I must admit I am much more of a non-Poker gambler, but this question intrigued me. The more players that are at a table, the more likely it is that a given card will be in someone's hand and not "buried" in the deck. What does this do to the overall win/lose odds of a given hand? I saw it jokingly proposed that a Texas Hold'Em deck could technically accommodate 22 players, but then ALL cards from the deck would be in play (minus the 3 burn cards).
Before anyone speaks, no matter how many players there are the distribution is still totally random. Each card has, for example, exactly the same probability to be in anyone's hand.
However as soon as someone speaks then things change...
What does this do to the overall win/lose odds of a given hand?
Simply put: as soon as a person folds the probability is higher (a tiny bit higher, but higher nonetheless) that the next players will get better cards than if the same player didn't fold.
This can also be put as: "People do not fold AA" (neither KK, nor QQ, nor AKs, etc.).
So for example if you're, say, on the button with AK, the more people fold the more likely you are to catch an A or a K.
Contrarily to popular belief this effect is something that can be measured and some people have been doing just that: analysing billions of (online) hands and noticing that the flop distribution was definitely not perfectly random.
As I've already answered in another question, Barry Greenstein himself wrote, (page 150 of "Ace on the River"), the following:
"...If several players fold first, Ace-King suited is a favorite over most pairs. ...(snip)... The reason for this is that players are more likely to play hands having an Ace or King than those containing smaller cards. Therefore, as players fold, the probability of an Ace or King coming on the board increases"
So although in a heads-up game your AsKs is about a 47.6% underdog vs 8h8c, it becomes a favorite with over 50% to win in a 6 players game where 4 players folded.
So this is noticeable.
In game theory, poker is a game of "imperfect information" (as opposed to, say, chess which is a game of perfect information) and as soon as the first player either bets or fold, you have information. Not much information and very hard to exploit but it is still information.
Once again: it's not much, but it's enough to, say, change AK from 47.61% underdog to a favorite with a bit above 50% chance of beating a pocket pair.
I've answered basically the same in another question here (*).
Now if that fact can help a player or not, that is another topic altogether: I only know this AK example because it's a great example Barry Greenstein came up with...
I also remember a great blog post / article which was showing the distribution of cards over billions of flops and you could clearly see that it wasn't a totally random distribution but I never found that blog post / article back : (
Since all the cards except the two known to you, are unknown the odds do not change in respect to how you count you outs of hitting a particular hand or card.
Having said that Your odds against winning a particular pot go down the more players there are in a hand. Also particular hands play better AK for example against larger fields, and other hands, pairs for example, play better against small fields.