[Buzz]

Anonymous - It's difficult to know where to begin in terems of explaining away your confusion. You have actually asked more than one question, and each question you have asked involves a tedious counting procedure. Counting is somewhat of a misnomer, but that's what the necessary tabulating procedure is called.

Consider just one of the questions you have asked. "My question is what are the odds for (late position)hands like: ....68o...... I am trying to figue out how many limpers I need to play........"

To begin with, the odds of making a particular hand do not have anything to do with being in late position. Then you have hand odds, which are the odds of making a particular hand, to compare with pot odds (or better yet implied pot odds). David Sklansky does an excellent job explaining implied pot odds in his The Theory of Poker book. He took a couple dozen pages in this excellent book to explain odds.

Let's deal with the 68o hand.

You make a six high straight if the board at the river is any of the following

22345, 23345, 23445, 23455, 23456, 23458, A2345, 23459, 2345T, 2345J, 2345Q, 2345K.

Let's take one of these hands, 22345.

There are six different ways the board could have a pair of deuces, 2c2d, 2c2h, 2c2s, 2d2h, 2d2s, and 2h2s. Then there are four different ways the board could have a three, 3c, 3d, 3h, and 3s. Similarly there are four different ways for the board to have a four and four different ways for the board to have a five.

There are thus 6*4*4*4 = 384 distinct ways for the board to have 22345. There also would be 384 distinct ways for the board to have 23345, 23445, and 23455. Moving on, did you want to count 23456 a "play the board" hand. If so, there are 4*4*4*4*3 distinct ways for the board to be 23456. Then there are 4*4*4*4*4 distinct ways for the board to be each of the following: 23458, A2345, 23459, 2345T, 2345J, 2345Q, 2345K.

Have I accounted for all the possible six high straights or can I think of another way to make a six high straight? If I missed one, I have an error that may be difficult to find. Did I make a miscalculation somewhere along the line? If so I have an error which will be difficult to find. If I've got them all, then let's move on to seven high straights. Are there any of those possible?Actually, all the boards listed above as making six high straights for you might make seven high straights for an opponent. But we're just interested in seven high straights for you. Are there any? Since you don't have a seven in your hand, there would have to be a seven on the board, and that would seem to make an eight high straight for you. O.K. now we would get to listing all the possible eight high straights, then all the possible nine high straights and so forth.

When we are done, we have a table that may run a full page full or longer. Then we tabulate or
"count" the possibilities. You might like to also include boards that would make you quads or a full house.

Next we figure the number of possibile board layouts. (50*49*48*47*46)/(1*2*3*4*5) is an expression that would give you this value. Sometimes this is written as 50!/(45!)/(5!), or as 50C5 (read as "50 choose 5"). 2118760 is the result I just got on my calculator. Is that correct? I don't know. I'd check it again once or twice to make sure if I was doing the problem.

Finally we'd divide the total of the boards that would make you a straight by the total number of possible boards (2118760, I think) to get the probability of your making a straight with 86o and then convert the probability to odds.

Looking at the above, you can see that what you have asked involves quite a tedious, time consuming procedure. Seems like someone must have already done this for a one gapper like 86o. I'll bet it's already be in a hold 'em odds table somewhere, probably available on the internet. I don't know where, offhand, because I don't play Texas hold 'em much. (Omaha-8 is my game of choice).

Could I answer your questions? Yeah, probably. Would you understand? Well, I'd expect anyone to have a lot of additional questions along the way.

Without knowing your background it's difficult to know what you should be expected to know and what would be "over your head."

I hope this helps straighten out your confusion, but I'm not sure it does. there really is quite a bit involved in answering your questions. I'd advise you to read Hold 'em Poker for Advanced Players by Sklansky and Malmuth. I think you'll get a good idea of what hands to play and how to play them.

Buzz