones you might be dealt. The point is, the ones you might be dealt (the top card) could be any one of the unknown cards, you don't know what the top card is.