Re: Tell me I\'m wrong
 

An unseen card is an unseen card is an unseen card. Calculating the probability of which unseen cards are in your opponents' hands is about as useful as calculating where they are in the deck.

Re: Tell me I\'m wrong
 

[ QUOTE ]
You have A s Q d
Board reads: K d Qs 5 h
If your opponent has KK means drawing dead.


[/ QUOTE ]

Coulnt you still catch runner-runner Aces to make a bigger full?

Re: Tell me I\'m wrong
 

My bad.

You have to hit a two outer in order to be able to hit your one outer. (What are those odds? 1 in 100 ? Less? - too lazy to run the odds right now.)

Re: Tell me I\'m wrong
 

A good example of discounting outs:

You have A c K c
Board Reads Jc 7c 2 s
You may think you have two overs and a flush draw for 15 outs putting as the stat favorite - but if your opponent has A d J s....

Re: Tell me I\'m wrong
 

the error in your example is in assuming what was dealt to your opponants; but set that aside.

there are specific times you can nail down with a comfortable degree of certainty that certain card are out of not out. The most obvious example, and maybe the most useful, is in counting the remaining aces. If you are at a loose table where people tend to play any ace, and the opening pot was not raised, then the cards mucked before the flop are unlikely to contain any aces. On the other hand . . when a player who was aggressive before the flop turns passive after a ragged flop like 9-3-2 . . . that is very likely AK or AQ, so if you played 45s and are thinking about hitting your straight, you would probably be wise to count one less ace.

Your post alluded to flush draws. I am not as strong mathmatically as many others, but here is what I worked out a long time ago, I think it is about right.

If: you have been dealt two clubs, and the flop contains two clubs, Then: it is about three-quarters likely that another player was dealt two clubs. Further, there is about a 1 1/2% chance that any given player was dealt two clubs. Obviously you need to observe their actions to decide if you think they really have the goods, but those numbers give you a starting point.

Re: Tell me I\'m wrong
 

[ QUOTE ]
would the calculation be any different if the dealer burned 19 cards and then dealt the 20th as opposed to just dealing the card off the top of the deck

[/ QUOTE ]

This is undoubtedly the correct way of looking at this situation but in your example you are not playing with a full deck. I have been accused of not "playing with a full deck" so often that it makes me wonder if the OP is wrong. The problem with me though is that I'm not usually playing cards when someone accuses me of this. I don't get it.

Vince

Re: Tell me I\'m wrong
 

Well, if you want to get beyond the basics, there's a somewhat arcane way in which your friend is correct. IF YOU HAVE SOME INDICATION WHAT CARDS ARE IN YOUR OPPONENTS' HANDS, then you can use that to change your estimate of probabilities of cards coming out of the stub.

For example, in Omaha 8/b, many more good hands have low cards (e.g. A2xx, preferably A23x or A24x) than high cards (usually all four above a ten). If you're playing O8 with knowledgeable players, you're in late position, and many have limped in, your high hand might go up in value. This is because you reason they wouldn't be in the pot without low cards; therefore, the stub must be rich in high cards, and it's more likely that you'll hit, or at least that they won't and you can steal the pot with a bet.

That's a very advanced application of this concept, and likely well beyond what your friend means. If you know there are 9 spades among 47 unseen cards, you have no indication whether people contesting the pot with you have zero, one, or two spades. After the flop, if there are two spades on board, and several have called a flop bet, then you can make an inference that someone else might have two spades, so you might need to shade your probabilities down slightly. So maybe it's more applicable than I thought. But if you can't put them on more or fewer spades, then the applicability to flush draws is nil. And for that matter, if you limit your inference to hands with many flop callers, then we're only talking about two suited cards out of several, hence probably not changing the probabilities in any appreciable way!

So you definitely don't want to go shading your flush draw decisions very far based on this concept. Leave this for the O8 writers.